Computing and Mathematical Sciences Papers

Permanent URI for this collectionhttps://researchcommons.waikato.ac.nz/handle/10289/6

This collection houses research from the School of Computing and Mathematical Sciences at the University of Waikato.

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Critical balance and the physics of magnetohydrodynamic turbulence
(American Astronomical Society, 2020) Oughton, Sean; Matthaeus, William H.
A discussion of the advantages and limitations of the concept of critical balance (CB), as employed in turbulence phenomenologies, is presented. The incompressible magnetohydrodynamic (MHD) case is a particular focus. The discussion emphasizes the status of the original Goldreich & Sridhar CB conjecture relative to related theoretical issues and models in an MHD description of plasma turbulence. Issues examined include variance and spectral anisotropy, influence of a mean magnetic field, local and nonlocal effects, and the potential for effects of external driving. Related models such as Reduced MHD provide a valuable context in the considerations. Some new results concerning spectral features and timescales are presented in the course of the discussion. Also mentioned briefly are some adaptations and variations of CB.
Angular dependence of third-order law in anisotropic MHD turbulence
(IOP Publishing, 2026) Jiang, Bin; Gao, Zhuoran; Yang, Yan; Pecora, Francesco; Gao, Kai; Li, Cheng; Oughton, Sean; Matthaeus, William H.; Wan, Minping
In solar wind turbulence, the energy transfer/dissipation rate is typically estimated using MHD third-order structure functions calculated using spacecraft observations. However, the inherent anisotropy of solar wind turbulence leads to significant variations in structure functions along different observational directions, thereby affecting the accuracy of energy dissipation rate estimation. An unresolved issue is how to optimise the selection of observation angles under limited directional sampling to improve estimation precision. We conduct a series of MHD turbulence simulations with different mean magnetic field strengths, B0. Our analysis of the third-order structure functions reveals that the global energy dissipation rate estimated around a polar angle of θ = 60^∘agrees reasonably with the exact one for 0 ≤ B0/brms ≤ 5, where brms denotes the rms magnetic field fluctuation. The speciality of 60^∘ polar angle can be understood by the mean value theorem of integrals, since the spherical integral of the polar-angle component (T̃θ) of the divergence of Yaglom flux is zero, and T̃θ changes sign around 60^∘. Existing theory on the energy flux vector as a function of the polar angle is assessed, and supports the speciality of the 60^∘ polar angle. The angular dependence of the third-order structure functions is further assessed with virtual spacecraft data analysis. The present results can be applied to measure the turbulent dissipation rates of energy in the solar wind, which are of potential importance to other areas in which turbulence takes place, such as laboratory plasmas and astrophysics.
Evolution of a Pickup Ion Ring-beam Population in Large-scale Interstellar Turbulence and Small-scale Self-generated Waves: Implications for the IBEX Ribbon
(IOP, 2026) Huang, Y; Guo, F; Sun, X; Noh, SJ; Zirnstein, EJ; Reisenfeld, DB; Li, H; Florinski, V; Heerikhuisen, Jacob
The secondary energetic neutral atom (ENA) mechanism proposed to explain the ribbon-like enhancement of ENA emission observed by Interplanetary Boundary Explorer (IBEX) involves a pickup ion (PUI) ring-beam population beyond the heliopause. The stability of this highly anisotropic PUI distribution is crucial for determining the physical process responsible for the ribbon formation. It has been proposed that PUIs with pitch angles near 90° can become trapped via the magnetic mirroring process in the turbulent magnetic field of the local interstellar medium. However, the turbulent mirroring scenario typically neglects self-generated waves excited by the kinetic instabilities of the ring-beam PUIs, which can efficiently scatter PUIs in pitch angle. Using a magnetohydrodynamics-particle-in-cell approach implemented in ATHENA++, we simulate the evolution of the ring-beam PUIs, incorporating both large-scale interstellar magnetic fluctuations and microscale self-excited instabilities. We examine the competition between turbulent mirroring and pitch-angle scattering by the self-generated waves. Our results show that the PUIs can be rapidly scattered toward a nearly isotropic distribution on the order of one day, much shorter than their characteristic lifetime of a couple of years. This suggests that theoretical difficulties remain for maintaining an anisotropic PUI distribution in physical models of the IBEX ribbon.
