Adding a barycentric interpolation layer to PINNs lifts their precision ceiling, achieving up to 1e-13 relative error on smooth PDEs, while exposing a tradeoff between accuracy and loss conditioning.
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BWLer: Barycentric Weight Layer Elucidates a Precision-Conditioning Tradeoff for PINNs
Adding a barycentric interpolation layer to PINNs lifts their precision ceiling, achieving up to 1e-13 relative error on smooth PDEs, while exposing a tradeoff between accuracy and loss conditioning.