A Security Framework for Resilient Smart Grids Based on Self-Organizing Graph Neural Cellular Automata

Abstract

As smart grids evolve into complex cyber-physical systems, conventional static defenses struggle to address time-varying topologies and Advanced Persistent Threats (APTs). We propose the Security Framework for Resilient Smart Grids based on Self-Organizing Graph Neural Cellular Automata (SG-GNC). Specifically, a Neural Homeostatic Embedding (NHE) mechanism utilizes variational graph autoencoders to construct a continuous health manifold for unsupervised anomaly detection, while a Neural Cellular Automata (NCA) engine employs shared-weight local rules to empower nodes with decentralized self-healing capabilities. Finally, a Generative Adversarial Immunity (GAI) strategy facilitates active defense co-evolution, enhancing robustness against zero-day attacks. Experimental results on the IEEE 118 and 300-bus systems demonstrate an average detection accuracy of 98.23%, significantly outperforming benchmarks. In scenarios involving dynamic topology and zero-day attacks, the framework maintains over 96% accuracy with an inference latency of only 9.45 ms. These findings validate the capability of SG-GNC to provide resilient, endogenous defense in complex heterogeneous environments.

1. Introduction

As modern energy infrastructure transitions toward highly interconnected cyber-physical systems (CPSs), the Smart Grid has emerged as a pivotal pillar for integrating renewable energy and achieving efficient power distribution. However, this profound integration simultaneously exposes traditionally isolated industrial control environments to open cyberspace, subjecting Internet of Things (IoT)-based renewable energy systems to unprecedented cybersecurity challenges [1]. Driven by Industrial Internet of Things (IIoT) technologies, the proliferation of heterogeneous edge devices has significantly expanded the attack surface, rendering power grids highly susceptible to malicious disruptions [2], such as Denial of Service (DoS) attacks and False Data Injection (FDI), which aim to compromise system availability and integrity [3,4]. Although existing Key Management Systems (KMSs) provide fundamental confidentiality assurances for data transmission [5], traditional static defense paradigms are appearing increasingly fragile and inadequate when identifying dynamic variations in network topology and facing potential asymmetric computational threats posed by future quantum computing [6]. Consequently, constructing a next-generation resilient security defense architecture capable of adapting to time-varying environments, possessing endogenous self-healing capabilities, and resisting Advanced Persistent Threats (APTs) has become an urgent imperative for both academia and industry.

Significant progress has been made in safeguarding the communication security of IoT and industrial control systems through advanced encryption and authentication mechanisms. To address increasingly complex cyber threats, researchers have extensively explored various defense measures ranging from fundamental cryptographic algorithms to cross-domain security protocols [7,8]. In specific application domains such as the Internet of Medical Things (IoMT) and the Internet of Vehicles (IoV), customized security architectures have been proposed to meet stringent requirements for data confidentiality and user privacy [9,10], while the integration of biometric recognition technologies has further enhanced the reliability of identity authentication [11]. Furthermore, research into physical layer security and novel cryptographic primitives has exhibited a diversified trend, encompassing schemes based on metasurfaces, chaos theory, and neuromorphic vision sensors [12,13], as well as Encryption-as-a-Service models oriented toward cloud environments [14]. For smart transportation and energy trading scenarios, efficient mutual authentication protocols have been developed to support Vehicle-to-Grid (V2G) interactions [15,16]. Concurrently, to mitigate potential threats from future quantum computing, Hybrid Quantum-Safe Cryptosystems have become a focal point of research, covering experimental integrations of Quantum Key Distribution (QKD) and Post-Quantum Cryptography (PQC) [17,18], the design of quantum-resistant protocols for 5G networks and Transport Layer Security (TLS) [19,20], and deep evaluations of related hardware implementation efficiency and migration trends [21,22].

Despite the significant efficacy of the aforementioned studies in fortifying defense boundaries and enhancing encryption strength, existing security models still reveal fundamental limitations when confronting the highly dynamic and heterogeneous characteristics of smart grids. Most current authentication and hybrid encryption frameworks essentially rely on static topological assumptions and pre-established trust anchors [23,24], lacking endogenous adaptability to handle sudden network structural changes, such as node failures or microgrid islanding [25]. Although information verification technologies for industrial control systems have developed, traditional deep learning intrusion detection models often manifest black-box characteristics, devoid of organism-like homeostatic perception and self-healing mechanisms [26]. This implies that when unknown zero-day attacks or large-scale data poisoning occur, existing systems cannot achieve immediate reconstruction of damaged data and self-recovery of functions through local interactions like biological tissues. To address these challenges, we propose a Security Framework of Resilient Smart Grids based on Self-Organizing Graph Neural Cellular Automata (SG-GNC), aiming to realize a transformation from passive to active defense by simulating biological mechanisms of homeostasis maintenance and morphogenesis. The primary contributions are as follows:

• We proposed a systemic Neural Homeostatic Embedding (NHE) mechanism that integrates variation graph auto-encoders to construct a differentiable health manifold, shifting anomaly detection from static threshold to dynamic unsupervised perception.
• We designed a topology-independent Neural Cellular Automata (NCA) engine that adapts shared-weight local rules to specific grid physics, enabling the first decentralized self-healing capability for cyber-physical state restoration.
• We introduced the Generative Adversarial Immunity (GAI) strategy that orchestrates a co-evolutionary game between the NCA and an Attack Generator, synthesizing these components into a closed-loop active defense system.

The remainder of this paper is organized as follows. Section 2 introduces related work, including methods such as lightweight security authentication. Section 3 describes the proposed method in detail. Section 4 presents a quantitative analysis of the proposed method against other security architectures to validate recognition and defense performance across different datasets. Section 5 discusses aspects such as hyperparameter settings within the method. Finally, Section 6 provides the conclusion and future research directions.

2. Related Work

2.1. Authentication and Cryptographic Protocols in Resource-Constrained Smart Grids

Given the scarcity of computational resources and limited communication bandwidth characteristic of smart grid edge devices, lightweight authentication and cryptographic protocols have emerged as the dominant paradigm for ensuring network security. Research in this domain primarily focuses on significantly reducing computational complexity and communication overhead while maintaining high security standards, encompassing diverse technological pathways ranging from identity-based encryption and Elliptic Curve Cryptography (ECC) to Physical Unclonable Functions (PUFs).

Regarding foundational algorithmic optimization, Thakor et al. [27] proposed a novel 5-bit S-box design, substantially enhancing the nonlinearity and attack resistance of lightweight algorithms. Building upon such efficient primitives, numerous studies have introduced improved protocols tailored to specific scenarios. Tanveer et al. [26] designed the LACP-SG protocol to address high-latency issues in grid data transmission, while Kook et al. [28] utilized hash functions to construct a low-overhead authentication scheme. To manage more complex V2G and fog computing environments, Irshad et al. [29] and Wei et al. [30] proposed authentication mechanisms based on the Energy Internet and multi-TA models, respectively, with Abbasi et al. [31] further extending such schemes to cloud-assisted architectures. For large-scale node management, Rosa et al. [32] explored the Light-SAE protocol for constrained devices, and Mutlaq et al. [33] innovatively combined ECC, biometrics, and Hamming distance to improve fault tolerance. Furthermore, physical layer security has attracted attention, with Zahoor et al. [34] leveraging PUF technology to achieve keyless authentication. At the key management level, Rana et al. [5] provided a comprehensive review, while Aquina et al. [35] discussed transition paths and performance trade-offs from traditional cryptography to the post-quantum era.

Although these solutions have proven effective in reducing resource consumption, they essentially remain static defense paradigms, heavily relying on pre-established trust roots or centralized servers (such as KGCs or cloud platforms). This dependence introduces risks of single points of failure and a lack of adaptability to time-varying topologies. Confronted with APTs and unknown zero-day attacks, these fixed encryption logics lack endogenous evolutionary and self-healing capabilities, failing to meet the urgent demands of modern smart grids for resilient security and active defense.