Poisson–Dirichlet approximation for the stationary distribution of the inclusion process
(Elsevier, 2026) Gan, Han L
We consider the approximation of the stationary distribution of the finite inclusion process with the Poisson–Dirichlet distribution. Using Stein’s method, we derive an explicit bound for the approximation error, which is of order 1/N in the thermodynamic limit. The results are achieved from a minor modification to Stein’s method for Poisson–Dirichlet distribution approximation developed in Gan and Ross, (2021). The derivatives used on test functions in Gan and Ross, (2021) were directional type derivatives specifically chosen for their measure preserving properties. Depending upon the application, these derivatives can prove cumbersome. In this note, we show that for certain test functions we can instead use more traditional derivatives, which simplifies the bounds for the Stein factors and is more amenable to the approximation of the inclusion process.
How should the information profession respond to generative artificial intelligence (GenAI)?
(SAGE Publications, 2026-07-08) Lueg, Christopher; Nichols, David M; Twidale, Michael
The internet-fueled digital information environment of the future will likely contain many contentious media objects as creation costs are significantly lower when using generative artificial intelligence (GenAI). We argue that responding to the impact of GenAI is a challenge to the whole information profession. Acknowledging the diversity among GLAM institutions (Galleries, Libraries, Archives, Museums) we propose that GLAM institutions along with their specific strengths are well placed for guiding, if not overseeing, proposed authenticity infrastructures to complement the demand for improved media literacies in the age of GenAI as these institutions are able to engage with the public in ways that often exceed the reach of more technology-focused organizations.
Magnetohydrodynamic turbulence and the associated spatial diffusion tensor of cosmic rays in dynamical galactic halos
(EDP Sciences, 2026-07-07) Kleimann, J; Fichtner, H; Stein, M; Dettmar, RJ; Bomans, DJ; Oughton, Sean
Context. A detailed understanding of cosmic-ray transport in galactic halos is essential for explaining various observations, such as the radio continuum measurements of synchrotron radiation from energetic electrons. Of central importance is the spatial diffusion tensor of cosmic rays, which can be computed in an ab initio manner if the turbulence in the background medium is known. Aims. The study aimed to establish a suitable framework to compute the evolution of magnetohydrodynamic (MHD) turbulence and, hence, the diffusion tensor in the dynamical halos of galaxies. Methods. The Reynolds-averaged single-fluid MHD equations were solved numerically on a cylindrical grid, assuming axial symmetry and fixed boundary conditions on a central ellipsoid representing the galaxy. The physical properties of both large-scale MHD and small-scale turbulent quantities, including the coefficients of parallel and perpendicular diffusion, were extracted from the resulting steady state. Results. Hydrodynamic validation revealed a persistent instability of the near-axis flow, which could be traced to the galaxy's gravitating mass. The results for the evolution of MHD turbulence in a galactic halo-using parameters approximating those of NGC 4631-enabled an ab initio computation of the spatial diffusion tensor of cosmic rays through the application of a state-of-the-art nonlinear theory. Conclusions. The simulation results reveal variation in turbulence quantities, (i.e., fluctuation energy, correlation scale, and cross helicity) in a dynamical halo. Furthermore, the corresponding diffusion tensor of cosmic rays exhibits significant variation throughout such a halo.
Steady-state Dirichlet approximation of the Wright-Fisher model using the prelimit generator comparison approach of Stein's method
(Applied Probability Trust, 2025-05-27) Braverman, A; Gan, Han L
The Wright–Fisher model, originating in Wright (1931) is one of the canonical probabilistic models used in mathematical population genetics to study how genetic type frequencies evolve in time. In this paper we bound the rate of convergence of the stationary distribution for a finite population Wright–Fisher Markov chain with parent-independent mutation to the Dirichlet distribution. Our result improves the rate of convergence established in Gan et al. (2017) from to . The results are derived using Stein’s method, in particular, the prelimit generator comparison method.
Ten simple guidelines for decolonising algorithmic systems
(Elsevier, 2025) O'Neale, Dion R.J.; Wilson, D; Brown, Paul T.; Dickinson, Pascarn; Rikus-Graham, Manakore; Ropeti, Asia
As the scope and prevalence of algorithmic systems and artificial intelligence for decision making expand, there is a growing understanding of the need for approaches to help with anticipating adverse consequences and to support the development and deployment of algorithmic systems that are socially responsible and ethically aware. This has led to increasing interest in "decolonising" algorithmic systems as a method of managing and mitigating harms and biases from algorithms and for supporting social benefits from algorithmic decision making for Indigenous peoples. This article presents ten simple guidelines for giving practical effect to foundational Māori (the Indigenous people of Aotearoa New Zealand) principles in the design, deployment, and operation of algorithmic systems. The guidelines are based on previously established literature regarding ethical use of Māori data. Where possible we have related these guidelines and recommendations to other development practices, for example, to open-source software. While not intended to be exhaustive or extensive, we hope that these guidelines are able to facilitate and encourage those who work with Māori data in algorithmic systems to engage with processes and practices that support culturally appropriate and ethical approaches for algorithmic systems.
