Deep neural networks are framed as discrete dynamical systems, and PINNs are shown to approximate the same PDE dynamics as classical discretization but through dense parameter representations rather than structured stencils.
A proposal on machine learning via dynamical systems.Com- munications in Mathematics and Statistics, 5(1):1–11, 2017
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Deep Neural Networks as Discrete Dynamical Systems: Implications for Physics-Informed Learning
Deep neural networks are framed as discrete dynamical systems, and PINNs are shown to approximate the same PDE dynamics as classical discretization but through dense parameter representations rather than structured stencils.