2.2. Decentralized Architectures: Post-Quantum, Blockchain, and Bio-Inspired Security

Facing the dual challenges of the explosive growth in quantum computing power and the lack of trust in large-scale heterogeneous networks, frontier security architectures are accelerating toward decentralized and quantum-resistant directions. The mainstream approach in this stream involves abandoning traditional centralized authorities in favor of integrating the distributed ledger technology of blockchain, the mathematical hardness of PQC, and the chaotic dynamic characteristics of bio-inspired algorithms, aiming to construct a next-generation defense system with theoretical security strength capable of resisting future computational attacks.

In the realm of quantum-resistant migration, Chawla et al. [36] mapped a roadmap for the transition of the Internet of Things from classical algorithms to PQC, while Zeng et al. [37] performed foundational optimizations on polynomial operations core to lattice-based cryptography. On this basis, Shim [38] and Mansoor et al. [39] validated the applicability of PQC signature schemes in IoT and e-health systems, with Khan [40] and Meng et al. [41] further enhancing key quantum hardness in UAV and industrial internet scenarios. To resolve distributed trust issues, Mutlaq et al. [42] successfully applied scalable blockchain frameworks to data trading protection in smart grids. In further fusion research, Dhar et al. [43] innovatively combined blockchain with quantum cryptography, and Aquina et al. [35] conducted an in-depth comparison of the deployment efficacy between QKD and PQC. Moreover, bionics has offered novel encryption perspectives; Singh [44] and Mougkogiannis et al. [45] utilized the chaotic properties of DNA sequences and protein-like assembly structures, respectively, to achieve high-entropy encryption.

Despite the qualitative leap in security achieved by these decentralized architectures, the substantial signature sizes of PQC and the consensus latency of blockchains remain difficult to reconcile with the stringent low-latency requirements of real-time smart grid control. Crucially, these schemes essentially focus on the fortification of defense boundaries and the transfer of trust, lacking biology-like morphogenetic mechanisms. When facing unknown attacks that breach boundaries or physical topology damage, such systems cannot spontaneously reconstruct data and self-heal based on local neural rules like biological organisms—a core pain point we seek to address through Neural Cellular Automata.

2.3. Research Motivation

(1) Conventional static and supervised detection models fail to adapt to the time-varying characteristics of dynamic grid loads. Current methods, relying on fixed features, suffer from black-box vulnerabilities and an inability to construct differentiable health manifolds. Unlike conventional supervised models that rely on fixed feature thresholds, the proposed NHE mechanism constructs a differentiable manifold to capture endogenous system health, enabling the unsupervised differentiation of normal fluctuations.

(2) Existing architectures rely heavily on centralized trust, introducing significant overhead and single-point failure risks in resource-constrained environments. Furthermore, deep learning models are inherently sensitive to graph structures, often failing to generalize during topological variations such as islanding. This structural rigidity necessitates the introduction of a morphogenetic mechanism based on Neural Cellular Automata to ensure topology-independent resilience and decentralized self-healing capabilities.

(3) Conventional models frequently exhibit catastrophic forgetting and passivity against zero-day threats. Current systems lack endogenous evolutionary mechanisms, where updates often overwrite prior knowledge. To address these limitations, a generative adversarial immune framework is essential to simulate attack-defense co-evolution, thereby establishing antifragility and facilitating proactive immunity against unknown threats.

3. Method

To mitigate APTs within the time-varying topologies of smart grids, a resilient defense framework grounded in biological morphogenesis principles, termed SG-GNC, is proposed. As depicted in Figure 1, the framework initially employs NHE to construct a continuous health manifold, thereby facilitating unsupervised anomaly perception. Subsequently, endogenous self-healing capabilities are conferred upon nodes via the local interactions of NCA, enabling the restoration of compromised states. Finally, the GAI strategy is integrated to bolster robustness against zero-day attacks through dynamic gaming, culminating in a closed-loop defense architecture characterized by homeostatic perception, morphogenetic self-healing, and active immunity.

3.1. Neural Homeostatic Embedding Mechanism

Existing anomaly detection methods for smart grids predominantly rely on static thresholds or supervised feature classification, which struggle to effectively adapt to the time-varying characteristics of system loads and the dynamic evolution of topological structures. This black-box mode, devoid of endogenous homeostatic perception, often fails to define the manifold boundaries of normal fluctuations when confronting APTs and data poisoning, leading to a significant decline in detection accuracy. To address this, this study proposes the Neural Homeostatic Embedding (NHE) mechanism, designed to construct a continuously differentiable health state manifold to achieve precise unsupervised perception of system anomalies.

As illustrated in Figure 2, the process begins by modeling the spatio-temporal operation data of the smart grid as a dynamic graph structure, defining node measurement attributes and communication topologies to capture the complex dependencies between physical connections and information interactions. Subsequently, a Variational Graph Autoencoder (VGAE) is introduced as the core manifold learning engine. By employing graph convolutional neural networks, high-dimensional features are mapped to a low-dimensional latent random variable distribution, thereby constructing the neural homeostatic manifold of the system. Finally, a composite loss function incorporating reconstruction error and Kullback–Leibler (KL) divergence is designed. Minimizing this objective function establishes an unsupervised homeostatic perception field, providing a baseline biological ontology template for subsequent anomaly discrimination.

Step 1: Smart Grid Dynamic Graph Construction and Feature Space Definition. To comprehensively characterize the physical state and information interaction of the smart grid, we first construct a dynamic graph $G_t=(V,E_t,X_t)$. Here, $V=\{v_1,\dots ,v_N\}$ represents the set of nodes composed of N smart meters or buses; $E_t$ denotes the set of communication links or physical transmission lines at time t.

The real-time measurement data of nodes (voltage magnitude, phase angle, active/reactive power) are mapped to a feature matrix $X_t\in {\mathbb{R}}^{N\times F}$, where F is the feature dimension. Simultaneously, an adjacency matrix $A\in {\{0,1\}}^{N\times N}$ is introduced to describe the connectivity between nodes. Symmetric normalization is applied to A to eliminate the impact of node degree distribution differences on subsequent graph convolution operations. The normalized Laplacian matrix $\widehat{A}$ is defined as follows to enhance the stability of signal propagation in the spectral domain. The process is shown in Equation (1).

$$\widehat{A}={\tilde{D}}^{-{\displaystyle \frac{1}{2}}}\tilde{A}{\tilde{D}}^{-{\displaystyle \frac{1}{2}}}$$

(1)

where $\tilde{A}=A+I$, with I being the identity matrix used to add self-loops to preserve node intrinsic feature information; $\tilde{D}$ is the degree matrix, with its diagonal elements represented as ${\tilde{D}}_{ii}={\displaystyle {\sum }_j}{\tilde{A}}_{ij}$. This step provides a standardized input space for the NHE mechanism, ensuring the model’s adaptability to varying grid topologies.

Step 2: Homeostatic Manifold Embedding based on Variational Graph Inference. Upon obtaining the normalized graph-structured data, NHE utilizes a variational inference framework to learn the distribution of data in the low-dimensional latent space, denoted as $q\left(Z\right|X,A)$. This study employs a two-layer Graph Convolutional Network (GCN) as the encoder (Inference Model) to map high-dimensional observation data X and structural information A to the parameters of the Gaussian distribution of latent variables Z: mean $\mu$ and variance ${\sigma }^2$. This process realizes a nonlinear projection from the discrete raw data space to a continuous differentiable homeostatic manifold.

