arXiv subjects

Souvik Chakraborty

Publications and source records attributed to Souvik Chakraborty.

At least 37 records · Page 2Linked to original sources

arXiv2026

Neuroscience Inspired Graph Operators Towards Edge-Deployable Virtual Sensing for Irregular Geometries

Predicting full-field physics through the real-time virtual sensing of engineering systems can enhance limited physical sensors but often requires sparse-to-dense reconstruction, complex multiphysics, and highly irregular geometries as well as strict latency and energy constraints for edge-deployability. Neural operators have been presented as a potential candidate for such applications but few architectures exist that explicitly address power consumption. Spiking neuron integration can provide a potential solution when integrated on neuromorphic hardware but the current existing neuron models result in severe performance degradation towards regression-based virtual sensing. To address the performance concerns and edge-constraints, we present the Variable Spiking Graph Neural Operator (VS-GNO) which integrates a sophisticated spectral-spatial convolutional analysis and a previously developed Variable Spiking Neuron (VSN) and energy-error balance loss function. With a non-spiking $L_2$ error baseline of $0.4\%$, VS-GNO can provide a reconstruction error of $0.71\%$ with $15\%$ average spiking in its spectral-only form and $1.04\%$ with $24.5\%$ spiking in its entire form. These results position VS-GNO as a promising step towards energy-efficient, edge-deployable neural operators for real-time sparse-to-dense virtual sensing in complex, highly irregular engineering environments.

cs.LG↗

arXiv2026

Beyond Uniform Sampling: Synergistic Active Learning and Input Denoising for Robust Neural Operators

Neural operators have emerged as fast surrogate models for physics simulations, yet they remain acutely vulnerable to adversarial perturbations, a critical liability for safety-critical digital twin deployments. We present a synergistic defense that combines active learning-based data generation with an input denoising architecture. The active learning component adaptively probes model weaknesses using differential evolution attacks, then generates targeted training data at discovered vulnerability locations while an adaptive smooth-ratio safeguard preserves baseline accuracy. The input denoising component augments the operator architecture with a learnable bottleneck that filters adversarial noise while retaining physics-relevant features. On the viscous Burgers' equation benchmark, the combined approach achieves a 2.04% combined error (1.21% baseline + 0.83% robustness), representing an 87% reduction relative to standard training (15.42% combined) and outperforming both active learning alone (3.42%) and input denoising alone (5.22%). More broadly, our results, combined with cross-architecture vulnerability analysis from prior work, suggest that optimal training data for neural operators is architecture-dependent: because different architectures concentrate sensitivity in distinct input subspaces, uniform sampling cannot adequately cover the vulnerability landscape of all models. These findings have potential implications for the deployment of neural operators in safety-critical energy systems including nuclear reactor monitoring.

cs.LG↗

arXiv2026

Gradient-Free Continual Learning in Spiking Neural Networks via Inter-Spike Interval Regularization

Continual learning, the ability to acquire new tasks sequentially without forgetting prior knowledge, is essential for deploying neural networks in dynamic real-world environments, from nuclear digital twin monitoring to grid-edge fault detection. Existing synaptic importance methods, such as Elastic Weight Consolidation (EWC) and Synaptic Intelligence (SI), rely on gradient computation, making them incompatible with neuromorphic hardware that lacks backpropagation support. We propose ISI-CV, the first gradient-free synaptic importance metric for SNN continual learning, derived from the Coefficient of Variation (CV) of Inter-Spike Intervals (ISIs). Neurons that fire regularly (low CV) encode stable, task-relevant features and are protected from overwriting; neurons with irregular firing are permitted to adapt freely. ISI-CV requires only spike time counters and integer arithmetic, all of which are native to every neuromorphic chip. We evaluate on four benchmarks of increasing difficulty: Split-MNIST, Permuted-MNIST, Split-FashionMNIST, and Split-N-MNIST using real Dynamic Vision Sensor (DVS) event data. Across three seeds, ISI-CV achieves zero forgetting (AF = 0.000 +/- 0.000) on Split-MNIST and Split-FashionMNIST, near-zero forgetting on Permuted-MNIST (AF = 0.001 +/- 0.000), and the highest accuracy with the lowest forgetting on real neuromorphic DVS data (AA = 0.820 +/- 0.012, AF = 0.221 +/- 0.014). On N-MNIST, gradient-based methods produce unreliable importance estimates and perform worse than no regularization; ISI-CV avoids this failure by design.

