Deep Neural Networks as Discrete Dynamical Systems: Implications for Physics-Informed Learning

arXiv:2601.00473v3 Announce Type: replace Abstract: We revisit the analogy between feed-forward deep neural networks (DNNs) and discrete dynamical systems derived from neural integral equations and their corresponding partial differential equation (PDE) forms. A comparative analysis between the numerical/exact solutions of the Burgers' and Eikonal equations, and the same obtained via PINNs is presented. We show that PINN learning provides a different computational pathway compared to standard numerical discretization in approximating essentially the same underlying dynamics of the system. With

Source: arXiv cs.LG — read the full report at the original publisher.

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