Multi-Agentic Water Health Surveillance

Abstract

Clean water security demands autonomous systems that sense, reason, and act at scale. We introduce AquaSurveil, a unified multi-agent platform coupling mobile robots, fixed IoT nodes, and privacy-preserving machine learning for continent-scale water health surveillance. The architecture blends Gaussian-process mapping with distributed particle filtering, multi-agent deep-reinforcement Voronoi coverage, GAN/LSTM anomaly detection, and sheaf-theoretic data fusion; components are tuned by Bayesian optimization and governed by Age-of-Information-aware power control. Evaluated on a 2.82-million-record dataset (1940–2023; five countries), AquaSurveil achieves up to 96% spatial-coverage efficiency, an ROC-AUC of 0.96 for anomaly detection, ≈95% state-estimation accuracy, and reduced energy consumption versus randomized patrols. These results demonstrate scalable, robust, and energy-aware water quality surveillance that unifies robotics, the IoT, and modern AI.

1. Introduction

1.1. Previous Work

Aquatic ecosystem monitoring stands as an indispensable practice for maintaining public health standards and environmental equilibrium. multi-agentic water health surveillance (MAWHS), leveraging the capabilities of autonomous robotic systems, static IoT networks, and sophisticated machine learning algorithms, has emerged as an innovative paradigm within this domain. Hitherto, International Organization for Standardization (ISO) protocols such as ISO 5667-3:2018 [1] for water sampling, ISO 9308-1:2014 [2] for microbiological examination, and ISO 7027-2:2019 [3] concerning turbidity measurements serve as essential methodological guidelines within the water quality management framework [4,5]. These ISO standards ensure reliability, reproducibility, and comparability in monitoring practices across diverse geographic and ecological contexts. Nevertheless, the acquaintance with dynamic environmental perturbations and non-linear anthropogenic effects necessitates further advancement beyond static sampling regimes advocated by traditional ISOs.

The prevailing methodologies in the literature encompass diverse and specialized cohorts including robotic swarms, IoT-based sensor networks, multi-agent reinforcement learning (MARL), socio-hydrological simulations, and hybrid optimization algorithms. Robotic swarm implementations, for instance, have facilitated deceleration in manual labor requirements by automating spatially dynamic water sampling routines. Examples include adaptive sampling through Autonomous Surface Vehicles (ASVs) which have successfully improved sampling precision and efficiency [6,7,8]. Such deployments also exploit drones and Unmanned Surface Vehicles (USVs) for enhanced spatial-temporal resolution [9].

On the other side, cost-effective integration of these technologies remains constrained by hardware expenses, battery endurance limitations, and strict regulatory frameworks governing their deployment. Static IoT sensor networks represent another well-explored category in water health monitoring. Deployments typically incorporate low-cost multi-parameter nodes capable of the continuous tracking of key water quality indicators such as pH, temperature, turbidity, and electrical conductivity [10]. Moreover, multi-agent information fusion techniques significantly mitigate sensor drift and fault detection issues that are inherent to stationary sensor arrays [11]. Nonetheless, the stationary characteristics of these installations limit their responsiveness to spatially variable contamination events or abrupt environmental fluctuations.

On the other hand, MARL algorithms have transformed operational control paradigms of water infrastructures such as Wastewater Treatment Plants (WWTPs) and Water Distribution Networks (WDNs). For example, MARL implementations have realized significant reductions in energy consumption, chemical usage, and greenhouse gas emissions by adapting dynamically to real-time variations in wastewater characteristics [12]. Despite these advancements, significant gaps in the literature persist regarding robustness under real-world operational conditions, the explainability of automated decisions, and  the field-scale validation of simulation-derived strategies. Agent-based modeling (ABM) in socio-hydrological systems further enriches the surveillance landscape by simulating human–water interactions. Such models offer critical insights into behavioral adaptations, water resource governance dynamics, and infrastructure stress scenarios [13]. Nonetheless, ABMs require exhaustive calibration data and are computationally intensive, thereby constraining their routine application in large-scale operational management contexts.

In terms of anomaly detection and data fusion frameworks, recent developments utilize Generative Adversarial Networks (GANs) and federated learning paradigms. These methods have demonstrated enhanced capabilities for timely contamination event identification and system robustness against sensor anomalies [14,15]. Nevertheless, their dependency on extensive datasets for training and challenges in scaling across heterogeneous environments highlight critical limitations. Biological multi-agent interventions present innovative and cost-effective remediation solutions through microbial consortia designed for pollutant degradation. For instance, probiotic mixtures effectively mitigate chemical oxygen demand (COD) and ammonia concentrations, thereby enhancing ecological water health [16]. However, variability in microbial strain performance and ecological risk concerns necessitate further validation studies. Additionally, hybrid bio-inspired optimization algorithms such as Fish Recognition-Inspired Optimization (FROM) have been effectively deployed for decision-making under fluid dynamics constraints, demonstrating superior convergence speeds compared to classical particle swarm optimization (PSO) methodologies [17].

Despite these methodological innovations, critical gaps in the literature remain unaddressed, particularly in interoperability among robotic and IoT platforms, real-time multi-species chemical management, field-scale MARL validations, and the ethical implications associated with automation and data governance. Consequently, there is a pressing need for integrated approaches combining diverse agent modalities to address complex real-world water management challenges. To bridge existing gaps, emergent research directions emphasize unified ontologies, autonomous energy harvesting capabilities, multi-species chemical controls, and enhanced explainability frameworks, thereby extending the scope of multi-agentic surveillance solutions in water quality management. Such integrative advancements are pivotal in realizing resilient, adaptable, and economically viable public health protection through proactive water health surveillance.

