arXiv subjects

Khemraj Shukla

Publications and source records attributed to Khemraj Shukla.

At least 19 recordsLinked to original sources

arXiv2026

Fixed and Adaptive Topological DeepONets: Functional Measurements on Hausdorff Locally Convex Spaces

Deep Operator Networks (DeepONets; arXiv:1910.03193) typically encode an input function through point values on a fixed discretization. Building on the Topological DeepONet framework of Ismailov (arXiv:2603.11972), we replace point samples by continuous linear functionals drawn from the continuous dual of a Hausdorff locally convex space $({V},\{p_α\}_{α\in A})$, whose topology is generated by a point-separating family of seminorms rather than a single norm, and develop fixed and adaptive functional measurement systems. Measurements are combined with the coefficient-space Two-Step procedure of Lee and Shin (arXiv:2309.01020), while a training-only decoder and regularization stabilize the adaptive coordinates. We derive a discrete error decomposition separating measurement, output-basis, and neural-approximation errors, together with a Barron-rate refinement. The framework is evaluated on the antiderivative operator, a non-normable locally convex input space, heterogeneous Darcy flow, a controlled operator, and fixed-time and time-evolving Navier-Stokes vorticity operators. In the heterogeneous Darcy problem, the functional models retain nearly resolution-independent errors of 5.5-5.6% on unseen grids, while in the controlled problem adaptive measurements reduce the mean error below 1.2%. For the fixed-time Navier-Stokes problem, the Adaptive Topological DeepONet is the most accurate DeepONet-based model, attaining a mean relative $L^2$ error of 1.685% +/- 0.017% using 128 functional coordinates. A comparably sized Fourier neural operator (FNO; arXiv:2010.08895) achieves the lower error 0.832% +/- 0.172%, but requires the full 64x64 input field, twice the training time, and 10.7x greater peak GPU memory. The formulation provides compact, interpretable, and discretization-portable coordinates in the continuous dual $V'$, including for non-normable input spaces.

cs.LG↗

arXiv2026

Uncertainty Quantification in PINNs for Turbulent Flows: Bayesian Inference and Repulsive Ensembles

Physics-informed neural networks (PINNs) have emerged as a promising framework for solving inverse problems governed by partial differential equations (PDEs), including the reconstruction of turbulent flow fields from sparse data. However, most existing PINN formulations are deterministic and do not provide reliable quantification of epistemic uncertainty, which is critical for ill-posed problems such as data-driven Reynolds-averaged Navier-Stokes (RANS) modeling. In this work, we develop and systematically evaluate a set of probabilistic extensions of PINNs for uncertainty quantification in turbulence modeling. The proposed framework combines (i) Bayesian PINNs with Hamiltonian Monte Carlo sampling and a tempered multi-component likelihood, (ii) Monte Carlo dropout, and (iii) repulsive deep ensembles that enforce diversity in function space. Particular emphasis is placed on the role of ensemble diversity and likelihood tempering in improving uncertainty calibration for PDE-constrained inverse problems. The methods are assessed on a hierarchy of test cases, including the Van der Pol oscillator and turbulent flow past a circular cylinder at Reynolds numbers Re=3,900 (direct numerical simulation data) and Re = 10,000 (experimental particle image velocimetry data). The results demonstrate that Bayesian PINNs provide the most consistent uncertainty estimates across all inferred quantities, while function-space repulsive ensembles offer a computationally efficient approximation with competitive accuracy for primary flow variables. These findings provide quantitative insight into the trade-offs between accuracy, computational cost, and uncertainty calibration in physics-informed learning, and offer practical guidance for uncertainty quantification in data-driven turbulence modeling.