cs.NE↗

arXiv2026

SCNO: Spiking Compositional Neural Operator -- Towards a Neuromorphic Foundation Model for Nuclear PDE Solving

Neural operators have emerged as powerful surrogates for partial differential equation (PDE) solvers, yet they are typically trained as monolithic models for individual PDEs, require energy-intensive GPU hardware, and must be retrained from scratch when new physics emerge. We introduce the Spiking Compositional Neural Operator (SCNO), a modular architecture combining spiking and conventional components that addresses all three limitations. SCNO maintains a library of small spiking neural operator blocks, each trained on a single elementary differential operator (convection, diffusion, reaction), and composes them through a lightweight input-conditioned aggregator to solve coupled PDEs not seen during block training. A small correction network learns cross-coupling residuals while keeping all blocks and the aggregator frozen, preserving zero-forgetting modular expansion by construction. We evaluate SCNO on eight PDE families including five coupled systems and a nuclear-relevant 1-group neutron diffusion equation. SCNO with correction achieves the lowest relative $L^2$ error on four of five coupled PDEs, outperforming both a monolithic spiking DeepONet (by up to 62%, mean over 3 seeds) and a standard ANN DeepONet (by up to 65%), while requiring only 95K trainable parameters versus 462K for the monolithic baseline. To our knowledge, this is the first compositional spiking neural operator and the first proof-of-concept for modular neuromorphic PDE solving with built-in forgetting-free expansion.

cs.LG↗

arXiv2026

Learning the Stellar Structure Equations via Self-supervised Physics-Informed Neural Networks

Stellar astrophysics relies critically on accurate descriptions of the physical conditions inside stars. Traditional solvers such as \texttt{MESA} (Modules for Experiments in Stellar Astrophysics), which employ adaptive finite-difference methods, can become computationally expensive and challenging to scale for large stellar population synthesis ($>10^9$ stars). In this work, we present an self-supervised physics-informed neural network (PINN) framework that provides a mesh-free and fully differentiable approach to solving the stellar structure equations under hydrostatic and thermal equilibrium. The model takes as input the stellar boundary conditions (at the center and surface) together with the chemical composition, and learns continuous radial profiles for mass $M_r(r)$, pressure $P(r)$, density $ρ(r)$, temperature $T(r)$, and luminosity $L_r(r)$ by enforcing the governing structure equations through physics-based loss terms. To incorporate realistic microphysics, we introduce auxiliary neural networks that approximate the equation of state and opacity tables as smooth, differentiable functions of the local thermodynamic state. These surrogates replace traditional tabulated inputs and enable end-to-end training. Once trained for a given star, the model produces continuous solutions across the entire radial domain without requiring discretization or interpolation. Validation against benchmark \texttt{MESA} models across a range of stellar masses yields a Mean Relative Absolute Error of $3.06\%$ and an average $R^2$ score of $99.98\%$. To our knowledge, this is the first demonstration that the stellar structure equations can be solved in a fully self-supervised and data-free fashion employing PINNs. This work establishes a foundation for scalable, physics-informed emulation of stellar interiors and opens the door to future extensions toward time-dependent stellar evolution.

astro-ph.SR↗

arXiv2026

TrustFed: Enabling Trustworthy Medical AI under Data Privacy Constraints

Protecting patient privacy remains a fundamental barrier to scaling machine learning across healthcare institutions, where centralizing sensitive data is often infeasible due to ethical, legal, and regulatory constraints. Federated learning offers a promising alternative by enabling privacy-preserving, multi-institutional training without sharing raw patient data; however, real-world deployments face severe challenges from data heterogeneity, site-specific biases, and class imbalance, which degrade predictive reliability and render existing uncertainty quantification methods ineffective. Here, we present TrustFed, a federated uncertainty quantification framework that provides distribution-free, finite-sample coverage guarantees under heterogeneous and imbalanced healthcare data, without requiring centralized access. TrustFed introduces a representation-aware client assignment mechanism that leverages internal model representations to enable effective calibration across institutions, along with a soft-nearest threshold aggregation strategy that mitigates assignment uncertainty while producing compact and reliable prediction sets. Using over 430,000 medical images across six clinically distinct imaging modalities, we conduct one of the most comprehensive evaluations of uncertainty-aware federated learning in medical imaging, demonstrating robust coverage guarantees across datasets with diverse class cardinalities and imbalance regimes. By validating TrustFed at this scale and breadth, our study advances uncertainty-aware federated learning from proof-of-concept toward clinically meaningful, modality-agnostic deployment, positioning statistically guaranteed uncertainty as a core requirement for next-generation healthcare AI systems.