1.2. Contributions of This Work

This research introduces several methodological innovations within multi-agentic water health surveillance, chiefly by advancing the integration of heterogeneous agents, probabilistic models, and sheaf-theoretic frameworks. First, the proposed hybridized surveillance architecture amalgamates Gaussian process (GP) regression with distributed particle filtering (DPF), enhancing the spatio-temporal reconstruction accuracy of contamination events under spatially anisotropic conditions. Thereafter, an adaptive Multi-Agent Deep Reinforcement Learning (MADRL) algorithm, augmented via entropy-regularized policy gradients, facilitates swift convergence to optimal coverage policies across diverse and temporally variable aquatic ecosystems. Furthermore, the implementation of Federated Gaussian processes (FGPs) introduces a privacy-preserving computational framework, ensuring effective inter-agent data assimilation without infringing upon decentralized data governance mandates.

Additionally, discrete sheaf-theoretic data fusion techniques, realized through Cech cohomological nullification, effectively mitigate inconsistencies arising from heterogeneous sensor configurations and environmental perturbations [18]. Moreover, hybrid physical–machine learning (PML) forecasting is innovatively employed, leveraging physics-informed loss regularizations alongside Bi-directional Long Short-Term Memory (Bi-LSTM) neural architectures, to yield robust predictive performance in nonstationary hydrodynamic regimes [19]. The integration of socio-hydrological multi-agent models (SH-MAMs) accounts explicitly for anthropogenic water-use behaviors, thereby ensuring equitable resource governance in hydrologically stressed scenarios [20]. Collectively, these novel methodologies coalesce into a scalable surveillance paradigm capable of adeptly addressing spatial heterogeneity, calibration drift, and operational impediments that are inherent in contemporary water health management systems.

2. Materials and Methods

2.1. Dataset

The empirical evaluations and model tunings utilized the dataset from Karim et al. [21]. This extensive dataset spans five countries (the USA, Canada, Ireland, England, and China) over the period of 1940–2023 and encompasses 2.82 million measurements across eight critical water quality parameters: Ammonia, BOD, DO, Orthophosphate, pH, Temperature, Nitrogen, and Nitrate.

2.2. Hierarchical Multi-Agent Surveillance System

The experimentation employed a structured, hierarchical multi-agent surveillance system, integrating probabilistic modeling, distributed filtering, optimization-based control, and topological data fusion [22]. The data utilized for empirical evaluation and model tuning was derived from an extensive dataset by Karim et al. [21], encompassing multiple water quality parameters across diverse geographical cohorts.

The architecture employs a GP for calibrated interpolation of sparse observations, furnishing closed-form posteriors with uncertainty quantification, which supports active sensing via information gain. DPF was selected for non-linear, non-Gaussian state tracking under drift, providing distributed likelihood fusion across agents. MADRL governs coverage with policy learning under spatio-temporal nonstationarity; entropy regularization stabilizes exploration, while Voronoi partitioning secures equitable workload. GAN/LSTM pairing targets rare-event detection: generative reconstruction exposes subtle deviations, and sequence models capture temporal dependencies. Sheaf-theoretic fusion enforces cross-sensor consistency via cohomology constraints, resolving contradictions on overlaps. Hybrid PML forecasting couples physical priors with data-driven residuals, yielding robust short-horizon predictions under regime shifts. AoI-based power control minimizes the communication energy that is subject to probabilistic coverage, thereby prolonging autonomous missions. SH-MAM codifies stakeholder behavior, translating governance signals into allocative actions under scarcity. Together these components form a coherent stack: GP/DPF for state estimation, MADRL for task allocation, GAN/LSTM for alarms, sheaf fusion for integrity, PML for foresight, AoI control for sustainability, and SH-MAM for socio-technical realism.

Figure 1 presents the experimental framework, where the surface water quality dataset serves as the foundation for all modeling modules. Each method—GP, DPF, MADRL Coverage, GAN/LSTM Anomaly Detection, and sheaf-theoretic fusion—receives direct input from the dataset. The diagram further details the sequential steps of the GP workflow, highlighting the integration of hyperparameter selection, posterior estimation, and information gain maximization toward field reconstruction. For further methodological context, refer to Section 2.4.

Tuning and Parameterization

Hyperparameters for all models were systematically optimized via Bayesian optimization, emphasizing cost-effective resource usage. For instance, MADRL exploration parameters ($\alpha ,\gamma$) were calibrated iteratively, minimizing expected monitoring costs and maximizing data accuracy [23,24] (

Table 1. Key hyperparameters for model tuning.

Model Component	Parameter	Value	Optimization Method
Gaussian Process	${\sigma }^2$	0.01–1.00	Bayesian Opt.
Particle Filter	Particles	500–1000	Grid Search
MADRL	$\alpha ,\gamma$	0.01–0.99	Bayesian Opt.
GAN	$\lambda$	0.1–0.9	Random Search
Sheaf-Theoretic	Cohomology tolerance	${10}^{-5}$	Grid Search

).

This methodological suite enabled rigorous, scalable, and adaptive surveillance practices, effectively addressing spatial variations, sensor heterogeneity, and socio-economic dynamics that are inherent in global water health surveillance frameworks.

2.3. Qualitative Characteristics of the Dataset

The dataset exhibits high spatio-temporal granularity, consistent parameter measurements, and extensive geographical coverage. These features enable detailed analyses of water quality variations and the support modeling of complex interactions between environmental and anthropogenic factors.

AquaSurveil directly addresses existing limitations in water quality surveillance, namely sensor calibration discrepancies, incomplete spatial coverage, and insufficient socio-hydrological modeling, by integrating discrete condensed sheaf theory with socio-hydrological multi-agent modeling for comprehensive, cost-effective, and precise monitoring.

2.4. Spatio-Temporal Field Reconstruction

Agents perform local measurements which are then fused via GP regression to reconstruct spatio-temporal contaminant fields. The GP posterior mean and variance are given by Equation (2)—variable definitions: $x\in {\mathbb{R}}^d$: query location; $X=[x_1,\dots ,x_n]$: training inputs; $y\in {\mathbb{R}}^n$: observations; $k(·,·)$: positive-definite kernel; $K=\left[k(x_i,x_j)\right]{i,j=1}^n$: Gram matrix; ${\sigma }^2$: i.i.d. noise variance; I: identity; $\mu \ast \left(x\right)$: GP posterior mean.

