Deepak Akhare

Deepak Akhare, Pan Du, Tengfei Luo et al.

Hybrid neural-physics modeling frameworks through differentiable programming have emerged as powerful tools in scientific machine learning, enabling the integration of known physics with data-driven learning to improve prediction accuracy and generalizability. However, most existing hybrid frameworks rely on explicit recurrent formulations, which suffer from numerical instability and error accumulation during long-horizon forecasting. In this work, we introduce Im-PiNDiff, a novel implicit physics-integrated neural differentiable solver for stable and accurate modeling of spatiotemporal dynamics. Inspired by deep equilibrium models, Im-PiNDiff advances the state using implicit fixed-point layers, enabling robust long-term simulation while remaining fully end-to-end differentiable. To enable scalable training, we introduce a hybrid gradient propagation strategy that integrates adjoint-state methods with reverse-mode automatic differentiation. This approach eliminates the need to store intermediate solver states and decouples memory complexity from the number of solver iterations, significantly reducing training overhead. We further incorporate checkpointing techniques to manage memory in long-horizon rollouts. Numerical experiments on various spatiotemporal PDE systems, including advection-diffusion processes, Burgers' dynamics, and multi-physics chemical vapor infiltration processes, demonstrate that Im-PiNDiff achieves superior predictive performance, enhanced numerical stability, and substantial reductions in memory and runtime cost relative to explicit and naive implicit baselines. This work provides a principled, efficient, and scalable framework for hybrid neural-physics modeling.

Mohammad Amin Nabian, Sudeep Chavare, Deepak Akhare et al.

Crashworthiness assessment is a critical aspect of automotive design, traditionally relying on high-fidelity finite element (FE) simulations that are computationally expensive and time-consuming. This work presents an exploratory comparative study on developing machine learning-based surrogate models for efficient prediction of structural deformation in crash scenarios using the NVIDIA PhysicsNeMo framework. Given the limited prior work applying machine learning to structural crash dynamics, the primary contribution lies in demonstrating the feasibility and engineering utility of the various modeling approaches explored in this work. We investigate two state-of-the-art neural network architectures for modeling crash dynamics: MeshGraphNet, and Transolver. Additionally, we examine three strategies for modeling transient dynamics: time-conditional, the standard Autoregressive approach, and a stability-enhanced Autoregressive scheme incorporating rollout-based training. The models are evaluated on a comprehensive Body-in-White (BIW) crash dataset comprising 150 detailed FE simulations using LS-DYNA. The dataset represents a structurally rich vehicle assembly with over 200 components, including 38 key components featuring variable thickness distributions to capture realistic manufacturing variability. Each model utilizes the undeformed mesh geometry and component characteristics as inputs to predict the spatiotemporal evolution of the deformed mesh during the crash sequence. Evaluation results show that the models capture the overall deformation trends with reasonable fidelity, demonstrating the feasibility of applying machine learning to structural crash dynamics. Although not yet matching full FE accuracy, the models achieve orders-of-magnitude reductions in computational cost, enabling rapid design exploration and early-stage optimization in crashworthiness evaluation.