cs.LG↗

arXiv2026

SPINONet: Scalable Spiking Physics-informed Neural Operator for Computational Mechanics Applications

Energy efficiency remains a critical challenge in deploying physics-informed operator learning models for computational mechanics and scientific computing, particularly in power-constrained settings such as edge and embedded devices, where repeated operator evaluations in dense networks incur substantial computational and energy costs. To address this challenge, we introduce the Separable Physics-informed Neuroscience-inspired Operator Network (SPINONet), a neuroscience-inspired framework that reduces redundant computation across repeated evaluations while remaining compatible with physics-informed training. SPINONet incorporates regression-friendly neuroscience-inspired spiking neurons through an architecture-aware design that enables sparse, event-driven computation, improving energy efficiency while preserving the continuous, coordinate-differentiable pathways required for computing spatio-temporal derivatives. We evaluate SPINONet on a range of partial differential equations representative of computational mechanics problems, with spatial, temporal, and parametric dependencies in both time-dependent and steady-state settings, and demonstrate predictive performance comparable to conventional physics-informed operator learning approaches despite the induced sparse communication. In addition, limited data supervision in a hybrid setup is shown to improve performance in challenging regimes where purely physics-informed training may converge to spurious solutions. Finally, we provide an analytical discussion linking architectural components and design choices of SPINONet to reductions in computational load and energy consumption.

physics.comp-ph↗

arXiv2026

CoNBONet: Conformalized Neuroscience-inspired Bayesian Operator Network for Reliability Analysis

Time-dependent reliability analysis of nonlinear dynamical systems under stochastic excitations is a critical yet computationally demanding task. Conventional approaches, such as Monte Carlo simulation, necessitate repeated evaluations of computationally expensive numerical solvers, leading to significant computational bottlenecks. To address this challenge, we propose \textit{CoNBONet}, a neuroscience-inspired surrogate model that enables fast, energy-efficient, and uncertainty-aware reliability analysis, providing a scalable alternative to techniques such as Monte Carlo simulations. CoNBONet, short for \textbf{Co}nformalized \textbf{N}euroscience-inspired \textbf{B}ayesian \textbf{O}perator \textbf{Net}work, leverages the expressive power of deep operator networks while integrating neuroscience-inspired neuron models to achieve fast, low-power inference. Unlike traditional surrogates such as Gaussian processes, polynomial chaos expansions, or support vector regression, that may face scalability challenges for high-dimensional, time-dependent reliability problems, CoNBONet offers \textit{fast and energy-efficient inference} enabled by a neuroscience-inspired network architecture, \textit{calibrated uncertainty quantification with theoretical guarantees} via split conformal prediction, and \textit{strong generalization capability} through an operator-learning paradigm that maps input functions to system response trajectories. Validation of the proposed CoNBONet for various nonlinear dynamical systems demonstrates that CoNBONet preserves predictive fidelity, and achieves reliable coverage of failure probabilities, making it a powerful tool for robust and scalable reliability analysis in engineering design.

stat.ML↗

arXiv2026

Adversarial Vulnerabilities in Neural Operator Digital Twins: Gradient-Free Attacks on Nuclear Thermal-Hydraulic Surrogates

Operator learning models are rapidly emerging as the predictive core of digital twins for nuclear and energy systems, promising real-time field reconstruction from sparse sensor measurements. Yet their robustness to adversarial perturbations remains uncharacterized, a critical gap for deployment in safety-critical systems. Here we show that neural operators are acutely vulnerable to extremely sparse (fewer than 1% of inputs), physically plausible perturbations that exploit their sensitivity to boundary conditions. Using gradient-free differential evolution across four operator architectures, we demonstrate that minimal modifications trigger catastrophic prediction failures, increasing relative $L_2$ error from $\sim$1.5% (validated accuracy) to 37-63% while remaining completely undetectable by standard validation metrics. Notably, 100% of successful single-point attacks pass z-score anomaly detection. We introduce the effective perturbation dimension $d_{\text{eff}}$, a Jacobian-based diagnostic that, together with sensitivity magnitude, yields a two-factor vulnerability model explaining why architectures with extreme sensitivity concentration (POD-DeepONet, $d_{\text{eff}} \approx 1$) are not necessarily the most exploitable, since low-rank output projections cap maximum error, while moderate concentration with sufficient amplification (S-DeepONet, $d_{\text{eff}} \approx 4$) produces the highest attack success. Gradient-free search outperforms gradient-based alternatives (PGD) on architectures with gradient pathologies, while random perturbations of equal magnitude achieve near-zero success rates, confirming that the discovered vulnerabilities are structural. Our findings expose a previously overlooked attack surface in operator learning models and establish that these models require robustness guarantees beyond standard validation before deployment.