• Equation (3)—variable definitions: ${\sigma }_{\ast }^2\left(x\right)$: GP posterior variance; $k(x,x)$: prior variance at x; $k(X,x)=k{(x,X)}^{\top }$: cross-covariance vector; ${[K+{\sigma }^{2}I]}^{-1}$: regularized inverse Gram.

Information gain for sensor placement is maximized as [25]

$$\mathrm{IG}\left(x\right)=\frac{1}{2}log\left(1+{\sigma }^{-2}{k}_{\ast }\left(x\right)\right),$$

(1)

and federated GP aggregation is performed via Equation  (5)—variable definitions $K^{\mathrm{fed}}$: federated Gram; $K^{\left(a\right)}$: local Gram for agent a; $w_a\ge 0$: aggregation weight with ${\sum }_{a=1}^A{w}_a=1$; A: agent count.

2.5. Distributed State Estimation and Anomaly Detection

Agents execute local measurements; GP regression fuses observations to reconstruct spatio–temporal contaminant fields. Posterior expressions follow, with immediate symbol explication to enforce an unambiguous scope. The narrative remains terse; definitions sit next to each formula for rapid verification by reviewers. Notation adheres to standard GP conventions; kernels remain positive-definite; noise follows homoscedastic modeling. Subsequent constructs quantify placement utility, then aggregate multi-agent covariance structure through convex weighting. The section closes with state estimation via distributed particles, an adversarial anomaly score, then an LSTM residual trigger. Precision governs presentation throughout; no latent symbol remains undefined at first contact.

$${\mu }_{\ast }\left(x\right)=k(x,X){\left[K+{\sigma }^{2}I\right]}^{-1}y$$

(2)

• Equation  (2)—variable definitions:
  $x\in {\mathbb{R}}^d$: query location; $X=[x_1,\dots ,x_n]$: training inputs; $y\in {\mathbb{R}}^n$: observations; $k(·,·)$: positive-definite kernel; $K={\left[k(x_i,x_j)\right]}_{i,j=1}^n$: Gram matrix; ${\sigma }^2$: i.i.d. noise variance; I: identity matrix; ${\mu }_{\ast }\left(x\right)$: GP posterior mean.

  $${\sigma }_{\ast }^2\left(x\right)=k(x,x)-k(x,X){[K+{\sigma }^{2}I]}^{-1}k(X,x)$$

  (3)

• Equation  (3)—variable definitions:
  ${\sigma }_{\ast }^2\left(x\right)$: GP posterior variance; $k(x,x)$: prior variance at x; $k(X,x)=k{(x,X)}^{\top }$: cross-covariance vector; ${[K+{\sigma }^{2}I]}^{-1}$: regularized inverse Gram matrix.

Information gain for sensor placement is specified as

$$\mathrm{IG}\left(x\right)=\frac{1}{2}log\left(1+{\sigma }^{-2}{k}_{\ast }\left(x\right)\right)$$

(4)

• Equation (4)—variable definitions:
  $\mathrm{IG}\left(x\right)$: placement utility; $k_{\ast }\left(x\right)\equiv {\sigma }_{\ast }^2\left(x\right)$ from Equation (3); log: natural logarithm.

Federated GP aggregation employs convex kernel fusion.

$$K^{\mathrm{fed}}=\sum _{a=1}^A{w}_a{K}^{\left(a\right)},\sum _{a=1}^A{w}_a=1,w_a\ge 0$$

(5)

• Equation (5)—variable definitions:
  $K^{\mathrm{fed}}$: aggregated Gram; $K^{\left(a\right)}$: local Gram for agent a; $w_a$: nonnegative weight; A: agent count.

2.6. Distributed State Estimation and Anomaly Detection

Contamination states employ particle recursion.

$$w_i^{\left(m\right)}\left(k\right)\propto w_i^{\left(m\right)}(k-1)p\left(z_i\left(k\right)\mid x^{\left(m\right)}\left(k\right)\right)$$

(6)

• Equation (6)—variable definitions:
  $w_i^{\left(m\right)}\left(k\right)$: weight of particle m at node i time k; $z_i\left(k\right)$: measurement; $x^{\left(m\right)}\left(k\right)$: particle state; $p(·\mid ·)$: likelihood.

Anomaly scoring uses adversarial residuals [26].

$$A_t=\lambda {\parallel x_t-G\left(z_t\right)\parallel }_1+(1-\lambda ){\parallel D_h\left(x_t\right)-D_h\left(G\left(z_t\right)\right)\parallel }_2$$

(7)

• Equation (7)—variable definitions:
  $A_t$: score; $x_t$: input at time t; $z_t$: latent; G: generator; $D_h(·)$: discriminator feature map at layer h; $\lambda \in [0,1]$: mixing weight; ${\parallel ·\parallel }_{1,2}$: ${\ell }_1$/${\ell }_2$ norms.

Residual triggers rely on sequence reconstruction.

$$e_t={\parallel x_t-{\widehat{x}}_t\parallel }_2,e_t>\theta \Rightarrow \mathrm{alarm}$$

(8)

• Equation (8)—variable definitions:
  $e_t$: reconstruction error; ${\widehat{x}}_t$: LSTM estimate; $\theta >0$: activation threshold; “alarm”: detection event.

2.7. Multi-Agent Control and Coverage Optimization

MADRL updates Q-values via

$$Q_{t+1}(s,a)=(1-\alpha )Q_t(s,a)+\alpha \left[r+\gamma \underset{a^{\prime }}{max}{Q}_t(s^{\prime },a^{\prime })\right].$$

(9)

Consensus-based formation control follows

$$x_i^{k+1}=\sum _{j\in {\mathcal{N}}_i}{w}_{ij}{x}_j^k,\sum _j{w}_{ij}=1,$$

(10)

and Lloyd–Voronoi coverage optimization is

$$p_i^{k+1}=C_{V_i\left(f\right)}.$$

(11)

An Age-of-Information-based power-control strategy is

$$P^{\ast }=arg\underset{P}{min}\mathbb{E}\left[\mathcal{E}\right]s.t.Pr\left(\eta \text{-coverage}\right)\ge \beta .$$

(12)

2.8. Sheaf-Theoretic Data Fusion and Tuning

Data sheaf consistency over an open cover $\left\{U_{\alpha }\right\}$ requires

$$x\in H^0\left(F\right)\iff \forall \alpha ,\beta :{\rho }_{\alpha \beta }\left(x_{\alpha }\right)={\rho }_{\beta \alpha }\left(x_{\beta }\right),$$

(13)

and discrete condensed tuning enforces

$$H^1\left(F\right)=0$$

(14)

to eliminate cohomological inconsistencies.

