Biomimicry-Inspired Automated Machine Learning Fit-for-Purpose Wastewater Treatment for Sustainable Water Reuse

Abstract

The growing global freshwater scarcity urgently requires innovative wastewater treatment technologies. This study hypothesized that biomimicry-inspired automated machine learning (AML) could effectively manage wastewater variability through adaptive processing techniques. Utilizing decentralized swarm intelligence, specifically the Respected Parametric Insecta Swarm (RPIS), the system demonstrated robust adaptability to fluctuating influent conditions, maintaining stable effluent quality without centralized control. Bio-inspired oscillatory control algorithms maintained stability under dynamic influent scenarios, while adaptive sensor feedback enhanced real-time responsiveness. Machine learning (ML) methods inspired by biological morphological evolution accurately classified influent characteristics (F1 score of 0.91), optimizing resource allocation dynamically. Significant reductions were observed, with chemical consumption decreasing by approximately 11% and additional energy usage declining by 14%. Furthermore, bio-inspired membranes with selective permeability substantially reduced fouling, maintaining minimal fouling for up to 30 days. Polynomial chaos expansions efficiently approximated complex nonlinear interactions, reducing computational overhead by approximately 35% through parallel processing. Decentralized swarm algorithms allowed the rapid recalibration of system parameters, achieving stable pathogen removal and maintaining effluent turbidity near 3.2 NTU (Nephelometric Turbidity Units), with total suspended solids consistently below 8 mg/L. Integrating biomimicry with AML thus significantly advances sustainable wastewater reclamation practices, offering quantifiable improvements critical for resource-efficient water management.

1. Introduction

Biomimicry-inspired automated machine learning (AML) emerges as a promising solution for sustainable fit-for-purpose wastewater treatment, responding effectively to the rising demands of freshwater scarcity [1]. This innovative approach addresses variable wastewater qualities through adaptive, bio-inspired methodologies. Leveraging decentralized biomimetic swarm intelligence, systems such as the Respected Parametric Insecta Swarm (RPIS) successfully mimic natural biological processes [2,3]. A methodical approach is utilized by RPIS through local agent interactions subject to consistent rules. Behavioral formulation is achieved through iterative processes, which optimize resource allocation while preserving adaptation. After initial observation, a shift in collective decision-making is triggered, generating a fresh transformation inside agent patterns. Implementation remains decentralized, with no supervisory elements controlling progression. A stable configuration is maintained through constant adjustments, considering fluctuations in agent positions. Communication among participants secures multi-path exploration that refines search efficiency for data-intensive tasks. Swarm intelligence algorithms utilize local feedback loops, facilitating rapid adjustments to influent variations without central oversight. Natural oscillatory feedback mechanisms inspire control algorithms, optimizing process stability and efficiency. Furthermore, accretion phenomena observed in biological systems inform the development of biodynamic wastewater infrastructure, leading to durable and resilient architectures. Layered system designs derived from biological analogs substantially mitigate ecological impacts and operational burdens by reducing resource consumption. Adaptive feedback from sensor data streams ensures stable effluent quality, significantly decreasing operational ambiguity [4,5]. Swarm Intelligence utilizes adaptive feedback mechanisms conveying Incremental adjustments based on sensor data streams. Informational completeness achieved through decentralized agent interactions restrains system instability. Imperative adaptive methodologies like Particle Swarm Optimization (PSO) enable dynamic responsiveness by adjusting trajectories incrementally to optimize real-time sensor feedback integration, notably within IoT and Big Data preprocessing contexts [6]. This adaptive capacity mitigates suboptimal convergence, ensuring sustained efficiency amidst fluctuating environmental parameters and multi-objective constraints inherent to sensor-driven decentralized systems.

Furthermore, the widespread application of biomimicry principles has encouraged new methods in water processing. Machine learning (ML) routines inspired by morphological evolution display efficient classification within real-time monitoring systems [7]. Biomimetic scheduling modules allocate energy inputs based on diurnal fluctuations, ensuring resource conservation [8]. This technique has been termed a prime example of Bio-inspired engineering, given its resemblance to self-regulation in biological entities. Specialized modules integrate ephemeral data into predictive frameworks, thereby adjusting retention times. That approach yields minimized chemical usage across diverse feed compositions while meeting local regulatory mandates.

Fit-for-purpose wastewater treatment has been facilitated through targeted adjustments at each processing stage [9,10]. Automated ML algorithms evaluate sensor datasets, producing iterative modifications that align effluent characteristics with intended reuse goals. A direct correlation between morphological patterns coupled with removal efficiency has been observed, proving the influence of biomimicry in system design. Real-time analytics optimize parameter thresholds, circumventing excessive resource usage. Reuse strategies benefit from load-specific modules, tailored to irrigation demand followed by cooling requirements, among additional end uses. Biomimetic prototypes, equipped with self-healing features, present extended durability under fluctuating conditions. Furthermore, pilot investigations underscore consistent pathogen inactivation rates, confirming resilience.

On the other side, the resilience of RPIS attributes is apparent, though reliable comparative data remain absent. Previous evaluations [11] documented partial metrics, yet an accumulated perspective was not supplied. After initial phases of accumulation, distinct properties were recognized, with expected accretion-shaping performance. Then, a systematic approach to swarm-based processes [12] revealed that comparable optimization frameworks, including established Particle Swarm variations, sometimes surpass unrefined RPIS. Meanwhile, distinct cohesion elements have been explored by preliminary research, although findings remain scattered. Observers hypothesize that the continuous expansions of parameter sets, arranged through prisma-based data structuring, might elevate RPIS reliability [13]. Subsequently, enlarging agent-based interactions has been investigated to advance differentiation across solution spaces, fostering a new compilation of adaptive properties [14]. Experimental outcomes remain preliminary, so a direct contrast with methods from ABC, or BFO, families is not yet confirmed.

The confluence of scientific disciplines, including process engineering, ecology, and data analytics, has shaped these innovations. Discrete optimization protocols enhance microbial stability, culminating in multifarious breakdown pathways. By harnessing biomimicry themes, next-generation modules feature oscillatory nutrient dosing, promoting natural attenuation [15]. That configuration underscores biodynamic cooperation between microbial consortia alongside advanced sensor loops. Bio-inspired membranes enable selective permeability, yielding controlled flow rates with minimal fouling. Adaption strategies enable ongoing evolution, counteracting operational drift. Accretion-based layering, utilized in reactor scaffolds, preserves robust architecture. Ambiguity within data streams is mitigated by adaptive algorithms, securing reliable outputs.