cs.LG↗

arXiv2026

Body-Free Simulation of Three-Dimensional Turbulent Cylinder Wakes

We present a body-free simulation framework for three-dimensional turbulent cylinder wakes, in which the upstream cylinder is not explicitly resolved. Instead, the incompressible Navier--Stokes equations are solved in a simplified rectangular domain, and the inflow is prescribed using velocity profiles extracted from experimental measurements or pre-computed direct numerical simulations (DNS). We show that, for the Reynolds numbers considered here, prescribing low-dimensional inflow information at a single downstream location is sufficient to reconstruct the principal wake dynamics, including three-dimensionality, coherent vortex shedding, Reynolds-stress distributions, and spectral content, for $Re=500$, $5{,}000$, and $11{,}000$. Comparisons with full-body DNS and particle image velocimetry (PIV) measurements show good agreement in mean velocity profiles, Reynolds stresses, and dominant shedding frequencies. A local stability analysis further shows that successful wake reconstruction is obtained when the imposed inflow is selected from the absolutely unstable near-wake region. The results support existing theory that the essential dynamics of bluff-body wakes are governed primarily by the instability of the near-wake profile rather than by the explicit presence of the body itself. The role of the onset of three-dimensionality is elucidated for first time. Relative to full DNS with the cylinder present, the proposed body-free simulation offers a substantial reduction in computational cost, providing a physically interpretable and computationally efficient route for wake reconstruction, reduced-complexity simulation, and flow-control studies.

physics.flu-dyn↗

arXiv2026

Curvature-Aware Optimization for High-Accuracy Physics-Informed Neural Networks

Efficient and robust optimization is essential for neural networks, enabling scientific machine learning models to converge rapidly to very high accuracy -- faithfully capturing complex physical behavior governed by differential equations. In this work, we present advanced optimization strategies to accelerate the convergence of physics-informed neural networks (PINNs) for challenging partial (PDEs) and ordinary differential equations (ODEs). Specifically, we provide efficient implementations of the Natural Gradient (NG) optimizer, Self-Scaling BFGS and Broyden optimizers, and demonstrate their performance on problems including the Helmholtz equation, Stokes flow, inviscid Burgers equation, Euler equations for high-speed flows, and stiff ODEs arising in pharmacokinetics and pharmacodynamics. Beyond optimizer development, we also propose new PINN-based methods for solving the inviscid Burgers and Euler equations, and compare the resulting solutions against high-order numerical methods to provide a rigorous and fair assessment. Finally, we address the challenge of scaling these quasi-Newton optimizers for batched training, enabling efficient and scalable solutions for large data-driven problems.

cs.LG↗

arXiv2026

Drug Release Modeling using Physics-Informed Neural Networks

Accurate modeling of drug release is essential for designing and developing controlled-release systems. Classical models (Fick, Higuchi, Peppas) rely on simplifying assumptions that limit their accuracy in complex geometries and release mechanisms. Here, we propose a novel approach using Physics-Informed Neural Networks (PINNs) and Bayesian PINNs (BPINNs) for predicting release from planar, 1D-wrinkled, and 2D-crumpled films. This approach uniquely integrates Fick's diffusion law with limited experimental data to enable accurate long-term predictions from short-term measurements, and is systematically benchmarked against classical drug release models. We embedded Fick's second law into PINN as loss with 10,000 Latin-hypercube collocation points and utilized previously published experimental datasets to assess drug release performance through mean absolute error (MAE) and root mean square error (RMSE), considering noisy conditions and limited-data scenarios. Our approach reduced mean error by up to 40% relative to classical baselines across all film types. The PINN formulation achieved RMSE <0.05 utilizing only the first 6% of the release time data (reducing 94% of release time required for the experiments) for the planar film. For wrinkled and crumpled films, the PINN reached RMSE <0.05 in 33% of the release time data. BPINNs provide tighter and more reliable uncertainty quantification under noise. By combining physical laws with experimental data, the proposed framework yields highly accurate long-term release predictions from short-term measurements, offering a practical route for accelerated characterization and more efficient early-stage drug release system formulation.

cs.LG↗

arXiv2026

Optimizing the Optimizer for Physics-Informed Neural Networks and Kolmogorov-Arnold Networks

Physics-Informed Neural Networks (PINNs) have revolutionized the computation of PDE solutions by integrating partial differential equations (PDEs) into the neural network's training process as soft constraints, becoming an important component of the scientific machine learning (SciML) ecosystem. More recently, physics-informed Kolmogorv-Arnold networks (PIKANs) have also shown to be effective and comparable in accuracy with PINNs. In their current implementation, both PINNs and PIKANs are mainly optimized using first-order methods like Adam, as well as quasi-Newton methods such as BFGS and its low-memory variant, L-BFGS. However, these optimizers often struggle with highly non-linear and non-convex loss landscapes, leading to challenges such as slow convergence, local minima entrapment, and (non)degenerate saddle points. In this study, we investigate the performance of Self-Scaled BFGS (SSBFGS), Self-Scaled Broyden (SSBroyden) methods and other advanced quasi-Newton schemes, including BFGS and L-BFGS with different line search strategies. These methods dynamically rescale updates based on historical gradient information, thus enhancing training efficiency and accuracy. We systematically compare these optimizers using both PINNs and PIKANs on key challenging PDEs, including the Burgers, Allen-Cahn, Kuramoto-Sivashinsky, Ginzburg-Landau, and Stokes equations. Additionally, we evaluate the performance of SSBFGS and SSBroyden for Deep Operator Network (DeepONet) architectures, demonstrating their effectiveness for data-driven operator learning. Our findings provide state-of-the-art results with orders-of-magnitude accuracy improvements without the use of adaptive weights or any other enhancements typically employed in PINNs.