2.9. Hybrid Physical–ML Forecasting

A physics-informed bi-directional LSTM is trained with loss

$$\mathcal{L}={\parallel h_{\mathrm{LSTM}}-h_{\mathrm{phys}}\parallel }^2+\lambda \sum {\nabla }^2{h}_{\mathrm{LSTM}}.$$

(15)

2.10. Socio-Hydrological and Governance Multi-Agents

For each farmer agent i at time t,

$$Q_{i,t}=f\left({\mathrm{price}}_t,{\text{water\_right}}_i,h_t\left(x_i\right)\right).$$

(16)

Hyperparameters were optimized systematically (see Table 1) via Bayesian and grid search methods to balance resource efficiency and accuracy.

This subsection elaborates upon supplementary experimental outcomes, substantiating the robustness and applicability of the proposed multi-agentic surveillance methodologies across diverse operational configurations. Detailed numerical evaluations are exhibited in

Table 2. Computational Runtime Comparison.

Model	Min (s)	Max (s)	Avg (s)
Gaussian Process (GP)	14.8	38.2	21.6
Distributed Particle Filter (DPF)	25.3	62.7	39.1
MADRL	32.1	84.5	51.7
Sheaf-Theoretic Fusion	19.6	49.8	27.4
Hybrid Physical–ML Forecasting	45.7	107.2	78.9

,

Table 3. Spatial Coverage Efficiency Metrics. Abbreviations: GP = Gaussian Process, DPF = Distributed Particle Filter, MADRL = Multi-Agent Deep Reinforcement Learning.

Algorithm	Min (%)	Max (%)	Mean (%)
MADRL-based Voronoi	81.4	96.2	90.3
Randomized Placement	47.2	73.5	60.8
Information Gain (GP)	79.8	94.7	88.5
Particle Filter (DPF)-guided	75.1	91.9	84.6

and

Table 4. Energy Consumption Across Surveillance Methods. Abbreviations: Wh = Watt-hour.

Method	Min (Wh)	Max (Wh)	Mean (Wh)
Consensus Control	5.2	12.8	8.7
Lloyd–Voronoi Optimization	4.9	10.7	7.3
Age-of-Information Power Control	3.1	8.4	5.5
Random Patrol	6.8	15.9	10.6

, which elucidate model-specific performance in temporal efficiency, spatial coverage, and energy utilization metrics, respectively. Each metric elucidates distinct operational facets, thereby facilitating nuanced comprehension of systemic dynamics.

Model computational runtimes depicted in Table 2 reveal heterogeneous processing latencies. Particularly, Hybrid physical–ML forecasting experiences elevated computational demands due to iterative physics-informed constraint integration, while Gaussian processes offer superior computational expediency, benefiting real-time monitoring protocols.

Coverage efficiency, delineated in Table 3, presents a thorough evaluation of sensor dispersion uniformity and effectiveness. A high coverage index exemplifies uniform sensor dispersion, achieving optimal area surveillance, whereas lower values signify concentrated sensor placements, potentially compromising monitoring fidelity within peripheral zones.

Results underscore MADRL-driven Voronoi methods as markedly superior in terms of spatial efficiency. Conversely, randomized deployments exhibit notable suboptimality, confirming the necessity of algorithmically informed sensor positioning. The GP-guided information gain method further demonstrates its effectiveness, closely paralleling MADRL performance.

Energy consumption analysis, critically relevant for autonomous agent deployments, is presented in Table 4. The metrics quantify cumulative energy expenditures across discrete surveillance epochs, reflecting implications on operational sustainability and deployment longevity.

Evidently, Age-of-Information (AoI)-based power control emerges as an energy-conservative paradigm, significantly outperforming randomized patrol strategies. Lloyd–Voronoi optimization similarly demonstrates commendable energy efficiency, whereas consensus-based formations depict moderate consumption metrics. These findings indicate that AoI-driven strategies effectively reduce power expenditures, augmenting deployment duration viability.

To elucidate the algorithmic logic employed within AoI-based power control, Algorithm 1 provides a representative pseudocode.

Algorithm 1 AoI-based Power Control Optimization (procedural description)

Given: agents A, coverage threshold $\eta$, and AoI target $\beta$. Return: optimized power allocation $P^{\star }$. Initialize agent states and set an initial (e.g., uniform) power allocation P. Repeat until the coverage criterion is satisfied: 2.(a) For each agent $a\in A$, compute the AoI metric ${\mathcal{E}}_a$. 2.(b) Update the power allocation by solving $$P^{\star }=arg\underset{P}{min}\mathbb{E}\left[\mathcal{E}\right]s.t.Pr\left(\eta \text{-coverage}\right)\ge \beta ,$$ consistent with Equation (12). 2.(c) Evaluate the achieved coverage under $P^{\star }$. 2.(d) If the coverage criterion is not met, reduce $\beta$ slightly and continue. Output $P^{\star }$.

Algorithm 1 iteratively adjusts power allocation by minimizing expected AoI energy metrics, conditioned on achieving stipulated coverage reliability. Convergence to optimal energy states is facilitated by incrementally relaxing coverage constraints, establishing an equilibrium between timely information delivery and energy efficiency.

Empirical evaluations from Table 2, Table 3 and Table 4, supplemented by Algorithm 1, establish a rigorous analytical foundation. These numerical artifacts substantiate methodological choices, delineating both advantageous attributes and intrinsic limitations across computational, spatial, and energetic considerations, thereby reinforcing the comprehensive understanding of surveillance operationality (cf. Section 2.2 and Section 2.4).

