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✅   Implicit Neural Differential Model for Spatiotemporal Dynamics

tech

:2504.02260v1 Announce Type: cross Abstract: 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.

arXiv     Apr 04, 2025