Interstellar conditions deduced from interstellar neutral helium observed by IBEX and global heliosphere modeling
(IOP Publishing, 2023) Swaczyna, Paweł; Bzowski, Maciej; Heerikhuisen, Jacob; Kubiak, Marzena A.; Rahmanifard, Fatemeh; Zirnstein, Eric J.; Fuselier, Stephen A.; Galli, André; McComas, David J.; Möbius, Eberhard; Schwadron, Nathan A.
In situ observations of interstellar neutral (ISN) helium atoms by the IBEX-Lo instrument on board the Interstellar Boundary Explorer (IBEX) mission are used to determine the velocity and temperature of the pristine very local interstellar medium (VLISM). Most ISN helium atoms penetrating the heliosphere, known as the primary population, originate in the pristine VLISM. As the primary atoms travel through the outer heliosheath, they charge exchange with He+ ions in slowed and compressed plasma, creating the secondary population. With more than 2.4 million ISN helium atoms being sampled by IBEX during ISN seasons 2009-2020, we compare the observations with the predictions of a parameterized model of ISN helium transport in the heliosphere. We account for the filtration of ISN helium atoms at the heliospheric boundaries by charge-exchange and elastic collisions. We examine the sensitivity of the ISN helium fluxes to the interstellar conditions described by the pristine VLISM velocity, temperature, magnetic field, and composition. We show that comprehensive modeling of the filtration processes is critical for interpreting ISN helium observations, as the change in the derived VLISM conditions exceeds the statistical uncertainties when accounting for these effects. The pristine VLISM parameters found by this analysis are the flow speed (26.6 km s−1), inflow direction in ecliptic coordinates (255.°7, 5.°04), temperature (7350 K), and B − V plane inclination to the ecliptic plane (53.°7). The derived pristine VLISM He+ density is 9.7 × 10−3 cm−3. Additionally, we show a strong correlation between the interstellar plasma density and magnetic field strength deduced from these observations.
Relative in-flight response of IBEX-Lo to interstellar neutral helium atoms
(IOP Publishing, 2023) Swaczyna, Paweł ; Bzowski, Maciej; Fuselier, Stephen A.; Galli, André; Heerikhuisen, Jacob; Kubiak, Marzena A.; McComas, David J.; Möbius, Eberhard; Rahmanifard, Fatemeh; Schwadron, Nathan A.
The IBEX-Lo instrument on the Interstellar Boundary Explorer (IBEX) mission measures interstellar neutral (ISN) helium atoms. The detection of helium atoms is made through negative hydrogen (H−) ions sputtered by helium atoms from the IBEX-Lo’s conversion surface. The energy spectrum of ions sputtered by ISN helium atoms is broad and overlaps the four lowest IBEX-Lo electrostatic analyzer (ESA) steps. Consequently, the energy response function for helium atoms does not correspond to the nominal energy step transmission. Moreover, laboratory calibration is incomplete because it is difficult to produce narrow-energy neutral atom beams that are expected for ISN helium atoms. Here, we analyze the ISN helium observations in ESA steps 1–4 to derive the relative in-flight response of IBEX-Lo to helium atoms. We compare the ratios of the observed count rates as a function of the mean ISN helium atom energy estimated using the Warsaw Test Particle Model (WTPM). The WTPM uses a global heliosphere model to calculate charge exchange gains and losses to estimate the secondary ISN helium population. We find that the modeled mean energies of ISN helium atoms, unlike their modeled fluxes, are not very sensitive to the very local interstellar medium parameters. The obtained relative responses supplement the laboratory calibration and enable more detailed quantitative studies of the ISN helium signal. A similar procedure that we applied to the IBEX-Lo observations may be used to complement laboratory calibration of the next-generation IMAP-Lo instrument on the Interstellar Mapping and Acceleration Probe (IMAP) mission.
