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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IR-PINNs improve long-time accuracy for evolution equations by enforcing integral constraints over time sub-intervals and using adaptive collocation point sampling.
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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.
- Sinc Kolmogorov-Arnold network and its application for solving PDEs with singularities