cs.LG↗

arXiv2026

Sensing Without Colocation: Operator-Based Virtual Instrumentation for Domains Beyond Physical Reach

Classical sensing rests on one foundational assumption: the quantity of interest must be colocated with the measurement device. This is not an engineering convenience. It is the organizing principle of every instrumentation standard developed over the past century, and it fails completely at aviation altitude, where no physical sensor can survive long enough to monitor the cosmic radiation field that irradiates millions of aircrew annually. We establish that this barrier is resolved by a new sensing principle: when the sensor manifold and the target field manifold are physically disjoint, a learned operator bridging them \emph{is} the instrument. We term this \textbf{operator-theoretic virtual sensing} and instantiate it in \textbf{STONe}, which maps \textbf{twelve} ground-based neutron monitors (sparse, indirect, surface-bound) to the complete global dose field at 10{,}000\,m across \textbf{180-day} horizons, achieving sub-millisecond inference where Monte Carlo transport requires hours. Deployed without modification on an NVIDIA Jetson Orin Nano embedded AI platform at 7.3\,W average system power and 143.3\,MB GPU memory footprint; within the envelope of photovoltaic-powered field hardware co-locatable with existing neutron monitor stations, STONe constitutes a physically realizable sensing device of a new category: an instrument whose measurement principle is operator-theoretic and whose deployment constraint is the power budget of remote environmental monitoring infrastructure, not the accessibility of the target domain.

cs.LG↗

arXiv2026

Neural Hodge Corrective Solvers: A Hybrid Iterative-Neural Framework

We introduce the Neural Hodge Corrective Solver (NHCS), a hybrid iterative-neural framework for partial differential equations that embeds learned corrective operators within the Discrete Exterior Calculus (DEC) formulation. The method combines classical Jacobi-Richardson iterations with data-driven corrections to refine numerical solutions while preserving the underlying topological and metric structure. NHCS employs a two-phase training strategy. In the first phase, DEC operators are learned through relative residual minimization from data. In the second phase, these operators are integrated into the iterative solver, and training targets the improvement of convergence through learned corrective updates that remain effective even for inaccurate intermediate solutions. This staggered training enables stable, progressive refinement while maintaining the structure-preserving properties of DEC discretizations. To improve multiscale adaptivity, NHCS introduces a convolutional neural network-based correction term capable of capturing fine-scale solution features via localized updates informed by global context, improving scalability over mesh component-wise neural approaches. Moreover, the proposed framework substantially reduces computational cost by avoiding Newton-Raphson-based training and the associated Jacobian evaluations of parameterized operators. The resulting solver achieves improved efficiency, robustness, and accuracy without compromising numerical stability.

physics.comp-ph↗

arXiv2026

Scalable Random Wavelet Features: Efficient Non-Stationary Kernel Approximation with Convergence Guarantees

Modeling non-stationary processes, where statistical properties vary across the input domain, is a critical challenge in machine learning; yet most scalable methods rely on a simplifying assumption of stationarity. This forces a difficult trade-off: use expressive but computationally demanding models like Deep Gaussian Processes, or scalable but limited methods like Random Fourier Features (RFF). We close this gap by introducing Random Wavelet Features (RWF), a framework that constructs scalable, non-stationary kernel approximations by sampling from wavelet families. By harnessing the inherent localization and multi-resolution structure of wavelets, RWF generates an explicit feature map that captures complex, input-dependent patterns. Our framework provides a principled way to generalize RFF to the non-stationary setting and comes with a comprehensive theoretical analysis, including positive definiteness, unbiasedness, and uniform convergence guarantees. We demonstrate empirically on a range of challenging synthetic and real-world datasets that RWF outperforms stationary random features and offers a compelling accuracy-efficiency trade-off against more complex models, unlocking scalable and expressive kernel methods for a broad class of real-world non-stationary problems.