To render this stochastic sampling process differentiable and support backpropagation training, the Reparameterization Trick is introduced. Specifically, the GCN encoder employs a two-layer architecture with dimensions $D_{in}\times 64$ (Hidden) and $64\times 32$ (Latent) to capture high-order topological features. To enable end-to-end training, the gradient of the loss function with respect to the encoder parameters $\theta$ is computed as in Equation (2).

$${\nabla }_{\theta }{\mathcal{L}}_{NHE}\approx {\displaystyle \frac{1}{L}}{\displaystyle \sum _{l=1}^L}{\nabla }_{\theta }\left[logp\left(A\right|\mu +\sigma \odot {ϵ}^{\left(l\right)})-D_{KL}(q\left(Z\right|X,A)\left|\right|p\left(Z\right))\right]$$

(2)

where ${ϵ}^{\left(l\right)}\sim \mathcal{N}(0,I)$ is the sampled noise, ensuring that the stochastic sampling process remains differentiable. The specific inference calculation process is defined as Equations (3)–(5).

$$H=\mathrm{ReLU}\left(\widehat{A}X{W}_0\right)$$

(3)

$$\mu =\widehat{A}H{W}_{\mu },log{\sigma }^2=\widehat{A}H{W}_{\sigma }$$

(4)

$$Z=\mu +\sigma \odot ϵ,ϵ\sim \mathcal{N}(0,I)$$

(5)

In these equations, $W_0$, $W_{\mu }$, and $W_{\sigma }$ are the weight matrices to be learned, and H represents the intermediate hidden layer features. The generated latent variable Z encapsulates the essential characteristics of the grid under healthy operating conditions, constituting a homeostatic core resilient to noise interference.

Step 3: Construction of Unsupervised Homeostatic Perception Field and Target Optimization. The final step of the NHE mechanism involves reconstructing the original graph structure via a decoder and defining homeostasis through a composite loss function. We utilize a generative model $p\left(A\right|Z)$ to rebuild the adjacency matrix A through the inner product of latent variables Z, thereby evaluating the capability of the latent manifold to preserve network topology.

The training objective of the model is to maximize the Evidence Lower Bound (ELBO), which entails minimizing the reconstruction error while constraining the KL divergence between the latent distribution and the prior distribution (standard normal distribution). This constraint forces the latent space to form a compact and continuous geometric structure, such that any attack behavior deviating from this manifold results in significant reconstruction loss. The total loss function ${\mathcal{L}}_{NHE}$ and the reconstruction probability are defined as Equations (6) and (7).

$$p(A_{ij}=1|z_i,z_j)=\sigma \left(z_i^{\top }{z}_j\right)$$

(6)

$${\mathcal{L}}_{NHE}={\mathbb{E}}_{q\left(Z\right|X,A)}[logp\left(A\right|Z)]-KL(q\left(Z\right|X,A)\parallel \mathcal{N}(0,I))$$

(7)

where $\sigma (·)$ is the Sigmoid activation function. In the inference phase, the anomaly score $S\left(v_i\right)$ of node $v_i$ is used to quantify the degree of its deviation from the homeostatic manifold. The process is shown in Equation (8).

$$S\left(v_i\right)={\parallel x_i-{\widehat{x}}_i\parallel }_2^2+\lambda {\displaystyle \sum _{j\in \mathcal{N}\left(i\right)}}(1-{\widehat{A}}_{ij})$$

(8)

The first term represents the feature reconstruction error, and the second term serves as a structural consistency penalty. This penalty term ${\displaystyle {\sum }_{j\in N\left(i\right)}}(1-{\widehat{A}}_{ij})$ quantifies the deviation between the observed local topology and the probabilistic connectivity inferred from the health manifold. Since the model is trained on valid $N-1$ contingencies, benign topology changes yield high reconstruction probabilities (${\widehat{A}}_{ij}\approx 1$), whereas malicious structural tampering (spoofed links inconsistent with power flow physics) results in low probabilities, significantly increasing the anomaly score.

When $S\left(v_i\right)$ exceeds a threshold $\tau$, the node is judged to be compromised. To ensure reproducibility, $\tau$ is defined statistically using the anomaly scores $S_{val}$ obtained from the fault-free validation dataset. Assuming the reconstruction errors of normal instances follow a Gaussian distribution, we apply the Three-Sigma Rule, as expressed in Equation (9).

$$\tau ={\mu }_{val}+3{\sigma }_{val}$$

(9)

where ${\mu }_{val}$ and ${\sigma }_{val}$ are the mean and standard deviation of $S_{val}$, respectively. This threshold corresponds to a 99.7% confidence interval (CI), effectively filtering out benign high-frequency fluctuations. This mechanism provides a precise trigger signal for the subsequent self-healing module of the NCA.

3.2. Neural Cellular Automata Engine

Traditional centralized deep learning defense models exhibit extreme sensitivity to network topological structures. Once the power grid undergoes physical structural changes due to fault isolation or microgrid integration, the fixed input dimensions of pre-trained models often lead to defense failures. Furthermore, existing methods lack endogenous self-healing capabilities when confronting local data corruption. They typically only provide passive alerts rather than actively repairing damaged states in a decentralized environment, making it difficult to ensure the continuity of critical control instructions. To address this, the smart grid Neural Cellular Automata (NCA) engine is designed to endow network nodes with topology independence and morphogenetic self-healing capabilities based on local interactions.

As illustrated in Figure 3, each smart grid node is first instantiated as a neural cell characterized by an independent high-dimensional state vector, thereby establishing a discrete state space predicated on local neighborhood perception. Subsequently, a parameter-sharing neural update rule network is designed to function as a universal genome, guiding nodes to compute evolutionary increments for the subsequent time step based on neighboring states. Finally, a structure maintenance loss function and a random damage training mechanism are introduced to compel the network to acquire the capability of spontaneously reconstructing global steady-state patterns using solely residual local information, even under extreme conditions where partial node states are zeroed out or tampered with.

(1) Cell State Space Definition and Local Perception Field. To simulate the distributed nature of biological tissues, this study instantiates each node $v_i$ in the dynamic graph $G_t$ constructed in the previous module as a neural cell. Unlike traditional automata containing only simple discrete states (0/1), each cell in the SG-NCA maintains a continuous high-dimensional hidden state vector $h_i\left(t\right)\in {\mathbb{R}}^K$. The first C channels of this vector correspond to the node’s physical measurements (such as voltage and frequency), denoted as $h_i\left(t\right)[0:C]=x_i\left(t\right)$, while the remaining channels store implicit control information used for coordinating local communications.

To achieve local perception, each cell aggregates information solely from its first-order neighbors. This study utilizes a generalized form of the graph Laplacian or Sobel operator to extract gradient features of local states, serving as the sensory organs of the cell. The computation process for the perception vector $p_i\left(t\right)$ is as follows: $\mathcal{N}\left(i\right)$ denotes the set of neighbors for node $v_i$. The process is shown in Equations (10)–(12).

$$h_i\left(0\right)=\mathrm{Initialize}\left(Z_i\right),Z_i\in \mathrm{Latent}\mathrm{Space}\mathrm{from}\mathrm{NHE}$$

(10)

$$p_i\left(t\right)=\mathrm{Concat}\left(h_i\left(t\right),{\displaystyle \sum _{j\in \mathcal{N}\left(i\right)}}{\widehat{A}}_{ij}·(h_j\left(t\right)-h_i\left(t\right))\right)$$

(11)

$${\nabla }^2{h}_i\left(t\right)\approx p_i\left(t\right)·W_{perc}$$

(12)

Here, ${\widehat{A}}_{ij}$ represents the element of the normalized adjacency matrix, ensuring the perception process is undisturbed by differences in node degrees. This step decouples the global state of the entire network into numerous local microscopic perception fields, laying the foundation for subsequent decentralized evolution.

(2) Shared-Weight Neural Update Rules and Stochastic Evolution. The core of the SG-NCA lies in learning a universal local update law, parameterized by a weight-sharing Multi-Layer Perceptron (MLP) $f_{\theta }$. This network acts as the universal update kernel for all cells, taking the current perception vector $p_i\left(t\right)$ as input and outputting the update increment $\Delta h_i\left(t\right)$ for the state vector.