cs.LG↗

arXiv2026

A Neural Operator Emulator for Coastal and Riverine Shallow Water Dynamics

Coastal regions and river floodplains are particularly vulnerable to the impacts of extreme weather events. Accurate real-time forecasting of hydrodynamic processes in these areas is essential for infrastructure planning and climate adaptation. Yet high-fidelity numerical models are often too computationally expensive for real-time use, and lower-cost approaches, such as traditional model order reduction algorithms or conventional neural networks, typically struggle to generalize to out-of-distribution conditions. In this study, we present the Multiple-Input Temporal Operator Network (MITONet), a novel autoregressive neural emulator that employs latent-space operator learning to efficiently approximate high-dimensional numerical solvers for complex, nonlinear problems that are governed by time-dependent, parameterized partial differential equations. We showcase MITONet's predictive capabilities by forecasting regional tide-driven dynamics in the Shinnecock Inlet in New York and riverine flow in a section of the Red River in Louisiana, both described by the two-dimensional shallow-water equations (2D SWE), while incorporating initial conditions, time-varying boundary conditions, and domain parameters such as the bottom friction coefficient. Despite the distinct flow regimes, the complex geometries and meshes, and the wide range of bottom friction coefficients studied, MITONet displays consistently high predictive skill, with anomaly correlation coefficients above 0.9, a maximum normalized root mean square error of 0.011, and computational speedups between 100x-1,250x, even for 175 days of autoregressive rollout forecast from random initial conditions and with unseen parameter values.

cs.CE↗

arXiv2026

Complex Valued Deep Operator Network (DeepONet) $[\mathcal{G}]$ for Three Dimensional Maxwell's Equations: $\mathcal{G} \in \mathbb{C}^{m \times n}$

Maxwell's equations, a system of linear partial differential equations (PDEs), describe the behavior of electric and magnetic fields in time and space and are essential for many important electromagnetic applications. Although numerical methods have been applied successfully in the past, the primary challenge in solving these equations arises from the frequency of electromagnetic fields, which depends on the shape and size of the objects to be resolved. Since the domain of influence for these equations is compactly supported, even a small perturbation in frequency necessitates a new discretization of Maxwell's equations, resulting in substantial computational costs. In this work, we investigate the potential of neural operators, particularly the Deep Operator Network (DeepONet) and its variants, as a surrogate model for Maxwell's equations. Existing DeepONet implementations are restricted to real-valued data in $R^n$, but since the time-harmonic Maxwell's equations yield solutions in the complex domain $C^n$, a specialized architecture is required to handle complex algebra. We propose a formulation of DeepONet for complex data, define the forward pass in the complex domain, and adopt a reparametrized version of DeepONet for more efficient training. We also propose a unified framework to combine a plurality of DeepONets, trained for multiple electromagnetic field components, to incorporate the boundary condition. We conduct computational experiments on a 3D metallic sphere without singularities and on a metallic almond-shaped target to demonstrate the effectiveness of the proposed method for problems involving singularity-prone solutions. As shown by computational experiments, our method significantly enhances the efficiency of predicting scattered fields from a spherical object at arbitrary high frequencies.

physics.comp-ph↗

arXiv2025

GIMLET: Generalizable and Interpretable Model Learning through Embedded Thermodynamics