The effect of adipose tissue on transdermal monochromatic light presented to the human fetus using Monte Carlo simulations
(Springer Nature, 2025) Isaac, Zac; Heerikhuisen, Jacob; Reid, Vincent
The extent to which transdermal light sources illuminate the uterine environment is unknown. Recent work indicates the human fetus responds to external visual stimuli, such as laser diodes, and initial modeling suggests the fetus may not develop in a completely dark environment as previously assumed. Development of the human visual system begins within the womb, and there is motivation in fields such as developmental psychology, transabdominal oximetry, and photoacoustics to explore the extent to which light penetrates maternal abdominal tissue and understand how transdermal stimuli appear to the fetus. We develop and adapt a Monte Carlo model utilising third trimester histological properties of maternal tissue to simulate transdermal monochromatic collimated light sources, with particular focus on the 650 nm wavelength used in experimental applications. We determine approximate levels of third trimester uterine illumination from such stimuli, ranging from being comparable to an overcast night to a full moon in clear conditions. We further discuss the scope for multiple stimuli to be visibly distinct in utero for experimental applications. This modeling provides quantitative guidance on the interactions between transdermal monochromatic collimated source laser diode stimuli and maternal tissue to practitioners and researchers in the fields of fetal vision, ultrasound, and developmental psychology.
The effect of angular scattering imposed by charge exchange and elastic collisions on interstellar neutral hydrogen atoms
(American Astronomical Society, 2023) Rahmanifard, Fatemeh; Swaczyna, Paweł; Zirnstein, Eric J.; Heerikhuisen, Jacob; Galli, André; Sokół, Justyna M.; Schwadron, Nathan A.; Möbius, Eberhard; McComas, David J.; Fuselier, Stephen A.
Angular scattering (AS) in charge exchange and elastic collisions between interstellar ions and neutral (ISN) atoms has been assumed to be negligible in previous studies. Here, we investigate the momentum transfer associated with the AS of H atoms using Monte Carlo calculations to simulate their transport through the outer heliosheath. We consider two cases where charge exchange and elastic collisions between ISN H atoms and protons occur with and without AS in the outer heliosheath. We show that considering AS decelerates and heats primary ISN H, reducing the effect of selective charge exchange in the outer heliosheath. Secondary ISN H atoms, on the other hand, are not significantly affected by AS. We then simulate the transport of ISN H atoms inside the heliosphere to simulate count rates observed in the lowest energy bin of IBEX-Lo. We study the effect of radiation pressure on the ISN H measurements for the cases with and without AS and compare them with our previous findings. We find an effective radiation parameter (μeff, which represents force associated with radiation pressure relative to gravity) for the years 2009–2018 based on the longitudinal shift of the ISN H signal. The two cases with and without AS reproduce the longitudinal shift in accordance with variations in solar activity, in agreement with our previous results, and they result in similar values for the μeff, which is ∼22%–23% larger than the value found based on solar Lyα profile observations.
Securing educational LLMs: a generalised taxonomy of attacks on LLMs and DREAD risk assessment
(Elsevier, 2026-03-15) Zahid, Farzana; Kumar, Vimal
Due to perceptions of efficiency and significant productivity gains, various organisations, including in education, are adopting Large Language Models (LLMs) into their workflows. Educator-facing, learner-facing, and institution-facing LLMs, collectively, Educational Large Language Models (eLLMs), complement and enhance the effectiveness of teaching, learning, and academic operations. However, their integration into an educational setting raises significant cybersecurity concerns. A comprehensive landscape of contemporary attacks on LLMs and their impact on the educational environment is missing. This study presents a generalised taxonomy of fifty attacks on LLMs, which are categorised as attacks targeting either models or their infrastructure. The severity of these attacks is evaluated in the educational sector using the DREAD risk assessment framework. Our risk assessment indicates that token smuggling, adversarial prompts, direct injection, and multi-step jailbreak are critical attacks on eLLMs. The proposed taxonomy, its application in the educational environment, and our risk assessment will help academic and industrial practitioners to build resilient solutions that protect learners and institutions.
Branches: Efficiently seeking optimal sparse decision trees via AO*
(PMLR, 2025) Chaouki, Ayman; Read, Jesse; Bifet, Albert
Decision Tree (DT) Learning is a fundamental problem in Interpretable Machine Learning, yet it poses a formidable optimisation challenge. Practical algorithms have recently emerged, primarily leveraging Dynamic Programming and Branch & Bound. However, most of these approaches rely on a Depth-First-Search strategy, which is inefficient when searching for DTs at high depths and requires the definition of a maximum depth hyper-parameter. Best-First-Search was also employed by other methods to circumvent these issues. The downside of this strategy is its higher memory consumption, as such, it has to be designed in a fully efficient manner that takes full advantage of the problem’s structure. We formulate the problem within an AND/OR graph search framework and we solve it with a novel AO*-type algorithm called BRANCHES. We prove both optimality and complexity guarantees for BRANCHES and we show that it is more efficient than the state of the art theoretically and on a variety of experiments. Furthermore, BRANCHES supports nonbinary features unlike the other methods, we show that this property can further induce larger gains in computational efficiency.