To simulate the continuity and stochasticity of biological biochemical reactions, a stochastic update strategy is adopted. At each time step t, every cell independently decides whether to execute an update with probability $p_{update}$. This asynchronous mechanism not only enhances the model’s robustness against network delays but also avoids deadlock oscillation problems common in discrete systems. The evolution of the cell state follows a discretized differential equation in Euler integration form. The process is shown in Equations (13)–(16).

$$\Delta h_i\left(t\right)=f_{\theta }\left(p_i\left(t\right)\right),\theta \in {\mathsf{\Theta }}_{shared}$$

(13)

$$m_i\left(t\right)\sim \mathrm{Bernoulli}\left(p_{update}\right)$$

(14)

$$h_i(t+1)=h_i\left(t\right)+m_i\left(t\right)·\Delta h_i\left(t\right)$$

(15)

$$f_{\theta }:{\mathbb{R}}^{K\times 3}\to {\mathbb{R}}^K$$

(16)

In these equations, $m_i\left(t\right)$ is the stochastic update mask. Through this approach, complex macroscopic dynamic behaviors of the entire network are decomposed into the iterative application of simple microscopic local rules. Consequently, once trained, the model can directly generalize to power grids of arbitrary scale or topology, achieving true “train once, run everywhere” capability.

(3) Structure Maintenance Loss and Damage Self-Healing Training. To endow the system with regenerative capabilities against attacks, a self-supervised training process based on morphogenesis is designed. The objective is to enable the cellular automaton to evolve from a damaged initial state and converge to the steady-state manifold Z defined by the NHE module.

During training, a damage operator D is introduced to randomly set the observation channels of partial nodes to zero or inject noise, simulating data loss or FDI attacks. The optimization goal of the model is to minimize the difference between the state $h\left(T\right)$ after evolving T steps and the target steady state Z, while introducing an overflow penalty term to prevent numerical explosion. The loss function ${\mathcal{L}}_{NCA}$ comprises reconstruction loss and stability regularization terms, as shown in (17) and (18).

$$h_{damaged}\left(0\right)=D\left(Z\right),D:\mathrm{Random}\mathrm{Masking}$$

(17)

$${\mathcal{L}}_{NCA}={\displaystyle \frac{1}{N}}{\displaystyle \sum _{i=1}^N}\parallel h_i\left(T\right)[0:C]-Z_i{[0:C]\parallel }_2^2+\lambda {\displaystyle \sum _{t=1}^T\sum _{i=1}^N}\mathrm{ReLU}\left(\right|h_i\left(t\right)|-1.0)$$

(18)

By minimizing ${\mathcal{L}}_{NCA}$, the neural update rule $f_{\theta }$ acquires a form of swarm intelligence. When neighboring nodes detect that a specific node has deviated from the steady state, they transmit correction signals through local interactions, forcing the node’s state to regress to a healthy trajectory. This mechanism realizes active self-healing defense against various types of attacks.

Although a formal proof of contraction dynamics is beyond the scope of this work, the convergence mechanism can be interpreted through Lyapunov stability theory. The loss function component $V\left(h_t\right)=\left|\right|h_t-Z{\left|\right|}^2$ serves as a candidate Lyapunov function (energy potential), where the target manifold Z represents the global attractor. The training objective optimizes the update rule $f_{\theta }$ such that the state trajectory satisfies the condition $\Delta V=V\left(h_{t+1}\right)-V\left(h_t\right)<0$ for damaged states, effectively guiding the system down the energy gradient. The introduced penalty term $\sum \mathrm{ReLU}\left(\right|h|-1.0)$ imposes a boundedness constraint, preventing the state vector from diverging to infinity (gradient explosion) and ensuring the system state remains within a compact region.

3.3. Generative Adversarial Immunity Strategy

Although the SG-NCA engine endows the system with self-healing capabilities against known perturbations, fixed neural rules remain susceptible to reverse engineering via gradient estimation-based adversarial samples and unknown zero-day attack patterns. Furthermore, traditional deep learning models frequently encounter catastrophic forgetting when updating defense strategies to accommodate new threats, resulting in decayed efficacy against historical attack modes. To address these issues, this module introduces a Generative Adversarial Immunity (GAI) strategy. By constructing a co-evolutionary game framework between attackers and defenders, the system is empowered to actively evolve endogenous immune robustness against unknown threats during virtual drills.

As illustrated in Figure 4, a reinforcement learning-based bi-level game model is first established, wherein the Attack Generator is defined to identify NCA blind spots to maximize damage payoff, while the Immune Evolver is tasked with optimizing local update rules to minimize defense costs. Subsequently, a policy gradient-based adversarial training algorithm is designed to facilitate the co-evolution of attack strategies and immune rules within a dynamic equilibrium through multi-round virtual offensive–defensive iterations, thereby compelling the NCA to explore a broader steady-state solution space. Finally, an immune memory replay mechanism is introduced to construct and periodically replay a repository of high-value attack samples, ensuring the retention of robust response capabilities against historical attack patterns while simultaneously acquiring novel defense characteristics.

First, we define the bi-level game model and design the payoff function. To simulate realistic offensive–defensive confrontations, GAI is modeled as a zero-sum game process. To ensure defense rigor, we explicitly distinguish between training and deployment threat landscapes.

(1) White-box training (worst-case): During the GAI co-evolutionary training, we assume a white-box attacker with full access to the NCA model parameters $\theta$ and gradient information ${\nabla }_h{L}_{NCA}$. This aligns with Kerckhoffs’s principle, ensuring the defense is robust against the strongest possible adversary who has reverse-engineered the system.

(2) Black-box deployment: In the testing/inference phase, attackers are assumed to be black-box (external intruders) or gray-box (insiders with partial topology knowledge), lacking direct access to the defense model’s gradients. By training against the white-box upper bound, the system guarantees resilience against these lower-tier threats.

The Attack Generator (Pathogen Generator), denoted as $G_{\varphi }$, assumes the intruder role, aiming to generate minute perturbation masks $\delta$ capable of deceiving the NCA engine. The Immune Evolver corresponds to the aforementioned SG-NCA model $f_{\theta }$, tasked with maintaining system morphogenetic homeostasis. The attacker takes gradient information of the current NCA model relative to the input state $h\left(0\right)$ as input and outputs an attack vector.

The optimization objective constitutes a min–max problem. The attacker seeks to maximize the residual error of the damaged state following NCA repair, while the defender strives to minimize this error. The attack payoff $R_{att}$ and the joint objective function $J(\varphi ,\theta )$ are defined as Equations (19)–(22).

$$\delta =G_{\varphi }\left({\nabla }_h{\mathcal{L}}_{NCA}(h\left(0\right),Z)\right)$$

(19)

$$h_{adv}\left(0\right)=h\left(0\right)+ϵ·tanh\left(\delta \right),\mathrm{s}.\mathrm{t}.{\parallel \delta \parallel }_{\infty }<\xi$$

(20)

$$R_{att}\left(\varphi \right)=\parallel \mathrm{Evolve}(h_{adv}\left(0\right);f_{\theta }){-Z\parallel }_2^2-\gamma {\parallel \delta \parallel }_0$$

(21)

$$\underset{\theta }{min}\underset{\varphi }{max}J(\varphi ,\theta )={\mathbb{E}}_{h\sim p_{data}}\left[R_{att}(\varphi ,f_{\theta })\right]$$

(22)

Here, $\mathrm{Evolve}(·)$ denotes the evolution result of the NCA after T time steps, and $\gamma$ is a sparsity penalty coefficient limiting attack costs. This step establishes the mathematical foundation for the system’s self-attack mechanism. Theoretically, this interaction constitutes a non-zero-sum Stackelberg game, where the Immune Evolver acts as the leader, minimizing reconstruction loss, and the Attack Generator acts as the follower, maximizing perturbation damage. While finding a global Nash Equilibrium in non-convex deep learning landscapes is intractable, the bounded nature of the payoff functions ensures the existence of a Local Stackelberg Equilibrium, to which the system converges via alternating gradient descent.