We develop a data-driven framework for discovering constitutive relations in models of fluid flow and scalar transport. Under the assumption that velocity and/or scalar fields are measured, our approach infers unknown closure terms in the governing equations as neural networks. The target to be discovered is the constitutive relations only, while the temporal derivative, convective transport terms, and pressure-gradient term in the governing equations are prescribed. The formulation is rooted in a variational principle from non-equilibrium thermodynamics, where the dynamics is defined by a free-energy functional and a dissipation functional. The unknown constitutive terms arise as functional derivatives of these functionals with respect to the state variables. To enable a flexible and structured model discovery, the free-energy and dissipation functionals are parameterized using neural networks, while their functional derivatives are obtained via automatic differentiation. This construction enforces thermodynamic consistency by design, guaranteeing monotonic decay of the total free energy and non-negative entropy production. The resulting method, termed GIMLET (Generalizable and Interpretable Model Learning through Embedded Thermodynamics), avoids reliance on a predefined library of candidate functions, unlike sparse regression or symbolic identification approaches. The learned models are generalizable in that functionals identified from one dataset can be transferred to distinct datasets governed by the same underlying equations. Moreover, the inferred free-energy and dissipation functions provide direct physical interpretability of the learned dynamics. The framework is demonstrated on several benchmark systems, including the viscous Burgers equation, the Kuramoto--Sivashinsky equation, and the incompressible Navier--Stokes equations for both Newtonian and non-Newtonian fluids.

physics.flu-dyn↗

arXiv2025

Retrofitting Earth System Models with Cadence-Limited Neural Operator Updates

Coarse resolution, imperfect parameterizations, and uncertain initial states and forcings limit Earth-system model (ESM) predictions. Traditional bias correction via data assimilation improves constrained simulations but offers limited benefit once models run freely. We introduce an operator-learning framework that maps instantaneous model states to bias-correction tendencies and applies them online during integration. Building on a U-Net backbone, we develop two operator architectures Inception U-Net (IUNet) and a multi-scale network (M\&M) that combine diverse upsampling and receptive fields to capture multiscale nonlinear features under Energy Exascale Earth System Model (E3SM) runtime constraints. Trained on two years E3SM simulations nudged toward ERA5 reanalysis, the operators generalize across height levels and seasons. Both architectures outperform standard U-Net baselines in offline tests, indicating that functional richness rather than parameter count drives performance. In online hybrid E3SM runs, M\&M delivers the most consistent bias reductions across variables and vertical levels. The ML-augmented configurations remain stable and computationally feasible in multi-year simulations, providing a practical pathway for scalable hybrid modeling. Our framework emphasizes long-term stability, portability, and cadence-limited updates, demonstrating the utility of expressive ML operators for learning structured, cross-scale relationships and retrofitting legacy ESMs.

cs.LG↗

arXiv2025

Representation Meets Optimization: Training PINNs and PIKANs for Gray-Box Discovery in Systems Pharmacology

Physics-Informed Kolmogorov-Arnold Networks (PIKANs) are gaining attention as an effective counterpart to the original multilayer perceptron-based Physics-Informed Neural Networks (PINNs). Both representation models can address inverse problems and facilitate gray-box system identification. However, a comprehensive understanding of their performance in terms of accuracy and speed remains underexplored. In particular, we introduce a modified PIKAN architecture, tanh-cPIKAN, which is based on Chebyshev polynomials for parametrization of the univariate functions with an extra nonlinearity for enhanced performance. We then present a systematic investigation of how choices of the optimizer, representation, and training configuration influence the performance of PINNs and PIKANs in the context of systems pharmacology modeling. We benchmark a wide range of first-order, second-order, and hybrid optimizers, including various learning rate schedulers. We use the new Optax library to identify the most effective combinations for learning gray-boxes under ill-posed, non-unique, and data-sparse conditions. We examine the influence of model architecture (MLP vs. KAN), numerical precision (single vs. double), the need for warm-up phases for second-order methods, and sensitivity to the initial learning rate. We also assess the optimizer scalability for larger models and analyze the trade-offs introduced by JAX in terms of computational efficiency and numerical accuracy. Using two representative systems pharmacology case studies - a pharmacokinetics model and a chemotherapy drug-response model - we offer practical guidance on selecting optimizers and representation models/architectures for robust and efficient gray-box discovery. Our findings provide actionable insights for improving the training of physics-informed networks in biomedical applications and beyond.

q-bio.QM↗

arXiv2025

H3PC: Hypersonic, High-Order, High-Performance Code with Adaptive Mesh Refinement and Real Chemistry

