The heart of the problem lies in how batteries are modeled. Traditional equivalent circuit models represent a cell as a network of resistors and capacitors, which is computationally cheap and therefore attractive for embedded battery management systems, but integer-order components carry hidden assumptions. Real batteries do not behave like ideal capacitors; their charge transfer and diffusion processes are distributed across time scales and across the physical volume of the electrodes, producing frequency-dependent impedance that lumped elements simply cannot replicate. The result is systematic voltage error, poor performance under varying temperatures, and the need for constant recalibration as the cell ages. Fractional-order models solve this by allowing non-integer exponents in the calculus that describes the system, capturing memory effects and non-exponential relaxation naturally. A key element is the constant phase element, whose exponent alpha slides continuously between the behavior of a resistor and a capacitor, and whose value of one half corresponds to the classic Warburg diffusion element seen in electrochemical impedance spectroscopy.

But fractional-order models come with a price: identifying their parameters is brutally difficult. The team adopted an R(RQ)(RQ)W structure, an advanced extension of classical second-order and PNGV models, in which an ohmic resistance is followed by two parallel resistor-constant-phase-element branches and a Warburg element. Each component maps onto a distinct region of the Nyquist plot, the standard graphical representation of impedance data. The ohmic resistance appears as the high-frequency intercept on the real axis, the two RQ branches form overlapping depressed semicircles in the mid-to-high frequency range corresponding to charge transfer and slower interfacial reactions, and the Warburg element produces the characteristic 45-degree low-frequency tail of solid-phase diffusion. Eight parameters must be extracted simultaneously, and they are strongly coupled, meaning an error in one drags the others off course. Metaheuristic optimizers, which explore search spaces without gradients, are the usual tool, but they frequently converge to local optima that look good numerically yet produce physically meaningless parameters.

To choose the best optimizer fairly, the researchers staged a systematic tournament of ten metaheuristic algorithms: three established methods, particle swarm optimization, grey wolf optimization, and artificial bee colony, against seven recent bio-inspired contenders including the sea lion, golden jackal, fox, honey badger, seahorse, sand cat, and marine predator algorithms. Each ran with an identical budget of 10,000 swarm members and 100 iterations across 20 independent trials. Scoring by root mean square error, mean absolute percentage error, and runtime, the Marine Predators Algorithm, which mimics the Lévy flight and Brownian motion strategies of foraging marine animals, emerged as the most robust performer. A Friedman statistical ranking placed it first with an average rank of 2.00, narrowly ahead of the Honey Badger Algorithm, and its mean runtime of 114 seconds comfortably beat both the honey badger’s 150 seconds and the artificial bee colony’s punishing 2,518 seconds. Yet even the winner showed troubling discrepancies for the second semicircle’s resistance and capacitance and the Warburg coefficient, confirming that raw optimization power alone was insufficient.

The first fix is elegantly physical. Instead of letting the optimizer start from arbitrary bounds, the team derived initial parameter estimates directly from the geometry of the Nyquist plot. A parallel resistor-capacitor circuit traces a perfect semicircle of radius R over two; replacing the capacitor with a constant phase element rotates that semicircle by an angle theta that depends analytically on the fractional exponent alpha, following the relation theta equals 90 degrees times one minus alpha. By extending the measured arcs to full circles, reading off their real-axis intercepts, and measuring the rotation angles of their apexes, the researchers could calculate the ohmic resistance, both branch resistances, both constant phase element exponents and capacitance offsets, and even the Warburg value from the lowest-frequency data point. Six of the eight parameters were thus estimated before optimization even began, shrinking the search space from bounds spanning twenty-fold in each direction to a tight window around physically consistent values.

The second fix attacks dimensionality. Rather than asking the optimizer to juggle all eight parameters at once, the two-stage refinement alternates between metaheuristic optimization of six parameters and analytical recovery of the remaining two. Once the first stage converges on R0, R1, Q1, alpha1, alpha2, and W1, the residual impedance, obtained by subtracting those known contributions from the measured spectrum, is fitted by global least squares to extract R2 and Q2 over the second branch’s frequency band. A Trust Region Reflective algorithm then polishes the estimates, and the cycle repeats for ten iterations with bounds that tighten by a factor of two at each stage. The swarm size drops from 10,000 in the brute-force baseline to just 2,000 in the first stage and 100 thereafter, cutting the iteration count by roughly 80 percent while improving precision.