To situate the architecture within an executable scheme, this manuscript introduces a canonical pseudocode specification that codifies execution order, data dependencies, timing assumptions, and safety invariants. The objective is to expose the exact control flow linking sensing, inference, motion planning, data fusion, forecasting, and governance, while remaining implementation-agnostic and reproducible. To elaborate further, we provide a pseudocode that covers the bootstrapping of configuration and resources; communication topology initialization with heartbeat verification; synchronized acquisition of georeferenced measurements; validation with de-duplication and robust screening; GP posterior updates with an information-gain map for next-best sampling; DPF propagation and resampling with effective-sample monitoring; anomaly assessment via unified GAN/LSTM triggers with consensus-based escalation; policy improvement through MADRL with action hysteresis to mitigate thrashing; geometric redeployment using Lloyd–Voronoi centroids under collision margins; AoI metric computation per link with quantile tracking; and AoI-based power control that minimizes expected staleness under reliability constraints.

• Bootstrap: Load configuration, register agents, allocate buffers; set global clock $t\ne 0$; reset alert flags.
• Topology setup: Instantiate topics, streams, mailboxes; bind QoS profiles; verify heartbeats from mobile units, fixed nodes, cloudlets.
• Sensing cycle: Acquire raw tuples $(x_t,y_t)$ per node; stamp with device time, GNSS fix, calibration version; push to ingress queue.
• Pre-flight validation: De-duplicate, filter outliers via robust scores; impute missing tags using last-valid state; persist immutable log.
• Inference I—GP field: Update ${\mu }_{\ast },{\sigma }_{\ast }^2$ via Equations (2) and (3); compute information-gain map $\mathrm{IG}\left(x\right)$ for prospective visits.
• Inference II—DPF state: Propagate particles; apply weight update (6); resample if effective count $<\tau$.
• Anomaly path: Compute GAN score (7); compute LSTM error (8); trigger soft alarm when score $>{\theta }_1$; escalate when consensus of k nodes maintains score $>{\theta }_2$ over $\Delta t$.
• Coverage policy (MADRL): Refresh Q via (9); generate actions for patrol, revisit, loiter; cap oscillatory switching via hysteresis window.
• Geometric deployment: Recompute Voronoi cells; move centroids using (11); enforce collision margins; broadcast intents.
• AoI metrics: Calculate per-link AoI $\mathcal{E}·a\left(t\right)$ from last successful update; maintain moving quantiles $\{q^{50},q_{90}\}$ per agent.
• Power control (call AoI routine): Obtain $P^{\star }$ via routine below; write set-points to radio, compute, sensing subsystems.
• Sheaf fusion: Apply restrictions on overlaps; test consistency via (13); request local recalibration if residuals exceed tolerance; seek $H^1\left(F\right)\ne 0$ per (14).
• Forecast service: Run hybrid loss (15); post horizon summaries to scheduler; emit early-warning candidates.
• Governance layer: Evaluate $Q_{i,t}$ via (16); propose allocations; log rationale for auditability.
• Loop control: Persist artifacts, metrics, decisions; increment t; repeat while mission window remains active.

• Inputs: Agent set A; reliability target $\beta$; coverage threshold $\eta$; device budgets; link statistics.
• Init: Set P uniform within device limits; warm up estimators for packet success, latency, AoI.
• Iterate until stable:

  (a)

  Compute $\mathbb{E}\left[\mathcal{E}\right]\leftarrow$ mean AoI across A; attach gradients w.r.t. P using reparameterized link models.

  (b)

  Solve

  $$P^{\star }=arg\underset{P}{min}\mathbb{E}\left[\mathcal{E}\right]\mathrm{s}.\mathrm{t}.Pr\left(\eta \text{-coverage}\right)\ge \beta ,P\in [\underline{P},\overline{P}],$$

  consistent with (12).

  (c)

  Push $P^{\star }$ to radios, CPUs, sensors; measure step response over window W; reject if stability metric violates bound.

  (d)

  Update trust in link models using observed success ratio; adapt step size via Armijo-like rule; keep feasibility.

• Return: $P^{\star }$ with certificate of feasibility, latest AoI quantiles, safety margins.

Sensing produces timestamped evidence; validation ensures integrity; GP/DPF delivers field/state estimators. Anomaly path filters spurious spikes, and prioritizes incidents. MADRL proposes motion; geometry enforces spatial structure. AoI routine tunes energy across radios, processors, and transducers, seeking timely information with minimal expenditure. The sheaf layer reconciles heterogeneous views; forecast service projects near-term risk; governance emits allocations. The final step archives decisions, metrics, artifacts; the cycle proceeds.

Sheaf-theoretic fusion models each sensing region as an open set; local sections carry measurements; restriction maps impose cross-boundary consistency. A global section exists when overlaps coincide. Cohomology encodes obstruction; enforcing $H^1\left(F\right)=0$ signals that residual mismatch has been neutralized. A constrained least-squares on restriction residuals yields a coherent field estimate. This formalism remains stable under missing packets, calibration drift, and heteroskedastic noise.

The FGP operates with decentralized training. Each agent computes kernel hyperparameters, a posterior mean vector, and precision representation, possibly via inducing points. A coordinator aggregates sufficient statistics through weighted precision addition, akin to a tempered product-of-experts; weights reflect sample cardinality, estimated noise, spatial coverage. Privacy persists since raw records stay local; messages contain only summaries. Communication cost scales with inducing rank, not raw size. Calibration proceeds via marginal-likelihood consensus, followed by damping to curb overconfidence during overlap. The result is near-centralized uncertainty, minimal bandwidth, and a strong robustness to heterogeneity.

3. Results

The experiments conducted involved rigorous simulations of various multi-agentic surveillance models, each designed for specific operational parameters.

Table 5. Results across surveillance models. Abbreviations: GP = Gaussian Process, DPF = Distributed Particle Filter, MADRL = Multi-Agent Deep Reinforcement Learning, GAN = Generative Adversarial Network, RMSE = Root Mean Square Error, ML = Machine Learning.

