H^{-1} norm equivalence to expected squared evaluations on domain-dependent random test functions enables SV-PINNs that recover accurate solutions to challenging second-order elliptic PDEs faster than standard PINNs.
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paFEMU enables rapid constitutive model discovery by integrating sparse regression, physics augmentation, and finite element adjoint optimization on multi-modal data for interpretable transfer learning.
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Random test functions, $H^{-1}$ norm equivalence, and stochastic variational physics-informed neural networks
H^{-1} norm equivalence to expected squared evaluations on domain-dependent random test functions enables SV-PINNs that recover accurate solutions to challenging second-order elliptic PDEs faster than standard PINNs.
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Towards Rapid Constitutive Model Discovery from Multi-Modal Data: Physics Augmented Finite Element Model Updating (paFEMU)
paFEMU enables rapid constitutive model discovery by integrating sparse regression, physics augmentation, and finite element adjoint optimization on multi-modal data for interpretable transfer learning.