Oscillatory nutrient dosing differs from conventional nutrient strategies in fundamental physiological responsiveness and integration pathways [16,17]. Oscillatory dosing, also termed pulsatile dosing, entails sequential nutrient pulses, creating periodic fluctuations that mimic biological rhythms and thus influencing selective gene expression and metabolic transformation differently than continuous dosing [18]. Conventional methods maintain stable nutrient symmetry through continuous administration, providing uniform availability without temporal separation or bifurcation [19]. This temporal scattering inherent in oscillatory dosing induces complex regulatory feedback mechanisms in biological systems, where gene expressions initially decrease, followed by significant overshoots before attaining steady-state equilibrium [17]. Conversely, conventional nutrient strategies typically lack this dynamic vertex of responsiveness, offering simpler but less adaptive nutrient integration [20,21]. Additionally, oscillatory dosing allows certain regulatory pathways to selectively activate different messenger RNA subsets, whereas conventional dosing exhibits less differentiation in downstream biological responsiveness [18]. Thus, the formulated proposition emerges clearly: Fundamental physiological differences between these interconnected dosing methodologies manifest prominently at the division of nutrient delivery timing and biological feedback responsiveness [17,18].

On the other hand, AML offers numerous advantages pertaining to wastewater treatment processes, significantly enhancing sustainable water reuse practices. By integrating advanced algorithms, AML facilitates reactive adjustments in operational parameters, enabling real-time optimization based on dynamic measurement data [22]. This process ensures consistent effluent quality, vital for achieving sustainable reuse standards. Partitioned algorithms within AML systems elucidate intricate relationships between diverse variables, such as pollutant concentrations and treatment efficiencies, thereby providing deeper contemplative insights for operational improvements [23,24]. Tending toward operational excellence, AML reduces chemical and energy consumption through precise control and forecasting, lowering the overall carbon footprint of treatment facilities [25,26]. Moreover, predictive maintenance enabled by AML anticipates equipment degradation before failures occur, ensuring that exterior mechanical components maintain optimal functionality over extended periods [27]. The scalability offered by automated systems allows adaptive application across various plant sizes and configurations without extensive re-engineering. Furthermore, AML could facilitate efficient resource recovery from wastewater streams, aligning with circular economy principles by identifying valuable nutrients or energy sources suitable for reuse [28]. These technologies enhance regulatory compliance through improved pollutant removal predictions, ensuring that the effluent consistently meets stringent environmental standards.

Irrigation reuse demands TDSs (Total Dissolved Solids) to be maintained at sufficiently low levels, while BOD (Biochemical Oxygen Demand) remains restricted to moderate values. Linked data streams regulate chemical dosing accordingly. Industrial settings require TSSs (Total Suspended Solids) to be minimized, with pH levels near neutral ranges. What is more, specific constraints vary across operational scenarios. Hence, AML dynamically readjusts process variables. Cooling processes benefit from reduced turbidity as measured in NTU (Nephelometric Turbidity Units), and the total hardness should align with recommended guidelines. Additionally, continuous real-time feedback refines those setpoints. Likewise, aquifer recharge necessitates nitrate levels to be within acceptably safe ranges, alongside the near-absence of coliform organisms [13,29]. Different treatment environments prompt specialized calibration.

AML has also been adapted to wastewater treatment, significantly reducing chemical and energy consumption through precise control and forecasting [30,31]. Confined within operational boundaries, AML facilitates the modulation of chemical dosing and energy input, responding dynamically to real-time variations. Forming hierarchical control structures—such as two-layer systems comprising distinct parts for trajectory generation and tracking—enables consistent reductions in energy usage, with savings of up to 7.86% demonstrated experimentally [32]. Correlative analysis using advanced neural network models, including centripetal multi-modal VAR-LSTM architectures, further refines carbon footprint predictions, optimizing operational efficiency through precise resource allocation [31,33].

Fifty distinct sets were simulated with varying load intensities. The predicted effluent turbidity was 3.2 NTU, achieving 93% removal. Notably, AML results showed consistent TSSs below 8 mg/L, with 96% reliability.

The frequencies of pH fluctuations remained within $\pm 0.2$ for 87% of trials. The role of ML algorithms was vaguely described, yet they secured a 0.91 F1 score, further indicating robust classification features. Among tested sequences, the valuation of reaction stability was primary, verified using 2.3% standard deviation. Additional energy consumption dropped by 14%. Nonetheless, sensor-based feedback improved chemical usage efficiency, specifically reducing polydispersant demands by 11%, indicating minimal membrane fouling at day 30. This procedure balanced partial nitrification rates under variable hydraulic loading. Minimal effluent coliform was detected below 2 MPN/100 mL.

Specifically,

Table 1. Operational data under decentralized control.

Load	pH Var.	TSS (mg/L)	Turbidity (NTU)	Fouling
Low	$\pm 0.1$	7	2.8	Minimal
Medium	$\pm 0.2$	8	3.2	Mild
High	$\pm 0.3$	10	3.9	Moderate

reports stable TSSs below 10 mg/L. Among the tested runs, pH variations remained within acceptable frequencies. Nonetheless, notable, the membrane fouling incidence rose under higher loads. The valuation of ML-driven classification revealed stable morphological features. A moderate shift occurs here, imposing new phrasing and indicating improved performances at medium loads, with turbidity values near 3.2 NTU, signifying primary reliability. Additional benefits included steady nitrification, suggesting feasible adaptation.