The validation was unusually thorough. On 50 synthetic impedance profiles generated by Latin Hypercube Sampling, where the true parameter values were known exactly, the full framework achieved an overall mean absolute percentage error of just 7.27 percent, compared with a catastrophic 24,462 percent for standard marine predator optimization and an even worse result for two-stage refinement without informed initialization. The mean root mean square error fell to 1.74 times ten to the minus five, a 92.4 percent reduction relative to the baseline, with a median near ten to the minus six. Scatter plots of estimated versus true parameters clustered tightly along the ideal 45-degree line for all eight quantities, while competing methods showed dispersion spanning orders of magnitude. Crucially, the team demonstrated a subtle pitfall: methods 1 and 2 sometimes achieved low numerical error while their simulated Nyquist plots visibly failed to match the target data, proof that a low objective function value does not guarantee a physically accurate model.

Robustness testing added further confidence. Under 1 percent Gaussian noise the overall parameter error rose only from 7.27 to 12.92 percent, and under 2 percent noise to 18.41 percent, with no instability or divergence. Removing the five lowest-frequency data points, simulating instruments that cannot capture the Warburg region, barely changed the error at 7.38 percent, because the initialization relies on mid-to-high-frequency arc geometry. A transfer test on the simpler R(RQ)W structure showed the initialization concept generalizes across model topologies when the correct structure is known, though the authors are careful to note that automatic model-structure selection from raw data remains an open challenge. Against three state-of-the-art published methods, chaotic adaptive fractional particle swarm optimization, hybrid genetic-particle swarm optimization, and complex-order beetle swarm optimization, the new framework delivered curve-fitting errors one to two orders of magnitude lower, with the rivals showing parameter errors often exceeding several hundred percent for the second branch and Warburg elements.

Finally, the method proved itself on real hardware. The team measured electrochemical impedance spectra from commercial LG INR21700M50LT nickel-manganese-cobalt cells in three states: pristine, initially degraded at 90 percent state of health, and significantly aged at 80 percent state of health and 50 percent state of charge. Across 20 independent runs per condition, the full framework reduced mean root mean square error by 38.0, 32.5, and 76.6 percent respectively compared with the standard optimizer, and achieved parameter coefficients of variation as low as 0.016 percent, meaning repeated identifications landed in the same parameter basin with remarkable consistency. That repeatability is what makes the parameters trustworthy inputs for state of charge and state of health estimation, the foundation of reliable battery diagnosis, degradation tracking, and second-life applications. The authors acknowledge their framework assumes the two impedance arcs remain geometrically distinct, and extending it to overlapping arcs and adaptive topology selection is future work. But the central lesson stands: injecting electrochemical knowledge into the starting point of an optimization can accomplish what brute-force computation cannot, at a fraction of the cost.

Subject of Research: Physics-informed parameter identification for fractional-order lithium-ion battery models using electrochemical impedance spectroscopy

Article Title: Physics-informed parameter identification of fractional-order battery models using Nyquist-based initialization and two-stage metaheuristic refinement

Article References: Wang, S.-C., & Liu, Y.-H. (2026). Physics-informed parameter identification of fractional-order battery models using Nyquist-based initialization and two-stage metaheuristic refinement. Results in Engineering, 32, Article 113425. https://doi.org/10.1016/j.rineng.2026.113425

Image Credits: AI Generated

DOI: 10.1016/j.rineng.2026.113425

Keywords: lithium-ion batteries, fractional-order models, electrochemical impedance spectroscopy, parameter identification, metaheuristic optimization, Marine Predators Algorithm, Nyquist plot, battery management systems, constant phase element, state of charge, state of health, equivalent circuit model

The research, led by Abhishek Kumar Mishra with Furquan Ahmad and Nityanand Singh Maurya, addresses a persistent problem in arsenic risk assessment: direct chemical testing of every well is slow, expensive, and logistically difficult across a densely populated state with millions of private and public extraction points. Predictive models offer a way to screen locations cheaply, flagging wells and districts where follow-up sampling is most urgent. The team built two models, named XGB-MPA and XGB-OOA, both of which use Extreme Gradient Boosting as the underlying learner but differ in how the algorithm’s internal settings are tuned. XGB-MPA employs the Marine Predators Algorithm, while XGB-OOA uses the Osprey Optimization Algorithm, both relatively recent metaheuristics that mimic biological foraging behavior to search vast parameter spaces efficiently.