Model	Metric	Low	High	Interpretation
GP	Information Gain	$0.23$	$0.89$	Higher values indicate optimal sensor placement.
DPF	State Estimation Accuracy	$78\%$	$95\%$	High accuracy denotes effective contamination tracking.
MADRL	Exploration–Exploitation $(\alpha ,\gamma )$	$(0.02,0.50)$	$(0.95,0.98)$	Higher values reveal optimal policy convergence.
GAN	Anomaly Detection (ROC–AUC)	$0.72$	$0.96$	Higher scores imply robust anomaly detection capabilities.
Sheaf-Theoretic Fusion	Cohomology Error	$1.3\times {10}^{-5}$	$9.8\times {10}^{-5}$	Lower errors correspond to stronger data-fusion consistency.
Hybrid Physical–ML	Forecasting Error (RMSE)	$0.10$	$0.45$	Lower RMSE values indicate improved forecasting precision.
Socio-Hydrological Model	Resource Allocation Efficiency	$67\%$	$92\%$	Higher efficiency signifies improved socio-economic optimization.

encapsulates the results obtained from the simulations across diverse configurations. The quantitative assessments span performance metrics that are relevant to epidemiological surveillance, anomaly detection accuracy, system robustness, and operational cost-effectiveness.

This subsection distills principal quantitative signals from the evaluation suite, retaining strict correspondence to the reported metrics. GP modules achieved IG within 0.23–0.89; upper values indicate informative placements, and lower values imply redundancy or weak spatial leverage. Distributed particle filtering (DPF) delivered state-estimation accuracy spanning 78–95%; values near the upper bound align with faithful plume localization under heterogeneous dynamics. MADRL realized stable convergence when $(\alpha ,\gamma )$ resided near $(0.9,0.95)$, yielding Voronoi coverage means near 90% with maxima above 96%, thus supporting rapid spatial acquisition under variable hydro-ecological regimes. GAN anomaly scoring produced an ROC–AUC within 0.72–0.96; the upper stratum aligns with precise separation between true contamination events and sensor noise. Sheaf-theoretic fusion reported cohomology errors between $1.3\times {10}^{-5}$–$9.8\times {10}^{-5}$; small magnitudes coincide with strong cross-sensor consistency across overlapping domains. Hybrid physical–ML forecasting recorded an RMSE between 0.10–0.45; the lower segment corresponds to robust constraint-aware predictions under nonstationary forcing. Socio-hydrological allocation efficiencies appeared within 67–92%; values exceeding 85% signal the effective integration of behavioral responses with hydrological limits. Runtime profiles showed GP as comparatively expeditious; hybrid physical–ML incurred a higher latency due to physics-regularized optimization and recurrent inference. Coverage metrics positioned MADRL–Voronoi at the top tier; GP information-gain strategies formed a close second, whereas uninformed placement trailed, reflecting spatial nonuniformity penalties. Energy analysis favored Age-of-Information (AoI) power control with mean consumption near 5.5 Wh across surveillance epochs; Lloyd–Voronoi remained modest; consensus formations occupied a midrange; uninformed patrols consumed the most. Collectively, these patterns motivate a deployment triad: MADRL for spatial sweep efficiency, GP/IG for targeted refinement, sheaf fusion for coherence maintenance. Under resource constraints, AoI-guided transmission scheduling reduces expenditure while preserving coverage targets $\eta$ at reliability $\beta$. For anomaly screening pipelines, GAN scores coupled with multivariate LSTM reconstruction errors sustain timely alarms under heterogeneous baselines. For forecasting pipelines, physics-informed regularization stabilizes temporal extrapolation, mitigating drift. Governance layers benefit from socio-hydrological agents that encode incentives, pricing signals, and entitlement rules, thereby shaping allocation efficiency without undermining monitoring fidelity.

Table 5 details the outcomes of the simulations. Information gain (IG) values ranging from 0.23 to 0.89 for GP underscore sensor placement strategies. Higher IG elucidates enhanced spatial coverage and data informativeness, proving integral for precise water quality reconstructions in variable contamination scenarios. Low IG values, conversely, highlight sensor redundancy or suboptimal placement, pointing to the necessity of iterative repositioning to avoid data paucity in critical surveillance zones.

State estimation accuracy provided by DPF ranged from 78% to 95%. Accuracy exceeding 90% signifies excellent contamination event localization capability, which is pivotal for epidemiological management, particularly in outbreak prevention contexts. Lower accuracy thresholds suggest potential sensor failures or model miscalibration, indicating a requisite for recalibration and robustness-enhancing interventions.

MADRL results exhibited a broad range for exploration–exploitation parameters $(\alpha ,\gamma )$, emphasizing the dynamics between immediate surveillance actions versus long-term coverage strategies. High values ($\alpha >0.9$, $\gamma >0.95$) revealed robust convergence toward optimal coverage strategies, which are essential in scenarios demanding rapid responses to emerging threats. Lower parameter values reflect exploratory behaviors that are suitable for initial deployments, though less optimal for immediate public-health threat mitigation.

The GAN anomaly detection framework delivered ROC-AUC values between 0.72 and 0.96. High ROC-AUC scores underscore the system’s adeptness at distinguishing genuine contamination anomalies from sensor noise, which is critical in safeguarding public health through timely contamination alerts. Lower ROC-AUC scores represent reduced anomaly detection sensitivity, necessitating algorithmic refinement, especially in scenarios with heterogeneous environmental backgrounds or highly variable contamination signatures.

Sheaf-theoretic data fusion displayed cohomological errors ranging narrowly between $1.3\times {10}^{-5}$ and $9.8\times {10}^{-5}$. Minimal errors signify robust consistency across disparate sensor measurements, reinforcing reliability in synthesized global water-quality profiles. Conversely, higher error magnitudes imply localized discrepancies—potentially driven by calibration inaccuracies or environmental heterogeneities—mandating strategic re-calibration or methodological adjustments to ensure the consistency and trustworthiness of surveillance data.

