Introduces Laplace-approximated Bayesian PINNs for automatic loss-weight optimization when solving PDEs such as heat, wave, and Burgers equations.
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Bilevel learning methods rely on implicit differentiation but are restricted by assumptions of unique lower-level solutions and struggle with constraints, and connections to broader bilevel optimization literature may enable more scalable general-purpose algorithms.
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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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Bilevel learning
Bilevel learning methods rely on implicit differentiation but are restricted by assumptions of unique lower-level solutions and struggle with constraints, and connections to broader bilevel optimization literature may enable more scalable general-purpose algorithms.