Unified generalization bounds for PINNs and VPINNs are derived by representing nonlinear differential operators via Taylor expansion and Koopman theory, showing high-rank networks generalize well while nonlinearity exponentially enlarges the bounds.
Physics-informed neural networks: A review of methodological evolution, theoretical foundations, and interdisciplinary frontiers toward next-generation scientific computing
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Unified generalization analysis for physics informed neural networks
Unified generalization bounds for PINNs and VPINNs are derived by representing nonlinear differential operators via Taylor expansion and Koopman theory, showing high-rank networks generalize well while nonlinearity exponentially enlarges the bounds.