We have developed a hypersonic high-order, high-performance code (H$^3$PC) utilizing the ``Trixi.jl" framework in order to simulate both non-reactive and chemically reactive compressible Euler and Navier-Stokes equations for complex three-dimensional geometries. H$^3$PC is parallel on CPU platforms and can perform exascale parallel computations of hypersonic turbulent flows. The numerical approach is based on the discontinuous Galerkin spectral element method, satisfying the entropy and energy stability conditions for the Euler equations. H$^3$PC can perform simulations of high-speed flows from subsonic to hypersonic speeds based on frozen, equilibrium, and non-equilibrium chemistry modeling of the gas mixture, using the \texttt{Mutation.jl} , which is a Julia package developed to wrap the C++-based Mutation++ library. H$^3$PC can also perform parallel adaptive mesh refinement for two- and three-dimensional Euler and Navier-Stokes discretizations with non-conforming elements. In this study, we first demonstrate the successful integration of Mutation++ into the H$^3$PC solver, and then verify its accuracy through simulations of Taylor-Green vortex flow, supersonic flow past a square and circular cylinder, and hypersonic P8-inlet.

physics.comp-ph↗

arXiv2025

Deep Operator Neural Network Model Predictive Control

In this paper, we consider the design of model predictive control (MPC) algorithms based on deep operator neural networks (DeepONets). These neural networks are capable of accurately approximating real and complex valued solutions of continuous time nonlinear systems without relying on recurrent architectures. The DeepONet architecture is made up of two feedforward neural networks: the branch network, which encodes the input function space, and the trunk network, which represents dependencies on temporal variables or initial conditions. Utilizing the original DeepONet architecture as a predictor within MPC for Multi Input Multi Output (MIMO) systems requires multiple branch networks, to generate multi output predictions, one for each input. Moreover, to predict multiple time steps into the future, the network has to be evaluated multiple times. Motivated by this, we introduce a multi step DeepONet (MS-DeepONet) architecture that computes in one shot multi step predictions of system outputs from multi step input sequences, which is better suited for MPC. We prove that the MS DeepONet is a universal approximator in terms of multi step sequence prediction. Additionally, we develop automated hyper parameter selection strategies and implement MPC frameworks using both the standard DeepONet and the proposed MS DeepONet architectures in PyTorch. The implementation is publicly available on GitHub. Simulation results demonstrate that MS-DeepONet consistently outperforms the standard DeepONet in learning and predictive control tasks across several nonlinear benchmark systems: the van der Pol oscillator, the quadruple tank process, and a cart pendulum unstable system, where it successfully learns and executes multiple swing up and stabilization policies.

math.OC↗

arXiv2025

FMEnets: Flow, Material, and Energy networks for non-ideal plug flow reactor design

We propose FMEnets, a physics-informed machine learning framework for the design and analysis of non-ideal plug flow reactors. FMEnets integrates the fundamental governing equations (Navier-Stokes for fluid flow, material balance for reactive species transport, and energy balance for temperature distribution) into a unified multi-scale network model. The framework is composed of three interconnected sub-networks with independent optimizers that enable both forward and inverse problem-solving. In the forward mode, FMEnets predicts velocity, pressure, species concentrations, and temperature profiles using only inlet and outlet information. In the inverse mode, FMEnets utilizes sparse multi-residence-time measurements to simultaneously infer unknown kinetic parameters and states. FMEnets can be implemented either as FME-PINNs, which employ conventional multilayer perceptrons, or as FME-KANs, based on Kolmogorov-Arnold Networks. Comprehensive ablation studies highlight the critical role of the FMEnets architecture in achieving accurate predictions. Specifically, FME-KANs are more robust to noise than FME-PINNs, although both representations are comparable in accuracy and speed in noise-free conditions. The proposed framework is applied to three different sets of reaction scenarios and is compared with finite element simulations. FMEnets effectively captures the complex interactions, achieving relative errors less than 2.5% for the unknown kinetic parameters. The new network framework not only provides a computationally efficient alternative for reactor design and optimization, but also opens new avenues for integrating empirical correlations, limited and noisy experimental data, and fundamental physical equations to guide reactor design.

cs.LG↗

arXiv2025

$PINN - a Domain Decomposition Method for Bayesian Physics-Informed Neural Networks