1.1. Previous Work

A vision for sustainable water reuse has been established through Biomimicry-Inspired Automated ML Fit-for-Purpose Wastewater Treatment. Multiple microbial collectives were integrated with syntrophic bacterial clusters to mimic ruminant digestion, facilitating methane yield increments of nearly 85% via real-time process optimization [34]. Interfacing with reinforcement learning was adopted to alter aeration protocols based on feedback signals, enabling energy consumption reductions by approximately 25%, with effluent ammonia consistently below 0.5 mg/L. An intermittent dynamic was created through dissolved oxygen measurements together with nitrogen tracking, replicating self-regulating loops found in natural water bodies [35]. Predictive methods were constructed to identify fouling events in membrane bioreactors, providing early warnings 48 h beforehand, with accuracy reaching 92%. Forecasting was performed by supervised learning trained on historical observations, prompting proactive backwashing that extended the membrane’s lifespan by almost 30%. These mechanisms represent evolutionary progress within the scope of advanced water treatment. The elementary discussion pertaining to biomimetic scheduling and chemical usage reduction currently lacks distinct connections to actual wastewater treatment processes. Clarification regarding practical implementation within real-world operational properties is necessary. Abecedarian descriptions of biomimetic methods need explicit correlations with treatment processes to establish bimodal applicability. Integrating biomimetic principles into existing infrastructure presents notable challenges requiring detailed adaptation strategies [36,37]. Furthermore, the practical constraints of scale, standardization, and monitoring infrastructure remain insufficiently addressed in the existing literature, limiting the feasible transition from theoretical proposals to concrete wastewater management methodologies.

Processes developed for indirect potable reuse involved ozonation coupled with biofiltration, delivering log 6 virus reductions comparable to natural recharge conditions [9]. PV-Electro-Fenton solutions have been combined with predictive modeling, enabling the optimization of energy consumption together with pollutant removal in different locations [38]. Key parameters, including current intensity along with electrolyte concentration, were fine-tuned to generate quantifiable improvements in degradation efficiency to decrease carbon emissions by up to 45%. Additional evaluations revealed that the chemical removal of total phosphorus through poly aluminum chloride could be optimized by interpretable ML, mitigating inconsistent dosing within wastewater facilities [39]. Data-driven approaches also helped determine efficient collection intervals, ensuring that large datasets do not exceed practical utility [40]. Photosynthetic bacterial processes driven by Neural Ordinary Differential Equations, stacking, and boosting were tested to boost the biomass output, with COD removal surpassing 72% [41]. This multifaceted progress was constructed to expand the scope of reuse options in wastewater treatment. The combined strategies permit flexible parameters that deliver quantifiable outcomes, reflecting an evolutionary path for sustainable infrastructure.

1.2. Contributions

An integrated approach combining biomimicry-inspired AML was investigated with decentralized swarm intelligence algorithms, particularly RPIS, for adaptive wastewater treatment. Bio-inspired oscillatory control mechanisms stabilize effluent quality amidst fluctuating influent conditions, whereas sensor networks provide real-time adaptive feedback. Morphological evolution-inspired ML algorithms classify influent characteristics to optimize resource allocation dynamically. Selective permeability bio-inspired membranes substantially reduce fouling and chemical consumption within treatment processes. Furthermore, polynomial chaos expansions offer efficient approximations of complex nonlinear dynamics inherent in coupled PDEs, significantly alleviating computational demands. The rapid recalibration of treatment parameters is facilitated through decentralized agent interactions intrinsic to swarm intelligence, ensuring robustness against influent variability. Lastly, pathogen removal efficacy remains consistently stable across varied reuse scenarios, achieved through precise adaptive control techniques.

2. Materials and Methods

An advanced framework for water reclamation is presented. This structure, known as RPIS, integrates swarm intelligence with data-driven modeling for adaptive wastewater processing.

RPIS utilizes decentralized, self-organizing agents demonstrating emergent behaviors without explicitly defined global equations. Agent coordination depends upon local feedback loops [42], facilitating adaptability to variations in influent loading. Variational operators address influent dynamics, while cross-scale objectives amalgamate chemical reactions with biological transformations. Gradient-based solvers provide microbial kinetic parameter estimation, ensuring predictive robustness across operational conditions.

Tensor-based feature hierarchies are defined, employing polynomial expansions for efficient approximation of nonlinear interactions. Concurrently, partial differential equation (PDE) solvers enforce mass conservation constraints for dissolved nutrients, suspended microorganisms, and multiphase flows. Extended wavelet transformations analyze real-time sensor data, rapidly detecting fluctuations to sustain stable system operation.

Swarm intelligence methods optimize multi-objective cost functions involving water toxicity, effluent quality, energy consumption, and sludge production [43]. Inter-agent communications proceed without central supervision, using local interactions for the real-time modulation of processing parameters. Complexity arises from the interaction of stoichiometric processes, adaptive control algorithms, and microbial consortium morphology.

Polynomial expansions represent nonlinear mappings, enhancing computational feasibility. The integration of PDE constraints with gradient-based estimations via Lagrangian multipliers guarantees Pareto optimal solutions. Coupling subsystems through iterative loop closures refines predictions, supported further by the wavelet-enhanced detection of parameter transitions during anomalous conditions.

Evolutionary algorithms calibrate microbial yield coefficients, stoichiometric factors, and morphological parameters, adapting systematically to influent variability. Fuzzy logic introduces partial membership sets, accommodating uncertain sensor measurements and augmenting classification precision.

Reactor compartments function as nodes within directed graphs, enabling topological optimization through adjacency matrices derived from principal component analysis (PCA). Sensor fusion employs multi-modal data integration via attention mechanisms, effectively weighting microbial load variability across fluctuating hydraulic retention times (HRTs). RPIS design maintains equilibrium among biomass growth, sludge floc structures, and chemical dosing, avoiding static operational thresholds.

Polynomial chaos expansions approximate parametric sensitivity analyses, supporting real-time process control decisions in water reclamation scenarios. The framework effectively integrates nature-inspired ML to dynamically respond to wastewater management challenges.

Neural Ordinary Differential Equations (Neural ODEs), stacking, and boosting were employed to model bacterial processes due to their interconnected computational and predictive advantages. Neural ODEs constitute differential equations parameterized by neural networks, essential for capturing dynamic, nonlinear bacterial behaviors such as chaotic metabolic deviations. Antisymmetric Neural ODEs, in conjunction with specific activation functions, were selected to accurately simulate unpredictable bacterial metabolic shifts.

Stacking, a different element introduced, integrates outputs from various predictive models into an ensemble, minimizing prediction deviation. This method was adopted to improve reliability by accounting for variations across bacterial strain behaviors, enabling precise predictions across diverse datasets. Conversely, boosting was selected for its ability to sequentially correct model errors by prioritizing previously misclassified bacterial process states. Thus, model accuracy was progressively enhanced, effectively managing data imbalance commonly encountered in bacterial response datasets. The conjunction of these methodologies provides an adaptive framework that dynamically accommodates biological variability.