cs.LG↗

arXiv2026

CortiNet: A Physics-Perception Hybrid Cortical-Inspired Dual-Stream Network for Gallbladder Disease Diagnosis from Ultrasound

Ultrasound imaging is the primary diagnostic modality for detecting Gallbladder diseases due to its non-invasive nature, affordability, and wide accessibility. However, the low resolution and speckle noise inherent to ultrasound images hinder diagnostic reliability, prompting the use of large convolutional neural networks that are difficult to deploy in routine clinical settings. In this work, we propose CortiNet, a lightweight, cortical-inspired dual-stream neural architecture for gallbladder disease diagnosis that integrates physically interpretable multi-scale signal decomposition with perception-driven feature learning. Inspired by parallel processing pathways in the human visual cortex, CortiNet explicitly separates low-frequency structural information from high-frequency perceptual details and processes them through specialized encoding streams. By operating directly on structured, frequency-selective representations rather than raw pixel intensities, the architecture embeds strong physics-based inductive bias, enabling efficient feature learning with a significantly reduced parameter footprint. A late-stage cortical-style fusion mechanism integrates complementary structural and textural cues while preserving computational efficiency. Additionally, we propose a structure-aware explainability framework wherein gradient-weighted class activation mapping is only applied to the structural branch of the proposed CortiNet architecture. This choice allows the model to only focus on the structural features, making it robust against speckle noise. We evaluate CortiNet on 10,692 expert-annotated images spanning nine clinically relevant gallbladder disease categories. Experimental results demonstrate that CortiNet achieves high diagnostic accuracy (98.74%) with only a fraction of the parameters required by conventional deep convolutional models.

cs.CV↗

arXiv2025

NeuroPINNs: Neuroscience Inspired Physics Informed Neural Networks

We introduce NeuroPINNs, a neuroscience-inspired extension of Physics-Informed Neural Networks (PINNs) that incorporates biologically motivated spiking neuron models to achieve energy-efficient PDE solving. Unlike conventional PINNs, which rely on continuously firing activations and therefore incur high computational and energy costs, NeuroPINNs leverage Variable Spiking Neurons (VSNs) to enable sparse, event-driven communication. This makes them particularly well-suited for deployment on neuromorphic hardware and for scenarios with constrained computational resources, such as embedded and edge devices. A central challenge, however, lies in reconciling the discontinuous dynamics of spiking neurons with the smooth residual-based loss formulation required in PINNs. Direct smoothing introduces systematic biases, leading to inaccurate PDE learning. To overcome this, we employ a novel stochastic projection method inspired from upscaled theory that faithfully captures spiking behavior while maintaining compatibility with gradient-based optimization. Standard surrogate backpropagation is used for parameter updates, ensuring computational tractability. We demonstrate the effectiveness of NeuroPINNs on four representative PDE problems across both regular and irregular domains. Furthermore, application of NeuroPINN for linear elastic micromechnics in three dimensions was also explored. Results show that NeuroPINNs achieve high accuracy while substantially reducing communication and energy demands, marking a step toward scalable, neuromorphic-ready scientific machine learning.

physics.comp-ph↗

arXiv2025

Event-driven physics-informed operator learning for reliability analysis

Reliability analysis of engineering systems under uncertainty poses significant computational challenges, particularly for problems involving high-dimensional stochastic inputs, nonlinear system responses, and multiphysics couplings. Traditional surrogate modeling approaches often incur high energy consumption, which severely limits their scalability and deployability in resource-constrained environments. We introduce NeuroPOL, \textit{the first neuroscience-inspired physics-informed operator learning framework} for reliability analysis. NeuroPOL incorporates Variable Spiking Neurons into a physics-informed operator architecture, replacing continuous activations with event-driven spiking dynamics. This innovation promotes sparse communication, significantly reduces computational load, and enables an energy-efficient surrogate model. The proposed framework lowers both computational and power demands, supporting real-time reliability assessment and deployment on edge devices and digital twins. By embedding governing physical laws into operator learning, NeuroPOL builds physics-consistent surrogates capable of accurate uncertainty propagation and efficient failure probability estimation, even for high-dimensional problems. We evaluate NeuroPOL on five canonical benchmarks, the Burgers equation, Nagumo equation, two-dimensional Poisson equation, two-dimensional Darcy equation, and incompressible Navier-Stokes equation with energy coupling. Results show that NeuroPOL achieves reliability measures comparable to standard physics-informed operators, while introducing significant communication sparsity, enabling scalable, distributed, and energy-efficient deployment.

