FK-PINNs add noisy Feynman-Kac Monte Carlo labels as an operator preconditioner to PINN losses, yielding smaller condition numbers and non-asymptotic L2 error bounds for tanh networks on PDEs admitting FK representations.
arXiv preprint arXiv:2410.06308 , year=
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Taming the Loss Landscape of PINNs with Noisy Feynman-Kac Supervision: Operator Preconditioning and Non-Asymptotic Error Bounds
FK-PINNs add noisy Feynman-Kac Monte Carlo labels as an operator preconditioner to PINN losses, yielding smaller condition numbers and non-asymptotic L2 error bounds for tanh networks on PDEs admitting FK representations.