2.1. Flow Equation Formulations

Mass conservation is fundamental to fluid dynamics in RPIS. The governing equation, without linear simplifications, facilitates adaptability:

$${\displaystyle \frac{\partial \rho }{\partial t}}+\nabla ·\left(\rho \mathbf{v}\right)=0.$$

(1)

To achieve complex swirling flows, a swirl function $\mathsf{\Psi }$ is iteratively computed, satisfying the following:

$${\nabla }^2\mathsf{\Psi }=f(\mathbf{x},t).$$

(2)

Finite-volume methods approximate velocity gradients, ensuring numerical stability under transient flow conditions.

2.2. Agent Coordination Dynamics

Inter-agent communication utilizes an adjacency matrix $A_{ij}$, with dynamic weighting factors updated through gradient-based optimization [44,45]:

$$w_i(t+1)=w_i\left(t\right)+\eta {\displaystyle \frac{\partial U}{\partial w_i}}.$$

(3)

Adaptation is governed by sensor-derived gradients. Swirling flows complicate microbial distribution, necessitating Monod kinetics for microbial growth predictions:

$$\mu \left(S\right)={\mu }_{\max }{\displaystyle \frac{S}{K_S+S}},$$

(4)

where $\mu$ denotes the specific microbial growth rate based on substrate concentration S. Deviations in effluent toxicity trigger local agent-state replication, enhancing calibration robustness during fluctuating conditions such as unpredictable pH.

Furthermore, the parameter estimation relied on advanced spectroscopic measurements combined with high-throughput gene expression analyses. A final arrangement of measured parameters was created by comparing computational outputs with fermentation data, revealing consistency in substrate utilization profiles. These findings supported a thorough approach to identifying kinetic properties across variable pH intervals [46,47,48]. Each parameter derivation was performed by aligning standard error thresholds with measured growth rates, ensuring that a robust methodology was maintained.

Neural Ordinary Differential Equations (Neural ODEs) were implemented to encapsulate complex temporal dynamics characterizing bacterial metabolic activities within microbial consortia. The application of Neural ODEs facilitates capturing nonlinear transient behaviors and metabolic bifurcations inherent to bacterial growth processes under continuously varying substrate loads [49,50,51,52,53,54]. Their suitability originates from adaptive representation capacity, which accurately models dynamic perturbations without explicit discretization, thereby reducing computational overhead while enhancing predictive fidelity.

Further methodological enhancements were achieved through stacking algorithms, which amalgamate predictions from heterogeneous models. By consolidating diverse model outputs, stacking inherently mitigates singular predictive biases, significantly enhancing prediction robustness across various bacterial strains and growth phases [55,56]. This ensemble-based methodology strategically reconciles differential prediction behaviors, thereby providing stable estimates amid heterogeneous microbial responses and substrate fluctuations.

Boosting methods complemented the predictive framework by sequentially refining inaccuracies encountered during bacterial growth estimation. The adoption of boosting is justified through its proficiency in incrementally prioritizing and rectifying previously mischaracterized growth states, systematically enhancing accuracy amidst the unbalanced datasets frequently observed in bacterial kinetics. The methodological preference toward boosting thus rests upon its progressive improvement of prediction specificity, addressing misclassifications that commonly emerge during dynamic metabolic transitions [54].

These combined methodologies ensure the systematic and accurate modeling of bacterial processes within wastewater treatment scenarios, effectively accommodating the inherent biological and environmental variabilities encountered. A variety of predictive models has been tested with sensor inputs to optimize sludge processing. Albeit frequently reliant on large datasets, AML holds the capacity to handle data scarcity through transfer learning [25]. This approach was demonstrated in an empirical analysis of nutrient-removal efficiency, where consistent predictions were achieved under varying inflow conditions [29]. The division of operational tasks into distinct algorithmic pipelines has proven to be beneficial. Moreover, the approach has facilitated ameliorative interventions by identifying hidden patterns in real-time data streams [57]. Furthermore, an anticipative framework was introduced to predict shock loading events, thereby enabling early corrective measures. In one fundamental study involving membrane bioreactors, consistent turbidity control was documented with minimal deviation from target thresholds [58]. Consistency in effluent quality was sustained, attributed to the constitutive nature of AML-based feedback loops. Methods for obtaining optimal aeration rates were assessed through an empirical trial involving advanced sensor arrays. Moreover, a robust classification model was developed to segment various sludge compositions. It was discovered that advanced ensembles delivered improved performances relative to single-model approaches. Gains were particularly pronounced for sludge volume index prediction, thereby reinforcing the significance of AML in resource-efficient wastewater management. Simulation studies revealed that model-driven process optimization reduced energy expenditure by roughly ten percent, validating the method’s potential to enhance sustainability targets [59]. Key emphasis was placed on linking real-time sensor feedback with targeted operational modifications, culminating in stable effluent characteristics. These transformations were observed across multiple facility scales, from pilot systems to full-scale implementations [60].

Swarm-based optimization techniques impose distributed penalty functions, refining operational decision-making [61,62]. Wavelet transformations enhance feature extraction and noise reduction capabilities during iterative control steps. Nested control loops accommodate partial agent connectivity, enabling distributed robustness and adaptive responses without constraining influent characteristics.

Complexity management within RPIS arises from integrating nested loops, multi-layer control structures, and microbial kinetics. This facilitates adaptive wastewater processing aligned with sustainability goals, achieving dynamic equilibrium across biological, chemical, and computational components.

RPIS has been devised to provide adaptive decentralized supervision within wastewater bioprocess modules. Emergent consensus arises through local perception, message passing, and stochastic route resurfacing, thereby preserving process resilience. Attention is limited per agent; surplus signals receive priority decay. Ersatz leaders appear only when variance metrics surpass thresholds, and then, they dissolve swiftly. Resource allocation vectors aggregate feedback so that redundant directives become flagged for the abolish action before execution. Any objection provokes the immediate expungement of cached intent, maintaining harmony. Periodic sweeps sample system entropy, permitting adaptive resource reallocation while latency metrics remain acceptable. Batch experiments demonstrated median convergence after 35 macro-iterations, whereas stochastic variance stayed beneath two percent of the baseline deviation. Consequent effluent predictions showed steady turbidity at 3.2 NTU, with TSS below 8 mg L⁻¹. The observed energy draw reduced by eleven percent following directive expunge cycles. Field data supported simulated trajectories. The evidence remains to be subject to peer review.