Second, co-evolution and policy gradient optimization are employed. During the game process, training on fixed datasets typically leads to overfitting. Therefore, a co-evolution strategy is adopted. In each iteration k, the Attack Generator $G_{\varphi }$ fixes the defense parameters ${\theta }_k$ and updates the attack parameters $\varphi$ via Policy Gradient or Projected Gradient Descent (PGD) to generate the most destructive “super-antigens” under the current defense strategy. Subsequently, the Immune Evolver fixes the attack parameters ${\varphi }_{k+1}$ and utilizes the generated adversarial samples $h_{adv}$ to update the NCA parameters $\theta$, thereby learning repair rules targeting the novel attack.

This alternating update mechanism drives the defense boundary to continuously expand toward low-density regions of the latent manifold. The parameter update process follows Equations (23) and (24):

$${\varphi }_{k+1}\leftarrow {\varphi }_k+{\alpha }_{att}{\nabla }_{\varphi }\mathbb{E}\left[R_{att}({\varphi }_k,f_{{\theta }_k})\right]$$

(23)

$${\theta }_{k+1}\leftarrow {\theta }_k-{\alpha }_{def}{\nabla }_{\theta }\left({\displaystyle \sum _{i=1}^N}\parallel h_i\left(T\right)[0:C]-Z_i{[0:C]\parallel }_2^2+\beta {\parallel \mathrm{Evolve}(h\left(0\right)+G_{{\varphi }_{k+1}};f_{{\theta }_k})-Z\parallel }_2^2\right)$$

(24)

Through this dynamic game, the system autonomously discovers and patches potential security vulnerabilities without external attack labels, achieving a qualitative leap from passive defense to active immunity.

Finally, we introduce an immune memory replay and an anti-forgetfulness mechanism. To prevent the model from forgetting defense capabilities against older attack patterns while optimizing for newly generated adversarial samples (catastrophic forgetting), the GAI strategy introduces an immune memory bank M. This repository stores high-payoff attack samples $(h_{adv}^{\ast },Z)$ produced during historical iterations—specifically, pathogens that successfully breached defenses.

When training the defender $f_{\theta }$, batches of historical samples are randomly sampled from M for mixed training alongside current adversarial samples. Through experience replay, the total loss function is modified to a weighted sum of the current adversarial loss and the memory replay loss, striking a balance between plasticity (learning new knowledge) and stability (retaining old knowledge), as shown in Equation (25).

$$M\leftarrow \mathrm{TopK}(M\cup \left\{(h_{adv},R_{att})\right\})$$

(25)

From a game-theoretic perspective, this memory mechanism approximates a fictitious play process. By optimizing against the cumulative distribution of historical attack strategies rather than solely the current iteration, it effectively prevents Mode Collapse, thereby stabilizing the convergence trajectory. This mechanism parallels memory cells in biological immune systems, ensuring that the smart grid security system continuously accumulates defense experience as attack methods evolve, ultimately forming a comprehensive defense repository.

3.4. Loss Function

To endow the system with morphogenetic and self-healing capabilities in a decentralized environment, the core objective of model training is to minimize the discrepancy between the evolved state and the Neuro-Homeostatic Manifold while simultaneously constraining the numerical stability of cell states to prevent gradient explosion or oscillation during recursive updates. The total loss function ${\mathcal{L}}_{Total}$ is formalized as Equation (26).

$${\mathcal{L}}_{Total}={\displaystyle \frac{1}{N}}{\displaystyle \sum _{i=1}^N}\parallel h_i\left(T\right)-Z_i{\parallel }_2^2+ \lambda ·{\displaystyle \frac{1}{N·T}}{\displaystyle \sum _{t=1}^T\sum _{i=1}^N\sum _{k=1}^K}\mathrm{ReLU}\left(\right|h_{i,k}\left(t\right)\left|\right)$$

(26)

where N represents the total number of grid nodes, K is the dimension of the state vector, and $\lambda$ is a balancing coefficient. This optimization objective not only drives the system to converge morphologically toward a healthy ontology template but also ensures the numerical robustness of the defense mechanism over long time sequences dynamically, thereby achieving effective suppression and repair of anomalous perturbations.

4. Experiments and Analysis

4.1. Experimental Environment and Evaluation Metrics

To validate the effectiveness and robustness of the SG-GNC framework under dynamic topologies, this study constructed time-varying graph datasets based on the IEEE 118-bus standard test system.

Table 1. Experimental environment and parameter settings.

Component	Specification	Parameter	Value
CPU	Intel Xeon Gold 6530 (4.00 GHz)	State Dimension K	64
GPU	NVIDIA GeForce RTX 4090	Evolution Steps T	32
OS	Ubuntu 20.04 LTS	Update Probability p	0.5
Python 3.7	PyTorch Geometric 2.0	Penalty Coefficient $\gamma$	${10}^{-3}$

presents the experimental environment and parameter configurations. In the data preprocessing phase, scenarios involving varying load levels and node failures (up to 30%) were simulated to generate normalized feature matrices containing voltage magnitudes and power injections, as well as dynamic Laplacian matrices. The NHE module employs a two-layer GCN encoder, where latent variables follow a Gaussian distribution. The experiment introduces three threat modes: random node faults, FDI, and adversarial zero-day attacks. Model performance is comprehensively evaluated using anomaly detection accuracy, reconstruction Mean Squared Error (MSE), and self-healing convergence time.

Implementation Details and Statistical Protocol: The proposed SG-GNC framework was implemented using PyTorch Geometric 2.0 on an NVIDIA RTX 4090 GPU. The model was trained using the Adam optimizer with an initial learning rate of ${10}^{-3}$ and a weight decay of $5\times {10}^{-4}$. We employed an Early Stopping strategy to prevent overfitting, terminating training if the validation loss did not decrease for 10 consecutive epochs. The hyperparameter $\lambda$ was selected via a grid search on the validation set, as detailed in Section 5.3. To ensure statistical reliability, all reported experimental results represent the average of 10 independent runs with different random seeds. Performance metrics are presented as mean ± 95% confidence interval (CI). Furthermore, we conducted paired t-tests to verify performance differences between SG-GNC and baseline models, considering results statistically significant at a significance level of $p<0.01$.

Anomaly Detection Efficacy Metrics: For the binary classification problem concerning data poisoning and intrusion detection in smart grids, Accuracy, Precision, Recall, and F1-Score are employed as core metrics. Defining TP, TN, FP, and FN as the counts of true positive, true negative, false positive, and false negative samples, respectively, the F1-Score is calculated as Equations (27)–(30).

$$\mathrm{Accuracy}={\displaystyle \frac{TP+TN}{TP+TN+FP+FN}}$$

(27)

$$\mathrm{Precision}={\displaystyle \frac{TP}{TP+FP}}$$

(28)

$$\mathrm{Recall}={\displaystyle \frac{TP}{TP+FN}}$$

(29)

$$\mathrm{F}1\text{-}\mathrm{Score}=2·{\displaystyle \frac{\mathrm{Precision}·\mathrm{Recall}}{\mathrm{Precision}+\mathrm{Recall}}}$$

(30)

Self-Healing Reconstruction Quality Metrics: To evaluate the regenerative capability of the model under conditions of node damage or data loss, Mean Squared Error (MSE) and Mean Absolute Error (MAE) are utilized to measure the deviation between the repaired node state $h_i\left(T\right)$ and the target homeostatic ontology $Z_i$. A lower MSE indicates that the model can reconstruct the physical state information of the power grid with high fidelity. Convergence Efficiency and Robustness Metrics: To assess the real-time response capability of the defense mechanism, Average Convergence Time (ACT) is defined as the number of evolutionary steps T required for the system to evolve from a damaged initial state to a stable state (state increment $\parallel \Delta h\parallel <ϵ$).

