PINNs fail on spurious solutions admitted by the residual loss; adaptive pseudo-time stepping with Jacobian-based step selection improves accuracy and robustness on PDE benchmarks.
Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations.Science, 367(6481):1026–1030
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DDS-PINN uses localized neural networks plus a unified global loss to model multiscale fluid flows with long-range dependencies, achieving CFD-comparable accuracy on laminar backward-facing step flow with zero data and O(10^-4) error on turbulent flow with only 500 supervision points.
citing papers explorer
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When PINNs Go Wrong: Pseudo-Time Stepping Against Spurious Solutions
PINNs fail on spurious solutions admitted by the residual loss; adaptive pseudo-time stepping with Jacobian-based step selection improves accuracy and robustness on PDE benchmarks.
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Multiscale Physics-Informed Neural Network for Complex Fluid Flows with Long-Range Dependencies
DDS-PINN uses localized neural networks plus a unified global loss to model multiscale fluid flows with long-range dependencies, achieving CFD-comparable accuracy on laminar backward-facing step flow with zero data and O(10^-4) error on turbulent flow with only 500 supervision points.