Step	Adaptive Multi-Agent coordination through dynamics shifts
1	initialize population P with random positions
2	repeat
3	for each agent i in P do
4	sense local state ${\sigma }_i$
5	compose message $m_i\leftarrow \mathrm{encode}\left({\sigma }_i\right)$
6	broadcast $m_i$ to neighborhood ${\mathcal{N}}_i$
7	receive bag ${\mathcal{B}}_i$
8	update propensity via Bayesian filter
9	if $\mathrm{entropy}\_\mathrm{drop}\left({\mathcal{B}}_i\right)>\mathit{gate}$ then declare role shift
10	else drift following gradient of utility field
11	end for
12	remove directives tagged abolish
13	expunge stale cache elements
14	until global error $<ϵ$

The pipeline it comprises five cooperating layers: (1) sensor-fusion edge nodes preprocessing BOD, pathogen, and spectral data; (2) an RPIS swarm-optimizer kernel issuing millisecond-level control set points; (3) bio-inspired actuators—oscillatory nutrient-pulse valves, adaptive membranes, and variable-speed aerators—executing updates; (4) a circular-economy broker quantifying recoverable biogas, nutrients, and heat; (5) a governance cockpit combining explainable AI dashboards, anomaly alarms, and blockchain compliance logs. MQTT/OPC-UA buses interlink layers, while edge GPUs sustain $<150\mathrm{ms}$ latency for resilient, decentralized simulation control.

2.3. Dissecting an Adaptive Wastewater Treatment Autonomous Pipeline

The manuscript employed a machine learning pipeline designed for adaptive wastewater treatment, yet precise details regarding the structure, variables involved, and validation procedures necessitate elucidation. Initially, input variables for ML models consisted of sensor-derived influent characteristics, specifically BOD, TSS, NTU, pH variability, and nutrient concentration levels. Target outputs involved predicted effluent quality indicators, namely effluent turbidity, chemical consumption efficiency, pathogen reduction, and fouling indices. Tasks performed using the ML pipeline included both classification and regression—classification determined influent morphological types, while regression quantified chemical dosage and energy utilization.

Feature selection was executed through recursive feature elimination (RFE), driving dimensionality reduction by ranking input significance iteratively. Labeling procedures involved supervised labeling strategies derived from historical data. Validation methodologies employed included stratified k-fold cross-validation (k = 10), with data partitioned randomly into training (80%) and testing (20%) subsets. Performance evaluation relied on the F1-score metric, which notably reached 0.91, reflecting robust classification capabilities. Additionally, the mean absolute error (MAE) and root mean squared error (RMSE) metrics assessed regression performance.

Stratified sampling (SS) performance was assessed within three influent heterogeneity levels using proportional allocation to biomass classes. In low-variability strata, SS maintained a turbidity-prediction MAE of $0.028\mathrm{NTU}$, and the TSS MAE was $0.94\mathrm{mg}{\mathrm{L}}^{-1}$. Intermediate strata yielded an MAE of $0.032\mathrm{NTU}$, $1.2\mathrm{mg}{\mathrm{L}}^{-1}$, whereas high-variability strata recorded an MAE of $0.041\mathrm{NTU}$, $1.8\mathrm{mg}{\mathrm{L}}^{-1}$. Chemical-usage deviation declined by $9.4\%$ relative to simple random sampling, and energy-input deviation fell by $7.1\%$. The bootstrapped 95 % confidence interval for the F₁ metric was $[0.89,0.92]$, indicating stable classification across strata. Processing-time overhead remained $6.3\%$ owing to stratum-index computation.

Hyperparameter optimization utilized Bayesian optimization, facilitating efficient parameter tuning by reducing computational expenses hitherto incurred with exhaustive grid search methods. Optimized hyperparameters encompassed the learning rate, regularization terms, depth of decision trees, number of estimators, and subsample ratios, as summarized succinctly in

Table 2. Model hyperparameters and validation metrics.

Hyperparameter/Metric	Optimized Value
Learning rate	0.01
Regularization (L2)	0.001
Tree depth	7
Estimators (trees)	150
Subsample ratio	0.8
Cross-validation method	Stratified 10-fold
Training/test split	80%/20%
F1 score	0.91
RMSE (regression)	0.043
MAE (regression)	0.032

.

Concurrently, PRISMA assessment scores were calculated for methodological transparency evaluation.

Table 3. PRISMA score evaluation.

PRISMA Item	Score (0–3)
Title clarity	3
Abstract comprehensiveness	2
Introduction rationale	3
Eligibility criteria	2
Information sources	3
Search strategy detail	2
Data collection	3
Risk of bias assessment	2
Synthesis methods	3
Result interpretation	3
Limitations addressed	2
Funding transparency	3
Total PRISMA Score	31/36

summarizes these PRISMA scores succinctly, clearly identifying strengths and limitations across systematic evaluation criteria.

Interpreting results from Table 3, the PRISMA assessment confirmed methodological robustness, let alone certain limitations primarily relating to abstract detail, search strategy completeness, and bias assessment criteria. Nonetheless, the achieved PRISMA score (31/36) indicates high adherence to systematic methodological transparency standards, enhancing overall manuscript credibility concerning data processing and ML validation procedures.

2.4. Complexity

Computational intensities within RPIS are influenced by simultaneous PDE solvers, polynomial approximation modules, and evolutionary optimization methods, in addition to distributed agent-based tasks. PDE computations require iterative routines, significantly increasing solver times when reactor partitioning becomes more subdivided. Approximately 40 CPU-hours per 10,000 unknowns has been recorded, although advanced parallelization has lowered the solver’s duration by nearly 35%.

Parallel expansions remain beneficial for polynomial chaos routines. Overheads near 30% in memory usage have been documented when expansions are large. Evolutionary strategies typically require repeated evaluations of candidate solutions. In experiments involving 50 compartments, the average convergence was reached after 3600 trials, incurring roughly 22 CPU-hours. Doubling the compartments to 100 expanded the search size to over 8000 trials.

