Introduces Laplace-approximated Bayesian PINNs for automatic loss-weight optimization when solving PDEs such as heat, wave, and Burgers equations.
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Bayesian statistics supplies an automatic Occam's razor that penalizes unnatural models needing precise fine-tuning to agree with data, justifying naturalness arguments without aleatoric uncertainty.
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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.
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It's all in your head -- fine-tuning arguments do not require aleatoric uncertainty
Bayesian statistics supplies an automatic Occam's razor that penalizes unnatural models needing precise fine-tuning to agree with data, justifying naturalness arguments without aleatoric uncertainty.