SGLT2 inhibitor use and disparities in all-cause mortality in type 2 diabetes: Insights from a multi-ethnic population
(Springer, 2026) Chepulis, Lynne; Gan, Han; Simmons, David; Rodrigues, Mark William; Keenan, Rawiri; Murphy, Rinki; Kenealy, Tim; Te Karu, Leanne; Magliano, Dianna; Scott-Jones, Jo; Moffitt, Allan; Lao, Chunhuan; Lawrenson, Ross; Paul, Ryan G.
Aims/hypothesis: Sodium-glucose cotransporter 2 inhibitors (SGLT2i) are known to reduce cardiovascular and all-cause mortality in people with type 2 diabetes, but there are limited data regarding mortality outcomes in different ethnic groups (including Indigenous peoples). This study reports on mortality outcomes in a population in Aotearoa New Zealand (hereafter New Zealand) with type 2 diabetes, following the funded availability of the SGLT2i empagliflozin with prioritised access for Māori and Pacific people. Methods: Data were collected from primary care records for those aged 18–75 years with type 2 diabetes (Auckland/Waikato regions of New Zealand; February 2021 to December 2023; n=59,505). These data were linked to national medication-dispensing and mortality records for 2021–2024 via national health identifier numbers. Following propensity matching and Cox modelling for ethnicity, age, gender, medication use, baseline HbA1c and cardiovascular and/or renal disease/risk (CVRD) status (yes/no), mortality rates were compared by ethnicity in those with and without CVRD and who did/did not initiate empagliflozin. This study was reported in accordance with the CONSIDER statement, used to strengthen the reporting of research involving Indigenous peoples. The study was funded by the Health Research Council of New Zealand. Results: Following matching, two groups of 12,792 individuals were identified. Annualised crude mortality (deaths per 1000 individuals per year) was higher in those not dispensed with SGLT2i than in those receiving SGLT2i (35.2 vs 13.1 in those with CVRD and 7.7 vs 3.6 in those without CVRD, respectively). After adjustment, the greatest difference in mortality with SGLT2i use was seen in Māori (HR 0.475; 95% CI 0.336, 0.672; p<0.001), followed by Pacific people (HR 0.507; 95% CI 0.395, 0.651; p<0.001) and European people (HR 0.667; 95% CI 0.545, 0.816; p<0.001). Conclusions/interpretation: The protective effect of SGLT2i use on mortality appears to differ by ethnicity and is greater in Indigenous Māori and Pacific populations in New Zealand with type 2 diabetes. SGLT2i use in Indigenous and minority populations may support improved health equity.
Slab turbulence in the very local interstellar medium and the IBEX ribbon
(IOP Publishing, 2025) Zirnstein, Eric J.; McComas, David J.; Giacalone, Joe; Zank, Gary P.; Guo, Fan; Heerikhuisen, Jacob; Li, Hui; Reisenfeld, Daniel B.
In this study, we analyze an important property of the very local interstellar medium, i.e., turbulence that affects the intensity and shape of the Interstellar Boundary Explorer (IBEX) ribbon. Specifically, we simulate the propagation of the ribbon’s parent ions before they become secondary energetic neutral atoms that can be observed at 1 au by IBEX. We then test how different slab/2D turbulence fractions affect the intensity and shape of the modeled ribbon and compare to the latest IBEX ribbon-separated data. We compare 1D cuts across the modeled and observed ribbon as a function of angle away from the ribbon center. We find that the intensities of the modeled ribbon are larger than most of the data, except near the ecliptic plane. However, the model intensities are sensitive to how we model the neutral solar wind, which forms the source ion population for the ribbon. We then compare the model and data by normalizing the fluxes to their respective peak intensities and find the peaks’ angular distances from the ribbon center. We find that most of the model peaks lie within 3° of the data peaks, which we consider our 1σ uncertainty (half the size of an IBEX pixel). By averaging the instances where the model peaks match the data peaks (within 3°), we find that the mean is slab-50%, with a standard deviation of ±28% and standard error of ±5%.