4.2. Datasets and Comparative Models

To comprehensively validate the generalization capability and robustness of the SG-GNC framework within complex cyber-physical systems, this study constructs a multi-dimensional heterogeneous data evaluation system encompassing topological complexity, network attack diversity, and random source-load fluctuations. First, the IEEE 118-bus standard test system is selected as the physical layer benchmark to evaluate the model’s state estimation accuracy under complex grid topologies and its reconstruction ability against FDI attacks, thereby verifying the adaptability of the Neural Cellular Automata to topological structures. Second, the MSU-ORNL industrial control dataset is introduced, which contains authentic SCADA network traffic and multiple attack patterns, such as DoS, to test the anti-fragility characteristics of the Generative Adversarial Immunity strategy when facing high-dimensional network-layer intrusions.

• IEEE 118-bus Dataset [46]. This dataset includes topological information (adjacency matrices) of the IEEE 118-node system alongside node state data (voltage, phase angle) under both normal operation and FDI attacks. It is highly suitable for training the SG-NCA engine and facilitates detection accuracy comparisons with existing graph-dependent benchmarks such as GCN and GAT models.
• IEEE 300-bus Dataset [47]. This dataset contains a standard power system test case consisting of 300 nodes, 69 generators, and 411 branches. Featuring a highly grid-based topology and elevated dimensionality, this dataset provides a rigorous testing platform for decentralized self-healing mechanisms.
• MSU-ORNL Dataset [48]. Comprising network traffic logs and physical process data from real SCADA systems, this dataset covers various attack modes, including DoS and command injection. It serves to validate the generalization capability and anti-fragility of the proposed method when confronting realistic and complex network-layer attacks.

To ensure the fairness of the experimental evaluation and the methodological completeness, this study selects state-of-the-art (SOTA) models covering diverse defense paradigms for a multi-dimensional comparative analysis. Regarding the security dimension, HTM-PQC and LiteQSign are chosen as baselines to compare how the proposed bio-inspired defense achieves equivalent resilience without relying on complex post-quantum algorithms. In the architectural dimension, Fog-AKA and EaaS-IoT are selected to represent centralized or semi-centralized defense modes, highlighting the advantages of the SG-GNC framework in terms of low latency and high independence within a decentralized self-organizing environment. Furthermore, lightweight and hardware fingerprinting schemes such as Chaos-DNA, PUF-V2G, and ASCON-Auth are introduced to verify the comprehensive efficiency advantages of the proposed model over traditional security solutions regarding computational overhead and software-defined security on resource-constrained edge nodes.

• HTM-PQC [41]. Integrating Hypergraph Theory with Post-Quantum Cryptography, this model enhances key resistance via topological associations, serving as a benchmark for verifying topological independence and key evolution.
• LiteQSign [38]. A lightweight post-quantum signature scheme optimizing IoT resource usage, this model is employed to benchmark the edge-side computational efficiency and efficacy of the SG-NCA engine.
• Fog-AKA [30]. Utilizing a fog-based Multi-TA model for low-latency authentication, this protocol is selected to demonstrate the superior communication latency of the proposed decentralized architecture over hierarchical structures.
• EaaS-IoT [49]. Employing CP-ABE-based cloud offloading to mitigate IoT computational bottlenecks, this architecture serves as a baseline to contrast local defense effectiveness against centralized cloud reliance.
• Chaos-DNA [44]. Combining chaotic maps and DNA coding for multimedia security, this model is utilized to validate the robustness of the Generative Adversarial Immunity strategy in processing high-entropy data.
• PUF-V2G [16]. Leveraging Physical Unclonable Functions for physical capture resistance, this scheme is used to assess the capability of SG-NCA to achieve hardware-level security through software mechanisms.
• ASCON-Auth [50]. Utilizing ultra-lightweight primitives for efficient privacy protection, this protocol serves as a baseline to verify the operational efficiency of the NHE mechanism on resource-constrained nodes.
• GCN-IDS [51]. Utilizing deep graph learning for multi-class DDoS detection, this model leverages traffic interaction graphs to improve attack differentiation capabilities. It serves as a baseline for assessing the proposed framework’s precision in classifying diverse, complex cyber threats against standard graph-based learning approaches.
• GAT-IDS [52]. Integrating Graph Attention Networks (GATs) with temporal GRU modules, this hierarchical framework explicitly models spatio-temporal grid dependencies to detect FDI. It is selected as a state-of-the-art baseline to verify the proposed method’s robustness in maintaining cyber-physical state consistency under dynamic topologies.

Graph-based intrusion detection models (GCN-IDS, GAT-IDS) serve as the primary benchmarks for evaluating the proposed SG-GNC’s performance in learning spatial-temporal dependencies and detecting anomalies. Cryptographic and authentication schemes (PUF-V2G, ASCON-Auth, LiteQSign) are included to demonstrate the limitations of identity-centric defenses against insider threats. While they provide robust protection against spoofing, they are fundamentally blind to content-level attacks (e.g., FDI) launched by compromised but authenticated nodes.

4.3. Performance Analysis of Anomaly Detection in Multi-Source Heterogeneous Environments

Table 2. Performance comparison of SG-GNC against diverse baselines on IEEE 118-bus and IEEE 300-bus datasets. Values are reported as mean ± 95% confidence interval over 10 independent runs. The best values are bold.

Model	Dataset	Accuracy (%)	Precision (%)	Recall (%)	F1-Score (%)
PUF-V2G	IEEE 118-bus	85.90 ± 0.25	93.50 ± 0.22	74.20 ± 0.30	82.74 ± 0.28
	IEEE 300-bus	84.50 ± 0.28	91.80 ± 0.25	72.50 ± 0.32	81.02 ± 0.29
ASCON-Auth	IEEE 118-bus	86.35 ± 0.21	94.80 ± 0.18	75.10 ± 0.25	83.81 ± 0.23
	IEEE 300-bus	85.10 ± 0.24	93.20 ± 0.20	73.40 ± 0.28	82.12 ± 0.25
LiteQSign	IEEE 118-bus	87.10 ± 0.20	96.20 ± 0.15	76.50 ± 0.22	85.22 ± 0.19
	IEEE 300-bus	85.80 ± 0.23	94.50 ± 0.18	74.80 ± 0.26	83.50 ± 0.22
Chaos-DNA	IEEE 118-bus	88.50 ± 0.19	87.40 ± 0.21	86.15 ± 0.20	86.77 ± 0.18
	IEEE 300-bus	87.20 ± 0.22	86.10 ± 0.24	84.90 ± 0.23	85.50 ± 0.21
Fog-AKA	IEEE 118-bus	90.25 ± 0.18	91.15 ± 0.16	86.80 ± 0.19	88.92 ± 0.17
	IEEE 300-bus	88.90 ± 0.20	89.80 ± 0.19	85.40 ± 0.21	87.55 ± 0.19
EaaS-IoT	IEEE 118-bus	91.80 ± 0.15	92.35 ± 0.14	88.50 ± 0.16	90.38 ± 0.15
	IEEE 300-bus	90.20 ± 0.18	90.80 ± 0.17	87.10 ± 0.19	88.92 ± 0.18
HTM-PQC	IEEE 118-bus	93.45 ± 0.14	95.10 ± 0.12	89.25 ± 0.15	92.08 ± 0.13
	IEEE 300-bus	91.80 ± 0.17	93.50 ± 0.15	87.80 ± 0.18	90.56 ± 0.16
GCN-IDS	IEEE 118-bus	95.20 ± 0.18	94.85 ± 0.16	94.50 ± 0.17	94.67 ± 0.15
	IEEE 300-bus	93.15 ± 0.22	92.80 ± 0.20	92.40 ± 0.23	92.60 ± 0.21
GAT-IDS	IEEE 118-bus	97.45 ± 0.12	97.10 ± 0.11	97.05 ± 0.13	97.08 ± 0.12
	IEEE 300-bus	96.10 ± 0.15	95.90 ± 0.14	95.80 ± 0.16	95.85 ± 0.15
SG-GNC	IEEE 118-bus	98.65 ± 0.12	98.42 ± 0.09	98.15 ± 0.11	98.28 ± 0.10
	IEEE 300-bus	97.82 ± 0.12	97.15 ± 0.11	96.90 ± 0.13	97.02 ± 0.12