Hybrid physical–machine learning models indicated RMSE forecasting errors from 0.10 to 0.45. Lower RMSE values, approaching 0.10, illustrate high predictive accuracy, supporting effective anticipatory public-health interventions. A higher RMSE reflects a compromised predictive capacity, potentially impacting the efficacy of timely preventative actions. Identifying root causes for elevated errors remains paramount, requiring iterative model enhancement and fine-tuning of physical constraints.

Resource allocation efficiency within socio-hydrological models exhibited a span from 67% to 92%. High efficiency levels above 85% reflect th optimal integration of socio-economic behaviors, environmental variability, and hydrological constraints, facilitating equitable and economically sustainable water resource governance. Conversely, efficiency below 70% highlights inadequate resource distribution, underscoring critical weaknesses in model assumptions or parameterizations requiring socio-economic recalibration to enhance equitable resource access.

The experimental simulations illuminate several epidemiological implications. Enhanced accuracy in state estimation and anomaly detection directly contributes to rapid outbreak identification, enabling targeted public health interventions, such as water treatment adjustments or targeted community alerts. Furthermore, superior forecasting accuracy from hybrid models translates into effective preventive resource deployments, which are vital for minimizing exposure risks and safeguarding community health proactively.

The Figure 2 compares GP, DPF, and MADRL on a triangular radar with axes of Accuracy, Random Patrol, and Energy Consumption (energy axis treated as inverted so outward indicates lower draw). MADRL expands nearest to the outer hull across all vertices, signaling top accuracy, superior performance relative to a random-patrol baseline, and efficient power use. GP occupies a mid-sized footprint—solid precision with moderate efficiency. DPF forms the smallest polygon, which is suitable when resources are tight. The nesting visualizes trade-offs succinctly, enabling rapid selection under distinct deployment constraints.

Critically, the analysis elucidates systemic vulnerabilities. Models exhibit sensitivity to parameterization and environmental variability, reflecting potential fragility under dynamic real-world conditions. Despite high accuracy metrics, operational scalability and real-world applicability demand further validation through extensive field deployments. Moreover, the requirement for continuous calibration and data quality assurance highlights practical impediments, such as logistical burdens and cost constraints, challenging widespread adoption in economically constrained regions. Taking everything into account, the experiments impart nuanced insights into multi-agentic water health surveillance, underscoring the potential and limitations that are inherent in contemporary methodologies. Real-world applicability necessitates rigorous validation, adaptive parameter tuning, and cross-platform integration to realize resilient, efficient, and economically viable surveillance systems, significantly enhancing public health preparedness against waterborne epidemiological threats.

4. Discussion

The aggregated performance metrics reveal heterogeneity across surveillance modalities. Although maximal information gain (IG) values achieved magnitudes approaching 0.89 attest to proficient active sampling in heterogenous contamination fields, minimal readings near 0.23 denote persistent sensor misallocation within regions exhibiting parametric uniformity. This dichotomy underscores the limitations of stationary covariance kernels predicated on isotropic assumptions. Consequently, the deployment of anisotropic kernel functions or nonstationary priors may mitigate observed misplacements. Furthermore, temporal autocorrelation within pollutant plumes undermines the efficacy of singular GP surrogates, advocating for hybridized spatio-temporal priors capable of dynamic covariance adaptation. Insights derived herein underscore the imperative of augmenting model flexibility to address environmental heteroscedasticity.

State estimation via DPF yielded accuracy ranges from 78% to 95%. While upper-tier performance reflects robust localization of contamination fronts, the lower extremities expose sensitivity to particle impoverishment and weight degeneracy. Instances of sub-optimal resampling frequencies precipitated sample impoverishment, resulting in biased posterior approximations. To rectify this, stratified resampling schemes or adaptive particle rejuvenation mechanisms may enhance posterior diversity. Furthermore, computational overhead associated with large particle ensembles presents logistic impediments under real-time constraints, suggesting a trade-off between ensemble magnitude and processing latency. Moreover, model mismatch between assumed transition kernels and empirical hydrodynamic dynamics compounds estimation error.

The MADRL algorithm demonstrated variable convergence characteristics contingent on exploration-exploitation hyperparameterization. Configurations with a learning rate $\alpha$ below 0.1 yielded protracted policy discovery, adversely impacting initial coverage metrics. Conversely, discount factors $\gamma$ surpassing 0.95 promoted excessive action greediness, culminating in local optima entrapment within recurrent contamination loci. A potential remedy involves scheduling exploration decay or incorporating entropy regularization to balance the recovery of novel trajectories. Implementation within field-scale networks further underscores the need for hierarchical policy abstractions to mitigate state-space dimensionality.

GANs for anomaly detection achieved ROC-AUC values spanning 0.72 to 0.96. Lower scores correlate with insufficient training samples representing rare contamination events, cascading into generator overfitting and discriminator saturation. The asymmetric loss weighting parameter $\lambda$ critically influences detection sensitivity; miscalibration can result in false negatives amidst high-variance noise profiles. Incorporating data augmentation protocols or curriculum learning may alleviate class imbalance. In pragmatic deployments, rapid adaptation to new anomaly signatures requires continual retraining schemes governed by drift detection metrics.

Cohomological error metrics within sheaf-theoretic fusion ranged from $1.3\times {10}^{-5}$ to $9.8\times {10}^{-5}$. Elevated error magnitudes are symptomatic of topological inconsistencies induced by sensor drift or inconsistent calibration across network partitions. Remedial strategies consist of dynamic gain adjustment protocols and localized mesh refinement to ensure the compatibility of restriction morphisms. Nevertheless, the iterative cohomology-nullification process introduces computational burdens that may impede near-real-time assimilation. Future enhancements could incorporate sparse sheaf constructions or approximate cohomology solvers to retain algebraic consistency with reduced complexity.

Hybrid physical–machine learning forecasting exhibited RMSE values between 0.10 and 0.45. Models achieving a lower RMSE leveraged physics-informed loss regularization, effectively constraining outputs to satisfy underlying hydrodynamic equations. Conversely, elevated RMSE figures emerged under conditions of transient flow regimes, where rapid parameter oscillations violate quasi-steady assumptions. This suggests that bi-directional LSTM architectures may require augmented memory cell gating or attention mechanisms to capture abrupt temporal shifts. Additionally, sensitivity to mesh discretization in the physical model component necessitates mesh adaptation techniques or multiscale coupling frameworks.

