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.
Config: Towards conflict-free training of physics informed neural networks
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HRGrad resolves gradient conflicts in multi-task learning for asymptotic-preserving neural networks by encoding small parameters and using a gradient alignment metric, enabling stable training across all Knudsen numbers for BGK and linear transport equations.
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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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Conflict-Aware Harmonized Rotational Gradient for Multiscale Kinetic Regimes
HRGrad resolves gradient conflicts in multi-task learning for asymptotic-preserving neural networks by encoding small parameters and using a gradient alignment metric, enabling stable training across all Knudsen numbers for BGK and linear transport equations.