6 papers · 1 filter
Physics Matters in PnP: Recovery Guarantees with the MMSE and NN Denoisers
Tobias Wolf, Jalal Fadili, Jin Guo +1
We investigate the forward-backward-splitting version of the Plug and Play (PnP) method for linear ill-posed problems with MMSE estimators as denoisers. In contrast to existing lit…
PDE Identification Using Noise Adaptive Differentiation in Strong Form (S-IDENT)
Roy Y. He, Sung Ha Kang
We explore identifying partial differential equations (PDEs) from noisy observations of single time-space trajectories. Recent developments show the benefits of identifying PDEs in…
Second-Order Path Kernel Interpolation Formulas in Machine Learning
Jin Guo, Roy Y. He, Jean-Michel Morel
Understanding how training data shape neural network predictions is a central problem in modern learning theory. In 2020, Pedro Domingos proposed an interpolation formula valid for…
On Interpolation Formulas Describing Neural Network Generalization
Jin Guo, Roy Y. He, Jean-Michel Morel
In 2020 Domingos introduced an interpolation formula valid for "every model trained by gradient descent". He concluded that such models behave approximately as kernel machines. In…
From Frequency Bias to Spectral Balance: Operator-Aware Preconditioners for PINNs
Roy Y. He, Ying Liang, Hongkai Zhao +1
When neural networks (NNs) are used as a type of nonlinear parametric representation to solve partial differential equations (PDEs), they often display frequency-dependent learning…
Phase-IDENT: Identification of Two-phase PDEs with Uncertainty Quantification
Edward L. Yang, Roy Y. He
We propose a novel method, Phase-IDENT, for identifying partial differential equations (PDEs) from noisy observations of dynamical systems that exhibit phase transitions. Such phen…