XGBoost itself is an ensemble technique that builds a sequence of decision trees, each new tree trained to correct the residual errors of its predecessors. Its predictive power depends heavily on hyperparameters such as tree depth, learning rate, and regularization strengths, and poor choices can leave substantial performance on the table. That is where the bio-inspired optimizers come in. The Marine Predators Algorithm, introduced in 2020, models the interaction between predators and prey in ocean ecosystems, alternating between Brownian and Levy flight movement patterns to balance exploration of the search space with exploitation of promising regions. The Osprey Optimization Algorithm, published in 2023, simulates how ospreys locate and capture fish, similarly guiding candidate solutions toward optimal configurations. By letting these algorithms automatically tune XGBoost’s settings, the researchers removed much of the guesswork that typically burdens machine learning applications in hydrology.

The models were trained on four major hydrogeochemical and depth-related variables: pH, electrical conductivity, total dissolved solids, and well depth. These parameters are routinely measured and are physically meaningful indicators of the geochemical conditions that govern arsenic mobilization in aquifer sediments. Arsenic release in the alluvial aquifers of the Ganges basin is closely tied to redox conditions, sediment chemistry, and groundwater flow paths, all of which leave fingerprints in the basic water chemistry that the models can learn to interpret. The target of prediction was the arsenic concentration itself, allowing the frameworks to estimate contamination levels rather than merely classify wells as safe or unsafe.

Performance evaluation was unusually thorough for a study of this kind. The researchers relied on a battery of statistical metrics, including the coefficient of determination (R²), root mean square error (RMSE), mean absolute error (MAE), the variance account for factor (VAF), and the ratio of root mean square error to the standard deviation of measured data (RSR). Beyond these, they subjected the models to k-fold cross-validation to test stability across different data partitions, applied the Wilcoxon signed-rank test to confirm that differences between the two models were statistically significant rather than artifacts of random variation, and used Anderson-Darling probability analysis to examine the distribution of prediction errors. This layered validation strategy is designed to guard against the most common failure mode of machine learning studies: models that look impressive on paper but collapse when confronted with new data.

The results favored the Marine Predators Algorithm variant. XGB-MPA achieved an R² of 0.9752 on training data and 0.9705 on testing data, with normalized RMSE values of 0.0370 and 0.0325 respectively, edging out XGB-OOA in predictive accuracy and generalization capacity. An R² approaching 0.97 means the model explains nearly all of the variance in observed arsenic concentrations within the dataset, a level of agreement that, if it holds up under independent testing, would represent a powerful screening tool. Complementary indices reinforced the picture: the a20 index, which measures the fraction of predictions falling within a factor of deviation of observed values, reached 84.29 percent for training and 76.67 percent for testing, while the index of agreement (IOA) exceeded 0.98 and the index of scatter (IOS) stayed below 0.19. Together these figures indicate that XGB-MPA’s predictions track measured concentrations closely and consistently across both phases of model development.

The stakes in Bihar could hardly be higher. State economic survey data cited in the study report massive groundwater contamination affecting 31 of the state’s 38 districts, and the World Health Organization’s drinking water guidelines identify arsenic as one of the most significant inorganic contaminants globally. Chronic exposure through drinking water is associated with skin lesions, cancers of the skin, bladder, and lung, heart disease, and cognitive and neurological deficits. Because arsenic is tasteless, colorless, and odorless, residents typically have no way of knowing their exposure level without chemical testing. A reliable predictive model, even one used only as a first-pass screening instrument, could direct scarce testing resources to the places where they will do the most good, potentially shortening the lag between contamination and intervention.

The authors are careful, and appropriately so, about the limits of what their frameworks can claim. They position the models as a data-driven preliminary screening aid for identifying locations that require further groundwater-quality investigation, not as a replacement for direct measurement. Operational water-management decisions and health-related interventions, they stress, should incorporate actual water-quality measurements and a broader set of hydrogeochemical indicators, including iron and manganese, which interact with arsenic in aquifer systems and were not part of the model’s input set. They also note that broader transferability of the framework requires validation using independent datasets that incorporate additional hydrogeochemical variables, a candid acknowledgment that the impressive statistics reported here describe performance within the investigated dataset rather than guaranteed performance across the full hydrological diversity of the Ganges plain.

That caveat matters because arsenic prediction is a notoriously difficult modeling problem. Concentrations can vary dramatically between wells separated by only a few hundred meters, reflecting the patchwork of buried organic matter, iron oxide minerals, and sedimentary history that controls where arsenic is released into solution. Models trained in one geomorphic setting often falter in another. The Bihar study’s use of only four input variables is both a strength and a limitation: it makes the screening approach practical, since pH, conductivity, total dissolved solids, and depth are cheap and widely measured, but it also means the models capture only part of the geochemical complexity that determines arsenic fate. Future iterations that fold in iron, manganese, redox indicators, and perhaps remote sensing or geological layers could sharpen predictions further and extend their reach.