Physics-Informed Neural Networks (PINNs) are a novel computational approach for solving partial differential equations (PDEs) with noisy and sparse initial and boundary data. Although, efficient quantification of epistemic and aleatoric uncertainties in big multi-scale problems remains challenging. We propose \$PINN a novel method of computing global uncertainty in PDEs using a Bayesian framework, by combining local Bayesian Physics-Informed Neural Networks (BPINN) with domain decomposition. The solution continuity across subdomains is obtained by imposing the flux continuity across the interface of neighboring subdomains. To demonstrate the effectiveness of \$PINN, we conduct a series of computational experiments on PDEs in 1D and 2D spatial domains. Although we have adopted conservative PINNs (cPINNs), the method can be seamlessly extended to other domain decomposition techniques. The results infer that the proposed method recovers the global uncertainty by computing the local uncertainty exactly more efficiently as the uncertainty in each subdomain can be computed concurrently. The robustness of \$PINN is verified by adding uncorrelated random noise to the training data up to 15% and testing for different domain sizes.

cs.LG↗

arXiv2025

Leveraging Deep Operator Networks (DeepONet) for Acoustic Full Waveform Inversion (FWI)

Full Waveform Inversion (FWI) is an important geophysical technique considered in subsurface property prediction. It solves the inverse problem of predicting high-resolution Earth interior models from seismic data. Traditional FWI methods are computationally demanding. Inverse problems in geophysics often face challenges of non-uniqueness due to limited data, as data are often collected only on the surface. In this study, we introduce a novel methodology that leverages Deep Operator Networks (DeepONet) to attempt to improve both the efficiency and accuracy of FWI. The proposed DeepONet methodology inverts seismic waveforms for the subsurface velocity field. This approach is able to capture some key features of the subsurface velocity field. We have shown that the architecture can be applied to noisy seismic data with an accuracy that is better than some other machine learning methods. We also test our proposed method with out-of-distribution prediction for different velocity models. The proposed DeepONet shows comparable and better accuracy in some velocity models than some other machine learning methods. To improve the FWI workflow, we propose using the DeepONet output as a starting model for conventional FWI and that it may improve FWI performance. While we have only shown that DeepONet facilitates faster convergence than starting with a homogeneous velocity field, it may have some benefits compared to other approaches to constructing starting models. This integration of DeepONet into FWI may accelerate the inversion process and may also enhance its robustness and reliability.

cs.LG↗

arXiv2025

Discovering Partially Known Ordinary Differential Equations: a Case Study on the Chemical Kinetics of Cellulose Degradation

The degree of polymerization (DP) is one of the methods for estimating the aging of the polymer based insulation systems, such as cellulose insulation in power components. The main degradation mechanisms in polymers are hydrolysis, pyrolysis, and oxidation. These mechanisms combined cause a reduction of the DP. However, the data availability for these types of problems is usually scarce. This study analyzes insulation aging using cellulose degradation data from power transformers. The aging problem for the cellulose immersed in mineral oil inside power transformers is modeled with ordinary differential equations (ODEs). We recover the governing equations of the degradation system using Physics-Informed Neural Networks (PINNs) and symbolic regression. We apply PINNs to discover the Arrhenius equation's unknown parameters in the Ekenstam ODE describing cellulose contamination content and the material aging process related to temperature for synthetic data and real DP values. A modification of the Ekenstam ODE is given by Emsley's system of ODEs, where the rate constant expressed by the Arrhenius equation decreases in time with the new formulation. We use PINNs and symbolic regression to recover the functional form of one of the ODEs of the system and to identify an unknown parameter.

cs.LG↗

arXiv2025

Neural Operator Modeling of Platelet Geometry and Stress in Shear Flow

Thrombosis involves processes spanning large-scale fluid flow to sub-cellular events such as platelet activation. Traditional CFD approaches often treat blood as a continuum, which can limit their ability to capture these microscale phenomena. In this paper, we introduce a neural operator-based surrogate model to bridge this gap. Our approach employs DeepONet, trained on high-fidelity particle dynamics simulations performed in LAMMPS under a single shear flow condition. The model predicts both platelet membrane deformation and accumulated stress over time, achieving a mode error of ~0.3% under larger spatial filtering radii. At finer scales, the error increases, suggesting a correlation between the DeepONet architecture's capacity and the spatial resolution it can accurately learn. These findings highlight the importance of refining the trunk network to capture localized discontinuities in stress data. Potential strategies include using deeper trunk nets or alternative architectures optimized for graph-structured meshes, further improving accuracy for high-frequency features. Overall, the results demonstrate the promise of neural operator-based surrogates for multi-scale platelet modeling. By reducing computational overhead while preserving accuracy, our framework can serve as a critical component in future simulations of thrombosis and other micro-macro fluid-structure problems.

physics.flu-dyn↗