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.
Solving pdes by variational physics-informed neural networks: an a posteriori error analysis.Annali dell’Universita di Ferrara, 68:575–595, 2022
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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.