cs.LG↗

arXiv2025

Competition is the key: A Game Theoretic Causal Discovery Approach

Causal discovery remains a central challenge in machine learning, yet existing methods face a fundamental gap: algorithms like GES and GraN-DAG achieve strong empirical performance but lack finite-sample guarantees, while theoretically principled approaches fail to scale. We close this gap by introducing a game-theoretic reinforcement learning framework for causal discovery, where a DDQN agent directly competes against a strong baseline (GES or GraN-DAG), always warm-starting from the opponent's solution. This design yields three provable guarantees: the learned graph is never worse than the opponent, warm-starting strictly accelerates convergence, and most importantly, with high probability the algorithm selects the true best candidate graph. To the best of our knowledge, our result makes a first-of-its-kind progress in explaining such finite-sample guarantees in causal discovery: on synthetic SEMs (30 nodes), the observed error probability decays with n, tightly matching theory. On real-world benchmarks including Sachs, Asia, Alarm, Child, Hepar2, Dream, and Andes, our method consistently improves upon GES and GraN-DAG while remaining theoretically safe. Remarkably, it scales to large graphs such as Hepar2 (70 nodes), Dream (100 nodes), and Andes (220 nodes). Together, these results establish a new class of RL-based causal discovery algorithms that are simultaneously provably consistent, sample-efficient, and practically scalable, marking a decisive step toward unifying empirical performance with rigorous finite-sample theory.

cs.LG↗

arXiv2025

Scalable h-adaptive probabilistic solver for time-independent and time-dependent systems

Solving partial differential equations (PDEs) within the framework of probabilistic numerics offers a principled approach to quantifying epistemic uncertainty arising from discretization. By leveraging Gaussian process regression and imposing the governing PDE as a constraint at a finite set of collocation points, probabilistic numerics delivers mesh-free solutions at arbitrary locations. However, the high computational cost, which scales cubically with the number of collocation points, remains a critical bottleneck, particularly for large-scale or high-dimensional problems. We propose a scalable enhancement to this paradigm through two key innovations. First, we develop a stochastic dual descent algorithm that reduces the per-iteration complexity from cubic to linear in the number of collocation points, enabling tractable inference. Second, we exploit a clustering-based active learning strategy that adaptively selects collocation points to maximize information gain while minimizing computational expense. Together, these contributions result in an $h$-adaptive probabilistic solver that can scale to a large number of collocation points. We demonstrate the efficacy of the proposed solver on benchmark PDEs, including two- and three-dimensional steady-state elliptic problems, as well as a time-dependent parabolic PDE formulated in a space-time setting.

stat.ML↗

arXiv2025

Physics- and geometry-aware spatio-spectral graph neural operator for time-independent and time-dependent PDEs

Solving partial differential equations (PDEs) efficiently and accurately remains a cornerstone challenge in science and engineering, especially for problems involving complex geometries and limited labeled data. We introduce a Physics- and Geometry- Aware Spatio-Spectral Graph Neural Operator ($π$G-Sp$^2$GNO) for learning the solution operators of time-independent and time-dependent PDEs. The proposed approach first improves upon the recently developed Sp$^2$GNO by enabling geometry awareness and subsequently exploits the governing physics to learn the underlying solution operator in a simulation-free setup. While the spatio-spectral structure present in the proposed architecture allows multiscale learning, two separate strategies for enabling geometry awareness is introduced in this paper. For time dependent problems, we also introduce a novel hybrid physics informed loss function that combines higher-order time-marching scheme with upscaled theory inspired stochastic projection scheme. This allows accurate integration of the physics-information into the loss function. The performance of the proposed approach is illustrated on number of benchmark examples involving regular and complex domains, variation in geometry during inference, and time-independent and time-dependent problems. The results obtained illustrate the efficacy of the proposed approach as compared to the state-of-the-art physics-informed neural operator algorithms in the literature.

cs.LG↗