Still, the study adds to a growing body of evidence that hybrid machine learning, in which gradient boosting ensembles are tuned by metaheuristic optimizers, can extract reliable predictive signal from modest environmental datasets. The head-to-head comparison of two recent optimization algorithms, validated with nonparametric statistical testing, offers a template for how such models should be evaluated before being proposed for real-world use. For the millions of Bihar residents who draw their drinking water from arsenic-prone aquifers, the practical promise is straightforward: a fast, data-driven way to identify which wells deserve urgent testing and which communities face the greatest hidden risk. If independent validation confirms what the training statistics suggest, frameworks like XGB-MPA could become a standard first line of defense in the ongoing effort to keep arsenic out of the region’s drinking water.

Subject of Research: Hybrid machine learning prediction of groundwater arsenic contamination in Bihar, India

Article Title: Optimization-driven hybrid XGBoost frameworks for predicting groundwater arsenic contamination in Bihar, India

Article References: Mishra, A. K., Ahmad, F., & Maurya, N. S. (2026). Optimization-driven hybrid XGBoost frameworks for predicting groundwater arsenic contamination in Bihar, India. Earth Science Informatics, 19(11), Article 207. https://doi.org/10.1007/s12145-026-02262-z

Image Credits: AI Generated

DOI: 10.1007/s12145-026-02262-z

Keywords: groundwater, arsenic contamination, XGBoost, machine learning, Marine Predators Algorithm, Osprey Optimization Algorithm, Bihar, hydrogeochemistry, drinking water safety, bio-inspired optimization, water quality prediction, India

Binary protocols, which encode data directly as compact byte sequences rather than human-readable text, form the backbone of much of the modern digital world. They underpin network devices, industrial control systems, and Internet of Things applications, where efficiency and low overhead are paramount. But their very compactness creates a security blind spot. Unlike text protocols, binary formats lack delimiters, tags, and other redundant markers that make field boundaries obvious. When implementations of these protocols mishandle malformed messages, the consequences can be severe. The researchers point to the infamous EternalBlue vulnerability in the SMB protocol, which arose from improper parsing of binary messages and enabled buffer overflow and remote code execution with global impact, as a stark reminder of what is at stake.

Mutation-based greybox fuzzing has become one of the most widely used techniques for discovering such flaws. Greybox fuzzers occupy a middle ground between blackbox and whitebox approaches: they do not require complete knowledge of a program’s internals, but they do use lightweight runtime feedback, such as coverage information gathered through instrumentation, to guide how inputs are mutated. Tools like AFL, AFL++, and MOPT generate malformed test cases by applying mutation operators such as bit flips and byte substitutions to well-formed seed messages, then monitor the target program for crashes, hangs, and other abnormal behavior. The approach has uncovered countless vulnerabilities, yet the authors argue that existing fuzzers stumble when confronted with structured binary messages.

The team identifies three core challenges. First, protocol parsing is difficult because binary protocols represent data as bit streams with unclear field boundaries and implicit semantics, making it laborious to determine which positions in a message can safely be mutated. Second, evaluating the mutation value of different fields is hard because the effect of changing a field depends on runtime behavior, field dependencies, and the target program’s responses, none of which can be reliably determined statically. Third, and perhaps most damaging, existing fuzzers schedule mutation operators blindly. A bit flip applied to a function code field may drive a program into entirely new logical states, while the same operation on a data field merely alters content. Worse, mutating a length field without adjusting the corresponding payload breaks the message structure, causing the test case to be discarded before it ever reaches deep parsing logic.

MPAuzz tackles these problems in two stages. The first is a feedback-based mutation position exploration module that partitions protocol messages at bit-level granularity rather than the coarser byte level used by most prior tools. This fine granularity matters: in an MQTT message, for example, the high four bits of the header flags field determine the message type while the low four bits serve as flags, a distinction that byte-level analysis cannot capture. The module flips one bit at a time, sends the mutated message to the target, and classifies the result. Normal responses mark a bit as mutable; format anomalies detected with protocol parsing tools such as Tshark mark it as restricted; and mutations of essential control fields such as protocol names and function codes mark regions as immutable. Adjacent bits with similar properties are then merged into continuous regions, giving the fuzzer a map of where mutation is safe, where it must respect constraints, and where it is forbidden.