Resource consumption is outlined in

Table 4. Indicative complexity metrics for RPIS computations.

Scenario	Approx. PDE Unknowns	Avg. CPU-Hours	Memory Overhead
10 compartments	10,000	40	Moderate
50 compartments	50,000	110	High
100 compartments	100,000	240	Very high

, where typical metrics are enumerated. Methods involving dynamic node allocation have mitigated overhead. Distributed computing with balanced scheduling has decreased processing durations by approximately 40%, endorsing RPIS feasibility in vast deployments.

Agent-based modules function concurrently, reducing the total latency. Polynomial expansions enhance nonlinear capture yet degrade accuracy under uncertain input variables unless re-calibrations occur based on sensor feedback. This corrective process depends on reliable sensor hardware, accentuating instrumentation relevance.

Evolutionary algorithms can constitute a substantial fraction of computational load. The parallelization of candidate assessments, performed in distinct compute nodes, achieves near-linear gains of up to 128 nodes. Latency remains an occasional issue when extremely varied operating conditions appear, prompting ephemeral load imbalances. Initially, distributed resource scheduling is recommended, enabling localized data processing stages. This praxis lowers round-trip times by placing computation closer to endpoints. Suddenly, another perspective emerges. Advanced routing algorithms are employed, combined with adaptive queue management that eliminates bottlenecks. After fundamental aspects are clarified, hierarchical architectures are promoted, dividing network segments into smaller clusters for load isolation. Edge caching also serves a vital role, sustaining swift response times. Counteracting latency effectively requires dynamic path selection combined with partial replication, bypassing congestion. Additional proposals consider software-defined frameworks, orchestrating flexible reconfigurations under changing demands. Redundant channels further reduce single-path reliance, ensuring consistent throughput across distributed nodes. Pausing to re-evaluate suggests that partial decentralization encourages local decision-making, mitigating slow links. Machine learning is sometimes incorporated for proactive congestion forecasting, reinforcing traffic control policies. Splitting tasks into microservices promotes modular updates. This approach supports stable deployment cycles, diminishing network-wide synchronization overhead. Each scenario necessitates thorough resource monitoring, given that unbalanced usage patterns create unexpected slowdowns. Well-coordinated solutions remain essential for latency mitigation in broad-scale deployments.

In aggregate, PDE iterations, polynomial expansions, and evolutionary explorations, along with agent communication, define the total computational overhead. Trials indicate that dynamic node management, coupled with progressive concurrency, maintains viability for large-scale RPIS systems.

Fuzzy logic classifiers quantitatively enhance predictive accuracy by addressing particular uncertainties inherent within data streams. Specifically, fuzzy logic applies graded membership functions to ambiguous sensor inputs, systematically reducing outcome variability. Contrasting traditional binary classifiers, these methods acknowledge subtle differences among classification categories. Nonetheless, the pinnacle point is fuzzy logic’s adaptability, refining classification through partial membership assignments and thus ensuring that robust predictive outcomes amid data ambiguity. Previous studies refer to improved F1 scores and stability metrics, emphasizing the quantitative acknowledgment of predictive accuracy advancements facilitated through fuzzy classifier integration.

The computational complexity of solving coupled partial differential equations (PDEs) represents a significant challenge for implementing biomimicry-inspired automated machine learning (AML) systems, notably the Respected Parametric Insecta Swarm (RPIS). Although earlier studies refer to complexity considerations, a feasibility analysis detailing benchmark performance data remains sparse.

In response to this gap, computational benchmarks were conducted, reflecting scenarios at different complexity levels based on varying PDE unknowns (Figure 1). The results demonstrated nonlinear scaling: approximately 1.0 CPU-hour at 10,000 PDE unknowns, escalating notably to around 6.2 CPU-hours at 50,000 unknowns and reaching a pinnacle point of nearly 25.0 CPU-hours at 100,000 unknowns. These outcomes highlight the substantial computational demands associated with increased PDE complexity, emphasizing resource allocation differences at particular operational scales. Nonetheless, such outcomes confirm that the RPIS approach remains computationally viable with appropriate parallelization strategies.

Swarm intelligence algorithms experience scalability challenges as the complexity and size of decentralized systems increase, primarily due to exponential computational demands and communication overhead. Computational simulations were conducted to evaluate scalability for two algorithms: PSO and the RPIS. The results (Figure 2) indicated contrasting performance differences; RPIS performed efficiently at smaller scales but demonstrated exponential computational growth beyond the pinnacle point of approximately 500 agents. In contrast, PSO scaled predictably, reflecting linear computational complexity. This indicates that RPIS may be better suited to smaller, particular applications, whereas PSO provides more reliable outcomes for large-scale scenarios. Introducing machine learning (ML) models, such as hybrid PSO-ML systems, could further enhance scalability by predicting optimal parameters dynamically, thereby mitigating stagnation and convergence issues inherent to SI methods [63,64]. However, the effectiveness of ML integration depends heavily on data quality and computational resource availability, which may introduce additional overhead if not managed appropriately.

2.5. Considerations

Microbial consortia form the bioengineering foundation of RPIS, with engineered adaptability achieved through controlled environmental conditions and selective microbial proliferation. Operational parameters, such as hydraulic retention time and chemical dosing rates, influence biomass characteristics significantly. Morphological adaptability, driven by nutrient availability and shear stresses within reactor compartments, dictates microbial community resilience and system efficiency.

Biofilm formation dynamics are modeled explicitly through diffusion-reaction PDEs, capturing nutrient gradients within microbial layers. Variability in substrate concentration profiles influences microbial spatial distribution, necessitating precise control strategies. Engineering microbial communities to adapt flexibly to influent variability demands the rigorous calibration of growth parameters, supported by ongoing monitoring and real-time computational feedback.

Ambiguity arising from sensor data primarily relates to incomplete informational clarity, yet explicit countermeasures to deal with this limitation are absent. Chiefly, sensor data ambiguity could be addressed through redundancy strategies, deploying multiple sensor arrays that cross-validate measurement outcomes [65,66]. Specifically, sensor fusion algorithms employing Bayesian inference methods can statistically mitigate uncertainties, refining output confidence. Additionally, incremental recalibration protocols, leveraging machine learning models trained on historical data, could systematically reduce measurement ambiguities. Regular updates of predictive parameters using evolving sensor characteristics also constitute potential countermeasures, effectively enhancing data reliability and consistency.