presents a comprehensive comparison across diverse security paradigms. The traditional authentication and cryptographic methods exhibit limited anomaly detection capabilities, with Recall scores generally below 90%. This performance gap stems from their design objective: while robust against external spoofing and replay attacks, they lack the physical state awareness required to identify FDI attacks launched by compromised internal nodes. Furthermore, their scalability is constrained. For instance, the accuracy of HTM-PQC drops from 93.45% to 91.80% on the IEEE 300-bus system, reflecting the challenge of maintaining synchronized hypergraph security contexts in large-scale dynamic topologies. The results in Table 2 reveal a critical distinction between the two defense paradigms. Authentication-based methods (ASCON-Auth, LiteQSign) achieve high Precision (>93%), indicating their effectiveness in rejecting illegitimate access. However, their Recall is notably lower (≈75%), confirming that they cannot identify malicious data injected by valid identities (insider threats). In contrast, SG-GNC and the graph-based baselines (GAT-IDS) achieve a balance of high Precision and Recall (>96%) by verifying the physical consistency of the data rather than just the source identity. This comparison highlights that SG-GNC complements, rather than replaces, traditional authentication by closing the gap against data integrity attacks.

In contrast, graph-based deep learning models (GCN-IDS, GAT-IDS in Table 2) significantly outperform cryptographic baselines by learning spatial correlations. However, GCN-IDS exhibits a scalability bottleneck, with accuracy dropping to 93.15% on the 300-bus dataset, indicating that fixed spectral filters struggle to generalize to larger, more complex graphs. While GAT-IDS remains robust due to its attention mechanism, SG-GNC achieves the highest performance and stability. The experimental results indicate that the proposed SG-GNC framework significantly outperforms comparative benchmarks, achieving a detection accuracy of $98.65\pm 0.12\%$. Statistical analysis confirms that this improvement over the second-best model (GAT-IDS) is significant ($p<0.001$). This superiority is attributed to the GAI strategy and the locality of the NCA engine, which allows the system to effectively learn and restore physical consistency rules regardless of the global network size.

4.4. Analysis of Adversarial Immunity and Dynamic Topological Robustness

Figure 5 details the robustness performance of each model when confronting sudden grid topology changes and adversarial attacks. Experimental results demonstrate that the SG-GNC framework significantly surpasses comparative benchmarks in detection accuracy under both extreme scenarios. In the N-1 dynamic topology test on the IEEE 118-bus system, SG-GNC achieved an accuracy of 96.35%. This advantage is attributed to the topology-independent design of the SG-NCA engine, which trains shared-weight local neural rules to enable nodes to perform state inference by perceiving only their first-order neighborhood. By comparison, HTM-PQC, which relies heavily on predefined hypergraph structures, failed to adapt to topological changes, resulting in a decline in accuracy to 86.50%. In the adversarial zero-day attack test on the MSU-ORNL dataset, the detection accuracy of SG-GNC reached 96.55%. GAT-IDS shows noticeable retraction in its metrics on the complex IEEE 300-bus topology, while Fog-AKA exhibits a heavily skewed profile, visually indicating a severe imbalance between Precision and Recall due to its inability to detect internal FDI threats. In contrast, authentication-based schemes such as LiteQSign and ASCON-Auth exhibited detection accuracies below 70% in attack scenarios, as they were unable to identify adversarial perturbations that passed legitimate signature verification. This confirms that static identity authentication alone is insufficient to defend against content-level APTs.

5. Discussion

5.1. Edge-Side Computational Efficiency and Convergence Analysis

Table 3. Comprehensive evaluation of computational efficiency. Inference and training costs. The best values are bold.

Model	Time Complexity	Inference (ms)	Throughput (S/s)	Params (MB)	Train Time (s/ep)	Train Mem (MB)
EaaS-IoT	N/A (Cloud)	128.50	780	N/A	N/A	N/A
Fog-AKA	$O(N·K)$	45.60	2190	5.20	N/A	N/A
HTM-PQC	$O(H·|E\left|\right)$	32.40	3085	12.65	2.45	850
Chaos-DNA	$O(NlogN)$	22.15	4515	8.40	N/A	N/A
GAT-IDS	$O\left(\right|V|F+|E\left|F^{\prime }\right)$	18.20	6200	4.50	1.15	1280
LiteQSign	$O\left(1\right)$	14.20	7040	1.85	N/A	N/A
GCN-IDS	$O(L·|E|·F)$	11.50	9500	2.10	0.42	450
SG-GNC	$\mathbf{O}(\mathbf{T}·|\mathbf{E}|·\mathbf{C})$	9.45	10,580	3.82	0.68	320
ASCON-Auth	$O\left(1\right)$	0.85	117,650	0.15	N/A	N/A

provides a detailed comparison of the computational efficiency and convergence performance of various defense models in resource-constrained scenarios. The experiment evaluated inference latency using the MSU-ORNL dataset and assessed system steady-state convergence speed using the IEEE 118-bus system. The results indicate that SG-GNC achieves an optimal balance between complexity and efficiency. With an inference latency of 9.45 ms, it is faster than GCN-IDS (11.50 ms) and significantly outperforms GAT-IDS (18.20 ms). The higher latency of GAT-IDS is attributed to the computational overhead of its attention mechanism ($O\left(V^2\right)$ complexity), whereas SG-GNC utilizes shared-weight local rules that parallelize efficiently on edge devices. While the ultra-lightweight ASCON-Auth remains the fastest (0.85 ms), it lacks the deep feature learning and self-healing capabilities provided by the neural models.

To assess scalability, we analyzed the asymptotic complexity of the core engines. The GAT-IDS baseline scales as $O\left(\right|V|F+|E\left|F^{\prime }\right)$ but suffers from a high memory footprint due to the storage of attention coefficients for every edge. In contrast, the SG-NCA engine operates with a complexity of $O(T·|E|·C)$, where T is the number of evolution steps. Empirically, as shown in the revised Table 3, SG-GNC demonstrates superior memory efficiency, which is 75% lower than GAT-IDS. This reduction is attributed to the weight-sharing mechanism of the cellular automata, where a single small MLP (the Digital DNA) is applied universally across all nodes, independent of the graph size. Although the iterative evolution process results in a slightly higher training time compared to the non-iterative GCN-IDS, this trade-off is justified by the gain in self-healing capabilities and is well within the acceptable limits for edge training.

5.2. Decentralized Morphogenesis and Self-Healing Reconstruction Quality Evaluation

Table 4. Decentralized morphogenesis and self-healing reconstruction quality assessment (results shown for repair capability under node damage with masking ratio = 20%). The best values are bold.

Model	MSE ($\times {10}^{-3}$)	MAE ($\times {10}^{-2}$)
HTM-PQC	13.40	12.10
Fog-AKA	5.62	5.95
EaaS-IoT	3.88	4.12
GCN-IDS	2.85	3.10
GAT-IDS	1.95	2.25
SG-GNC	0.82	1.15

details the decentralized self-healing and reconstruction performance of each method on the IEEE 118-bus standard test system. Experimental results demonstrate that the proposed SG-GNC framework achieves optimal performance across all metrics. In terms of self-healing, the graph-based baselines (GCN-IDS and GAT-IDS) outperform the cryptographic methods but still fall short of the proposed framework. Specifically, GAT-IDS achieves an MSE of $1.95\times {10}^{-3}$, improving upon EaaS-IoT ($3.88\times {10}^{-3}$); yet, it remains higher than SG-GNC ($0.82\times {10}^{-3}$). This discrepancy arises because standard Graph Autoencoders are trained primarily for feature representation rather than iterative physical state restoration. In contrast, the SG-NCA engine’s morphogenetic training explicitly optimizes the trajectory from damaged states to the healthy manifold, ensuring higher fidelity in reconstructing lost physical data. Thus, SG-GNC not only possesses defense capabilities in terms of security but also demonstrates irreplaceable advantages in data availability and system resilience.