The second stage is where the ocean comes in. MPAuzz formulates mutation operator scheduling as a multidimensional optimization problem in which each dimension corresponds to the operator choice for one mutation region, and it solves this problem using the Marine Predators Algorithm, a metaheuristic inspired by how marine predators forage. The historically best operator combination plays the role of the predator, while candidate combinations act as prey. The algorithm dynamically switches between Lévy flights, long-distance jumps that enable broad exploration, and Brownian motion, small-step searches that enable fine-grained exploitation. The researchers deliberately chose MPA over alternatives such as multi-armed bandit strategies and particle swarm optimization because mutating one region of a binary message often depends on other regions; treating each region as an independent arm can produce structurally invalid test cases, while PSO’s velocity-based updates risk premature convergence when early coverage gains come from only a few regions.

The scheduling unfolds across three adaptive stages that mirror the fuzzing lifecycle. In the early, high-speed exploration stage, Lévy-distributed random vectors drive wide-ranging tests of operator combinations to avoid premature convergence. In the middle, balanced coordination stage, the population splits: half fine-tunes the elite combination using Brownian perturbations governed by a quadratically decreasing convergence factor, while the bottom-performing half continues exploring with Lévy motion. In the final, low-speed exploitation stage, an enhanced social learning term pulls candidate combinations toward the best-known strategy, changing only one or a few region assignments at a time. Crucially, a candidate combination is retained only if it satisfies region-specific constraints and improves coverage feedback. The framework also includes a repairing step for restricted regions: when a mutable payload region changes size, the associated length field is recalculated automatically, with nested dependencies repaired from the innermost region outward.

To validate the design, the team evaluated MPAuzz on four widely used binary protocol implementations covering MQTT, DTLS, DNS, and CoAP, comparing it against AFLNet and StateAFL, two of the most prominent greybox protocol fuzzers. Each fuzzer ran continuously for 24 hours per target, with each experiment repeated ten times to account for the inherent randomness of fuzzing. The results were decisive. MPAuzz’s valid-test-case ratio exceeded 97 percent on every target, compared with 83.1 percent for a multi-armed bandit variant and 79.5 percent for a PSO variant of the same tool. It reached comparable coverage 3.47 times faster than AFLNet and 2.22 times faster than StateAFL on average, with Vargha-Delaney effect sizes mostly at or above 0.85, indicating a consistent statistical advantage.

The vulnerability discovery results were equally compelling. Instrumenting targets with AddressSanitizer to capture memory-related faults, the researchers found that MPAuzz produced more crashes than both baselines on all four targets. On the Mosquitto MQTT broker, MPAuzz triggered an average of 87.8 crashes per run, compared with 3.9 for AFLNet and 43.2 for StateAFL, and exposed its first crash just 32 minutes into testing, whereas AFLNet failed to crash the target within the allotted time at all. On Tinydtls, MPAuzz found its first crash in 15 seconds. Analysis of the proof-of-concept inputs showed that the anomalies detected in Mosquitto and Libcoap correspond to real, documented vulnerabilities: the medium-severity CVE-2021-28166, a null pointer dereference triggered when an authenticated client sends a mutated SUBSCRIBE message before the server issues a PUBLISH message, and the high-severity CVE-2024-46304. These findings demonstrate that the fuzzer can surface genuine security flaws arising from abnormal protocol-state sequences, not merely superficial parsing errors.

The authors are candid about limitations. MPAuzz currently leans on external parsers such as Tshark and Scapy for protocol-format feedback, so for proprietary or undocumented protocols the precision of restricted and immutable region identification may degrade, though the fuzzer can still operate using runtime responses and coverage feedback alone. The automatic repair mechanism primarily supports length-related constraints; checksums, authentication fields, and state-dependent constraints require protocol-specific rules. The evaluation, while rigorous, covers four protocol implementations, and the team notes that additional targets and longer experiments would strengthen the evidence. Still, the work makes a persuasive case that combining protocol-aware region classification with staged, nature-inspired operator scheduling is a practical path forward for binary-protocol fuzzing, and the researchers plan to reduce reliance on external parsers and extend support for proprietary protocols with complex field dependencies in future work.

Subject of Research: A nature-inspired greybox fuzzing framework for discovering vulnerabilities in binary network protocol implementations

Article Title: Binary protocol greybox fuzzing driven by marine predators algorithm

Article References: Jiang, C., Hong, Z., Zhang, G., Li, Y., & Gu, J. (2026). Binary protocol greybox fuzzing driven by marine predators algorithm. Cybersecurity, 9(1), Article 214. https://doi.org/10.1186/s42400-026-00646-8

Image Credits: AI Generated

DOI: 10.1186/s42400-026-00646-8

Keywords: binary protocols, greybox fuzzing, Marine Predators Algorithm, vulnerability discovery, mutation scheduling, network security, MQTT, DTLS, DNS, CoAP, software testing, cybersecurity