Socio-hydrological multi-agent models realized resource allocation efficiencies from 67% to 92%. Efficiency deficits often originated from simplified utility functions that failed to encapsulate non-linear farmer behaviors in response to fluctuating commodity prices. Moreover, water-rights assignments modeled via static quota formulations lacked adaptability to episodic drought stress, thereby skewing allocation fairness indices. Introducing adaptive utility constructs with endogenous risk aversion parameters could enhance decision realism. The integration of game-theoretic equilibrium solvers may further refine governance mechanisms to preclude strategic misrepresentation by participants.

Translating simulated performance into operational contexts reveals multifarious considerations. In municipal water distribution systems, for instance, active sampling must negotiate regulatory sampling intervals and infrastructure constraints, wherein sensor mobility demands coordination with maintenance schedules. Agricultural runoff monitoring presents distinct challenges, as spatial heterogeneity induced by soil types and precipitation patterns mandates dynamic agent redeployment. During disaster scenarios, such as flood-induced contaminant influx, the rapidity of multi-agent coordination becomes paramount for averting acute public-health crises. The interoperability protocols between mobile robots and stationary nodes underline the exigency of unified communication ontologies to ensure seamless data exchange across heterogeneous platforms.

Real-world deployments expose pragmatic impediments, including power limitations, regulatory compliance, and hardware reliability. Battery constraints that are inherent in USVs restrict mission durations, necessitating autonomous docking or energy-harvesting solutions. Regulatory frameworks governing drone operations vary regionally, imposing no-fly zones that fragment surveillance coverage. Hardware susceptibility to biofouling and sediment accumulation diminishes sensor accuracy over prolonged deployments. Redundant sensor pathways can mitigate single-point failures; however, they incur capital expenditures that may exceed municipal budgets. Thus, cost–benefit analyses must integrate total cost-of-ownership metrics alongside performance gains.

Maintenance cycles and calibration protocols significantly influence the long-term fidelity of multi-agentic systems. Sensor drift mandates periodic zeroing routines and inter-calibration procedures, which, if neglected, skew anomaly detection thresholds. Agent navigation accuracy likewise degrades in GNSS-denied environments, compelling the adoption of visual-inertial odometry or beacon-based localization. The operational cadence of calibration events imposes logistical burdens on field teams, highlighting the need for autonomous in situ calibration modules. Embedding self-calibrating transducers with built-in reference standards could reduce manual interventions and sustain measurement veracity in remote deployments.

Although algorithmic performance metrics provide quantitative validation, explainability remains an under-addressed dimension. The opacity of deep belief networks within MADRL modules and GAN discriminators challenges stakeholder trust in automated decisions. Techniques such as layerwise relevance propagation or attention visualization may elucidate decision pathways [27,28,29,30], yet their integration into resource-constrained agents demands careful optimization. Without transparent interpretative outputs, field operators may misjudge system alerts, precipitating either overreaction or complacency. Embedding interpretable surrogate models alongside black-box learners could balance performance with intelligibility.

Data governance and privacy concerns emerge when sensor networks interface with the detection of industrial effluents or private property intrusions. Federated learning mitigates raw data centralization, yet model inversion attacks remain feasible, risking the inference of sensitive location patterns. Implementing differential privacy guarantees may preserve confidentiality, but at the expense of reduced model fidelity [31,32]. Governing bodies must delineate permissible data usage policies and enforce cryptographic message authentication to prevent spoofing. Furthermore, cross-jurisdictional data sharing agreements require standardized legal frameworks to facilitate collaborative water quality management without infringing on sovereign data rights.

Collectively, the empirical findings delineate several guiding principles for future deployments. Model adaptability to nonstationary environments emerges as a principal requirement, urging the design of dynamic kernels and memory-enhanced architectures. Calibration autonomy represents another pivotal axis, advocating for self-referencing sensors and automated drift compensation. Resource allocation models should incorporate endogenous behavior parameters to reflect stakeholder incentives accurately. Explainability mechanisms are essential to bridge the gap between algorithmic outputs and operational decision-making. Finally, governance protocols must harmonize privacy safeguards with data sharing imperatives to support federated surveillance frameworks effectively [33,34,35,36,37].

Field deployment will progress through multi-site pilots across rivers, lakes, and treatment outfalls; each site will receive a fixed KPI set, acceptance tests, red-team drills, service runbooks, plus incident postmortems. A staged rollout schedule will codify replication rules, fault budgets, escalation paths, and technician competencies. Hardware upgrades will prioritize Energy-Harvesting Modules (EHM) using solar, microbial fuel cells, and tidal micro-turbines; autonomous docking cradles will enable hot-swap battery bays, sealed connectors, and salt-spray coatings. Corrosion-resistant fasteners, gasket kits, and moisture ingress monitors will accompany every field kit. Sensing reliability will employ Auto Self-Calibration (ASC) via on-board zero-check cartridges, microfluidic reference packs, and optical turbidity verifiers; anti-biofouling layers using zwitterionic coatings will reduce drift. A calibration ledger will record offsets, timestamps, operator IDs, and environmental covariates.

5. Conclusions

This study examined the operational efficacy and limitations of a multi-agentic water quality surveillance architecture integrating Gaussian process surrogates, distributed particle filters, deep reinforcement learning, GANs, sheaf-theoretic fusion, hybrid forecasting, and socio-hydrological models. Empirical results demonstrated that model performance is contingent on hyperparameter calibration, environmental heterogeneity, and system interoperability constraints. Recommendations include the adoption of nonstationary covariance kernels, stratified resampling techniques, entropy-regularized policy optimization, and automated calibration mechanisms. Emphasis on interpretability and privacy safeguards is also warranted to cultivate trust and facilitate data sharing. Future work should prioritize extensive field validation, energy-autonomous agent design, and legal frameworks for federated data governance. Collectively, these directions will enhance the resilience and adaptability of water health surveillance in real-world applications.