AW-PINN uses dynamic wavelet basis adaptation in PINNs to solve PDEs with localized high-magnitude sources, outperforming prior methods on loss imbalances up to 10^10:1 while deriving a Gaussian process limit and NTK structure under assumptions.
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Numerical study comparing feedforward NN and DeepONet with data-driven and physics-informed losses on stochastic heat equation, highlighting larger errors at distribution tails due to extrapolation.
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An adaptive wavelet-based PINN for problems with localized high-magnitude source
AW-PINN uses dynamic wavelet basis adaptation in PINNs to solve PDEs with localized high-magnitude sources, outperforming prior methods on loss imbalances up to 10^10:1 while deriving a Gaussian process limit and NTK structure under assumptions.
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A numerical study into neural network surrogate model performance for uncertainty propagation
Numerical study comparing feedforward NN and DeepONet with data-driven and physics-informed losses on stochastic heat equation, highlighting larger errors at distribution tails due to extrapolation.