A novel inversion method for electrical impedance tomography with a radial basis operator network
(MDPI, 2026) Kurz, Jason A.; Pangia, Andrew; Khan, Taufiquar
We apply a new operator neural network to solve the Electrical Impedance Tomography (EIT) inverse problem. The EIT inverse problem involves reconstructing the conductivity inside a specific body or domain, given the electric potential along the boundary of said body. Mathematically speaking, the inverse problem is known to be severely ill-posed, that is, hard to reliably solve. However, we demonstrate the efficacy of our proposed algorithm utilizing the aforementioned neural network, dubbed the Radial Basis Operator Network (RBON) in its seminal work, when applied to the EIT inverse problem.
D-inverse constellations
(Shahid Beheshti University, 2026) Gould, Victoria; Stokes, Tim E.
Constellations are partial algebras in the sense that they possess a partial product, and a unary operation modelling domain. They were first used to give an ESN-style theorem for left restriction semigroups in terms of so-called inductive constellations. Here, we consider constellations in which elements have a suitable notion of inverse, giving the notion of a D-inverse constellation. We show that there is a categorical isomorphism between the category of ordered groupoids and the category of D-inverse constellations. This may be viewed as a generalisation of the ESN theorem, which relates the category of inductive groupoids to the category of inverse semigroups.
Particle transport from first principles in the early heliosphere: κ1 Ceti as a case study for the young Sun
(IOP Publishing, 2026) Engelbrecht, N. Eugene; Herbst, Konstantin; Scherer, Klaus; Oughton, Sean; Airapetian, Vladimir S.
Several studies of Galactic cosmic-ray (GCR) modulation within the astrospheres of stars deemed to be proxies for the young Sun have concluded that the intensities of these particles would, at early stages of the Sun’s evolution, be negligible at 1 au. These studies, however, do not take into account the varying interstellar conditions the young Sun would have encountered as it traversed its Galactic orbit, nor do they realistically model the transport of GCRs. The present study, for the first time, examines the influence of various interstellar parameters in the Galactic spiral arms on the astrosphere of κ1 Ceti, a young Sun proxy, through magnetohydrodynamic modelling. We demonstrate that these conditions lead to an astrosphere with considerably smaller dimensions than previous estimates. We also model the transport of turbulence parameters within said astrosphere for the first time, demonstrating that turbulence levels could be significantly higher than observed in the heliosphere. Finally, these insights are implemented in a 3D, ab initio GCR transport model to compute GCR intensities at 1 au, demonstrating the importance of drift effects in astrospheric modulation: full drift effects lead to GCR intensities comparable to modern observations, while turbulence-reduced drift coefficients lead to significantly smaller intensities.
Towards sustainable IoT: A digital signature‐enhanced federated learning approach
(Wiley, 2025) Qureshi, Shahida Hafeezan; Malik, Saif Ur Rehman; Haseeb, Junaid; Moqurrab, Syed Atif; Bukht, Tanvir Fatima Naik; Srivastava, Gautam
Federated Learning (FL) is emerging as a premier paradigm for privacy‐preserved Machine Learning (ML), enabling devices to train models without central data pooling collaboratively. In the contemporary Internet of Things (IoT) landscape, characterized by escalating energy consumption and associated carbon footprint, FL is recognized not merely for its privacy features. Intrinsic to decentralized architectures such as FL, secure communication is based on digital signatures to guarantee integrity. This is particularly evident in sensitive sectors such as the Internet of Vehicles (IoV), banking, and healthcare. Integrating FL becomes imperative and intricate as these sectors are intertwined with the IoT fabric. Our study unveils “Secure Federated Learning Framework (SecFL),” a pioneering decentralized framework combining FL and sustainable computing. SecFL offers defences against adversarial attacks such as data poisoning and label flipping. Utilizing the Rivest‐Shamir‐Adleman (RSA) asymmetric encryption algorithm for securing digital communications and transactions, combined with ElGamal encryption and a private Ethereum blockchain, ensures enhanced client‐specific security. Our research emphasizes the formal modeling of adversarial dynamics using High‐Level Petri nets (HLPN) within the FL‐IoT ecosystem, balancing system dynamics and energy conservation. Our model consistently outperforms contemporary solutions in accuracy and time efficiency after validation. As IoT burgeons into domains like environmental monitoring, smart cities, and energy grids, the SecFL framework, fostering FL, optimizes energy utilization and bolsters resource efficiency. In our comparative analysis, the Elliptic Curve Digital Signature Algorithm (ECDSA) algorithm demonstrates superior transaction latency and verification time compared to RSA and Elliptic Curve Cryptography (ECC).

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