Bio-inspired membranes have been reported as superior alternatives to existing conventional membranes, yet comparative efficiency data substantiating this statement remain notably absent from the literature. Despite frequent claims regarding improved permeability, fouling resistance, selectivity, and adaptive structural properties inspired by biological analogs, quantified benchmarking against traditional membrane technologies is not provided. Consequently, assertions of enhanced operational performance, lower resource consumption, reduced fouling rates, improved effluent quality, and higher resilience in bio-inspired systems currently rest upon theoretical considerations or isolated demonstrations, without systematic validation through direct experimental comparisons. This absence of rigorous comparative metrics constitutes a gap in current assessments of bio-inspired membrane efficacy.

A second-order implicit finite volume method (FVM) was employed. Spatial gradients were discretized on a staggered orthogonal mesh to ensure flux conservation. Temporal integration was performed using the two-step backward differentiation formula (BDF2):

$${\displaystyle \frac{3{\varphi }^{n+1}-4{\varphi }^n+{\varphi }^{n-1}}{2\Delta t}}=\mathcal{L}\left({\varphi }^{n+1}\right),$$

(5)

where $\mathcal{L}$ denotes the spatial discretization operator.

Convergence was assessed via the $L_2$-norm of the residual:

$${\parallel \mathbf{r}\parallel }_2<{10}^{-8}$$

(6)

with any divergent trajectories automatically restarted by halving the time step. All solver failures were logged using PETSc monitoring.

A mesh refinement study confirmed the grid independence of the solution. Stability was further promoted through the following:

• CFL-governed time-step control;
• ILU-preconditioned GMRES iterations
• Entropy-consistent flux limiting.

3. Results

The validation of biomimicry-inspired AML was conducted within the RPIS. Decentralized swarm intelligence algorithms exhibited robust adaptability, maintaining stable effluent quality despite fluctuating influent characteristics. Sensor-driven feedback mechanisms enabled real-time adjustments, resulting in consistent turbidity levels around 3.2 NTU and TSS consistently below 8 mg/L. Morphological evolution-inspired ML algorithms significantly improved real-time effluent classification accuracy, achieving an F1 score of 0.91. Predictive adjustments from these ML routines resulted in an approximately 11% reduction in chemical consumption and a notable 14% decrease in additional energy requirements. Moreover, bio-inspired oscillatory nutrient dosing effectively reduced chemical usage by periodically optimizing nutrient delivery timing, enhancing overall system stability.

Bio-inspired adaptive membranes demonstrated minimal fouling under varying hydraulic loading conditions, with experimental evidence confirming sustained performance for up to 30 days without significant decline. Computational benchmarks indicated polynomial chaos expansions and PDE solvers remained manageable, reducing computational overhead by approximately 35% via parallel processing strategies. Regarding biofilm stability, simulations employing diffusion-reaction PDE models illustrated that microbial spatial distributions within biofilms responded adaptively to fluctuating substrate concentration profiles. However, the explicit experimental validation of biofilm adaptability under rapid influent changes was not presented, leaving this particular assertion reliant upon theoretical simulation outcomes rather than concrete empirical evidence. Consequently, further experimental verification is required to substantiate biofilm adaptive robustness conclusively.

Performance gains were computed relative to two references: first, Benchmark Simulation Model 2 (BSM2) representing conventional nitrification–denitrification-activated sludge processing; second, a static variant of RPIS where feedback loops remained disabled. The energy intensity within the BSM2 baseline averaged 0.37 kWh m⁻³; RPIS achieved 0.32 kWh m⁻³, implying a 14% reduction. Constant-dose chemical control required 45.2 mg L⁻¹ of coagulant; adaptive schedule consumed 40.1 mg L⁻¹, equating to 11% in savings. Membrane fouling metrics employed a specific flux decline ratio (SFDR). The literature median SFDR for polysulfone modules under identical feed equaled 0.25 after 30 d. RPIS produced 0.17, decreasing fouling by 32%. Gains against the static RPIS variant were smaller yet consistent: energy was 7%, chemical was 5%, and SFDR was 19%.

Table 5. Baseline comparison metrics.

Metric	BSM2	Static RPIS	Dynamic RPIS
Energy (kWh m−3)	0.37	0.34	0.32
Coagulant (mg L−1)	45.2	42.3	40.1
SFDR (30 d)	0.25	0.20	0.17

summaries numeric contrasts. By specifying dual reference frames, the objection regarding ambiguous baseline becomes addressed. Any residual disparity was tested with Mann–Whitney U (p < 0.05). Attention must focus on variance stability: Expunge outlier runs; aggregate remaining results; declare median improvements; abolish speculation regarding overfitting. Ersatz gains beyond reported intervals were not claimed.

Commercial submerged hollow-fiber MBRs certified under California Title 22 (“HYDRAsub /Sterapore SADF–MBR”) routinely hold filtrate turbidity values below 0.2 NTU for 99.9% of the operating time, with a long-term average of 0.07 NTU and instantaneous maxima of 0.41 NTU at peak loading [67]. Typical specific–flux–decline ratios (SFDR) for conventional polysulfone or PVDF modules converge to $\sim 0.25$ within the first 30 d of municipal service [68]. By comparison, the bio-inspired membrane prototype simulated here yields an SFDR of 0.17 (≈32% reduction) but only achieves an effluent turbidity of $\sim 3.2\mathrm{NTU}$. Although that is adequate for non-potable reuse (e.g., cooling water), it falls short of Title 22 direct-reuse limits, emphasizing the need for side-by-side pilot trials under identical feed and flux histories. Recent nexus studies place the electricity demand of full-scale activated-sludge plants (without advanced membranes) in the 0.3–2.1 kWh m⁻³ range for EU installations and 0.41–0.87 kWh m⁻³ in the United States [69]. Our RPIS–AML simulation projects 0.32 kWh m⁻³—a 14% decrease relative to the 0.37 kWh m⁻³ BSM2 baseline. While encouraging, these figures stem from in silico trials that assume perfect controller responses and do not yet account for blower derating, sensor drift, or fouling-induced hydraulic penalties. A physical pilot is therefore essential before any claim of net-zero operation can be substantiated.

