The authors present a Python library and discrete variational framework for training neural networks to solve PDEs like Stokes equations with a robust loss function tied to the true discrete error.
URL https://www.sciencedirect.com/science/ article/pii/S0021999119307612
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Introduces Laplace-approximated Bayesian PINNs for automatic loss-weight optimization when solving PDEs such as heat, wave, and Burgers equations.
Comparative experiments on three chaotic systems find that architectures using integrator-like updates exhibit lower bias, reduced perturbation amplification, and more stable long-horizon rollouts than other common designs when model capacity is matched.
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Bayesian Reasoning for Physics Informed Neural Networks
Introduces Laplace-approximated Bayesian PINNs for automatic loss-weight optimization when solving PDEs such as heat, wave, and Burgers equations.