5.3. Analysis of the Impact of Stability Regularization Coefficient

Figure 6 illustrates the influence of the stability regularization coefficient $\lambda$ on self-healing reconstruction quality and numerical robustness, revealing a significant non-monotonic effect. In the low $\lambda$ range ($\lambda <{10}^{-4}$), the lack of effective constraints on cell state amplitude causes the recursive evolution process to easily trigger numerical oscillation or gradient explosion, resulting in a convergence rate below 70%. Conversely, when $\lambda$ is excessively large (>${10}^{-2}$), strong penalty terms force the latent state vectors to collapse toward zero, limiting the information capacity of neural cells to encode complex physical features (such as non-stationary load fluctuations), thereby leading to a significant increase in reconstruction error and underfitting. The model achieves an optimal balance between morphogenetic accuracy and dynamic stability only when $\lambda ={10}^{-3}$. This selection was determined through a coarse-to-fine grid search strategy on a validation set (10% of the IEEE 118-bus data). As shown in Figure 6, the optimal value represents the Pareto efficient point that balances reconstruction quality and convergence speed. Values of $\lambda <{10}^{-4}$ resulted in unconstrained state amplitudes leading to numerical overflow (ACT > 100), while $\lambda >{10}^{-2}$ caused the vanishing state problem, where latent vectors collapsed to zero. Thus, $\lambda ={10}^{-3}$ was selected to provide sufficient damping for numerical stability without suppressing the information capacity required for morphogenetic encoding. This result confirms the necessity of introducing an overflow penalty term in the total loss function. By applying appropriate system damping, it effectively resolves the numerical divergence problem of the decentralized self-healing mechanism during long-term evolution, ensuring the robustness of edge-side inference.

5.4. Empirical Convergence Analysis of Generative Adversarial Immunity

To validate the theoretical stability of the GAI game formulation, we conducted a convergence analysis tracking the adversarial loss trajectories over 200 co-evolutionary epochs. As illustrated in Figure 7, the interaction reveals a distinct two-phase dynamic consistent with game-theoretic learning. During the Exploration Phase (Epochs 0–120), the system exhibits high volatility as the Attack Generator maximizes perturbation damage, forcing the Immune Evolver to adapt. Subsequently, in the Equilibrium Phase (Epochs 120–200), both the attacker’s success rate and the defender’s reconstruction error converge. Specifically, the defender’s loss stabilizes at $1.5\times {10}^{-3}$, indicating the attainment of a Local Stackelberg Equilibrium where the defense strategy covers the manifold’s most vulnerable regions. Furthermore, the analysis of Defense Variance (${\sigma }^2$) highlights the critical role of the immune memory replay mechanism. The model incorporating memory replay demonstrates a monotonic decrease in variance, stabilizing at ${\sigma }^2\approx 0.01$. In contrast, the baseline without memory exhibits continuous high-frequency oscillations (${\sigma }^2>0.11$), confirming that the system is susceptible to Mode Collapse and cyclic forgetting in the absence of historical experience replay. This empirical evidence validates that the proposed mechanism effectively approximates a fictitious play process, ensuring robust convergence in non-convex optimization landscapes.

5.5. Ablation Experiments

To systematically validate the efficacy and synergistic mechanisms of the SG-GNC framework’s core components, a multi-level ablation study was conducted across the IEEE 118-bus, IEEE 300-bus, and MSU-ORNL datasets (

Table 5. Comprehensive ablation study of SG-GNC across IEEE 118-bus, IEEE 300-bus, and MSU-ORNL datasets. The best values are bold.

Configuration	Modules	IEEE 118-Bus		IEEE 300-Bus		MSU-ORNL
		MSE ($\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{3}}$) ↓	F1 (%) ↑	MSE ($\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{3}}$) ↓	F1 (%) ↑	Acc (%) ↑	F1 (%) ↑
Baseline	GCN	12.60	88.60	15.40	86.50	85.50	86.20
Individual	NHE	9.50	91.05	11.20	89.50	87.50	88.00
	NCA	6.10	89.20	7.80	87.50	86.50	87.00
	GAI	11.80	90.50	14.50	88.50	89.00	89.50
Pairwise	NHE + NCA	1.62	96.50	2.15	95.80	86.20	87.15
	NHE + GAI	8.45	94.20	9.10	92.50	93.80	94.10
	NCA + GAI	5.20	91.50	6.85	90.10	90.40	90.85
Proposed	SG-GNC	0.82	98.28	1.15	97.02	96.55	94.56

). Although individual modules outperformed the GCN baseline, distinct functional limitations were observed. Specifically, while the NHE module established a foundation for unsupervised perception via a variational health manifold (F1 > 90%), the absence of a morphogenetic mechanism resulted in elevated physical state reconstruction errors (MSE > 5.20). Conversely, the standalone NCA engine demonstrated local repair capabilities but struggled to precisely delineate anomaly boundaries without manifold constraints. Combinatorial analysis revealed significant modular complementarity. The synergy between NHE and NCA optimized reconstruction performance, reducing the MSE on the IEEE 118-bus to 1.62, thereby validating the role of the perception-repair loop in ensuring physical consistency. However, on the MSU-ORNL dataset featuring complex zero-day attacks, the lack of adversarial training limited detection accuracy to 86.2%, highlighting the vulnerability of static defenses against sophisticated, unknown threats. In contrast, the complete SG-GNC framework, augmented by the GAI strategy, demonstrated superior scalability on the large-scale IEEE 300-bus topology (F1 97.02%) and increased adversarial detection accuracy to 96.55%. These findings confirm that the integration of Neural Homeostatic Embedding, Cellular Automata, and Adversarial Immunity is critical for achieving endogenous security and self-healing resilience in complex, large-scale smart grids.

6. Conclusions

Addressing the defensive dilemmas faced by smart grids under time-varying topological evolution and APTs, we propose a resilient security defense framework based on self-organizing graph Neural Cellular Automata. This research moves beyond traditional static defense paradigms by modeling grid security mechanisms on self-organizing principles inspired by morphogenesis. The framework significantly enhances defense efficacy through three core mechanisms. First, the NHE mechanism utilizes variational graph inference to construct a continuously differentiable health state manifold, achieving precise unsupervised perception of anomalous behaviors under non-stationary load fluctuations. Second, the SG-NCA engine endows nodes with the capability for immediate self-healing of damaged data in a decentralized environment by training shared-weight local neural rules, fundamentally realizing the topological independence of the defense mechanism. Finally, the GAI strategy, through a bi-level game framework and memory replay mechanism, resolves the catastrophic forgetting problem, enhancing the system’s adversarial robustness against unknown zero-day attacks. Experimental results demonstrate that the proposed method significantly outperforms existing centralized architectures and static hypergraph defense schemes in terms of detection accuracy and restorative repair quality on datasets such as IEEE 118 and 300-bus and MSU-ORNL.

Although SG-GNC exhibits excellent resilient defense capabilities, the multi-step iterative evolution mechanism of Neural Cellular Automata may introduce additional inference overhead in scenarios requiring ultra-low latency. Furthermore, high-dimensional state vectors pose certain challenges to the storage capacity of resource-constrained edge nodes. Future work will focus on lightweight distillation techniques for neural update rules and explore semantic interpretation mechanisms combining quantum machine learning algorithms to further enhance the interpretability and computational efficiency of smart grid defense systems in the post-quantum era.