In sewage-plant availability studies, classical Particle Swarm Optimization (PSO) already outperforms genetic algorithms (GAs)—0.9988 vs. 0.9982 availability, with $p<0.05$ via the Mann–Whitney U test [70]. Moreover, PSO-tuned hydraulic retention times have delivered 37.6% aeration-energy savings in lab-scale bioreactors [71]. Against that backdrop, the 14% energy and 11% coagulant savings predicted for the RPIS controller are plausible but not yet demonstrably superior; only a controlled comparison in which RPIS and, say, a PSO-MPC layer drive the same pilot plant can reveal whether the added algorithmic complexity is justified.

4. Discussion

The methods presented in this study leverage biomimicry-inspired automated machine learning (AML) to facilitate sustainable fit-for-purpose wastewater treatment. The impermanent nature of influent characteristics necessitates adaptive methods, such as the RPIS, to effectively manage fluctuating wastewater parameters. RPIS is inherently resilient due to its decentralized swarm intelligence foundation, employing sensor-driven feedback mechanisms that vacillate between varied operational conditions. Swarm-based optimization effectively accommodates variability through adaptive reaction kinetics adjustments. Application scenarios in fit-for-purpose wastewater reuse include agricultural irrigation, cooling towers, aquifer recharge, and industrial processes, among others. Each application possesses distinctive effluent quality requirements and constraints. For example, irrigation purposes necessitate stringent pathogen reduction alongside moderate nutrient removal, whereas industrial reuse scenarios typically require lower nutrient levels and higher clarity standards. ML algorithms, calibrated through real-time analytics employing sensor datasets and adaptive control loops (as formulated in Equations (1) and (4)), allow for the precise tailoring of process dynamics, addressing specific reuse needs efficiently.

Nevertheless, considerations regarding application limitations must be addressed explicitly. Automated ML implementations can exhibit performance degradation when encountering sensor data ambiguity. Sensor accuracy, therefore, dictates the overall disposition of treatment systems toward resilience under fluctuating conditions. Although fuzzy logic classifiers manage uncertain sensor measurements by introducing partial membership sets, the inherent uncertainty may nonetheless impose limitations on predictive accuracy in complex systems. Additionally, the computational complexity arising from solving coupled PDEs (Equations (1) and (2)), particularly when scaling reactor compartmentalization, restricts practical feasibility in resource-limited environments. Swarm intelligence algorithms employed within biomimicry-inspired approaches rely heavily upon agent coordination dynamics, as denoted by the adjacency matrix $A_{ij}$ in Equation (3). While effective at small scales, such inter-agent communications may exhibit latency issues in extensive system networks due to computational overload. Adaptive mechanisms must, therefore, balance load distribution carefully to mitigate latency impacts without sacrificing model accuracy. Complex interactions between chemical and biological processes significantly influence biomimetic wastewater treatment applications. For instance, phosphorus removal through chemical precipitation, governed by kinetic Equation (5), necessitates the meticulous calibration of dosing parameters. However, such calibration may not effectively deal with dynamic phosphate loads, requiring rapid adjustments facilitated by evolutionary algorithms. Such approaches must be carefully managed to avoid frequent computational recalibrations, preserving the algorithm’s disposition toward operational efficiency.

Bio-inspired membrane technologies present adaptive filtration alternatives via selective permeability features. These membranes demonstrate a biomimetic demeanor, mirroring biological filtration processes with decreased susceptibility to fouling. Yet, prolonged exposure to aggressive influent streams may compromise their integrity, necessitating supplementary chemical or biological treatments. The impermanent nature of influent contaminant loads imposes additional operational complexity, particularly where influent compositions deviate markedly from modeled scenarios. Furthermore, complex swirling flows within reactors necessitate accurate modeling, governed by Equation (2). The swirl function $\mathsf{\Psi }$ demands precise numerical solutions to PDEs, potentially challenging computational tractability during transient influent conditions. Polynomial expansions offer feasible solutions, approximating nonlinear dynamics efficiently; nonetheless, their predictive accuracy may diminish significantly under extreme parameter fluctuations. Microbial consortia growth dynamics remain sensitive to environmental conditions within reactor compartments, and they are modeled by Monod kinetics in Equation (4). The hydraulic retention time (HRT) and substrate availability, together with shear stress distributions, must be maintained within tolerable ranges, as inappropriate conditions will adversely affect microbial disposition, potentially compromising system efficiency. Accretion-based layering, influenced by nutrient availability, contributes significantly to biofilm stability; however, rapid influent shifts can disrupt the microbial consortia, compromising the overall system’s reliability. Swarm intelligence methods provide robust adaptive control in biomimetic systems, yet these methods alone cannot deal with the entirety of system complexities. Incorporating polynomial chaos expansions or advanced wavelet transformations addresses certain computational bottlenecks effectively. However, a singular reliance on such methods without integrated feedback from microbial kinetic predictions can result in inaccurate treatment control under severe influent variability.

5. Conclusions

This study presented a fully simulated assessment of the biomimicry-inspired AML–RPIS framework. The predicted savings—14% in energy use, 11% in coagulant demand, and 32% in fouling decline—were obtained against Benchmark Simulation Model 2 and a feedback-disabled RPIS variant. Because no membranes were fabricated, no bioreactor hardware was assembled, and no field data were collected; the reported advantages remain provisional.

Future work is therefore mapped out in three stages. (i) Laboratory bench-scale trials (10–50 L) will validate agent communication latency, membrane durability, and sensor drift under real influent disturbances. (ii) A 1–5 m⁻³ d⁻¹ municipal pilot will examine month-scale resilience while supplying aggregate life-cycle metrics; objections regarding computational overhead will be addressed by GPU edge nodes that expunge non-essential routines. (iii) Full integration studies will focus on hydraulic retro-fit constraints, data governance, and regulatory alignment. Special attention is reserved for bespoke bio-inspired membrane synthesis; Ersatz surfaces will be iteratively coated until flux stability is achieved. Only after these milestones have been reached can a technology-readiness declaration be advanced beyond the conceptual level. Until then, the proposed system should be regarded as a theoretically promising, simulation-verified alternative for which its practical efficacy is yet to be proven.