4 papers
Energy-based Transport for Amortized Bayesian Inference
Hojjat Kaveh, Ricardo Baptista, Andrew M. Stuart
We consider amortized Bayesian inference for nonlinear inverse problems using only samples from the joint distribution of parameters and observations, including problems with unkno…
A Neural-Network Framework to Learn History-Dependent Constitutive Laws and Identifiability of Internal Variables
Mayank Raj, Lianghao Cao, Andrew Stuart +1
The identification of constitutive laws is ubiquitous in engineering: in modeling of materials where experimental data are fitted to mathematical models or learning surrogate model…
Bilevel optimization for learning hyperparameters: Application to solving PDEs and inverse problems with Gaussian processes
Nicholas H. Nelsen, Houman Owhadi, Andrew M. Stuart +2
Methods for solving scientific computing and inference problems, such as kernel- and neural network-based approaches for partial differential equations (PDEs), inverse problems, an…
Discretization Error of Fourier Neural Operators
Samuel Lanthaler, Andrew M. Stuart, Margaret Trautner
Operator learning is a variant of machine learning that is designed to approximate maps between function spaces from data. The Fourier Neural Operator (FNO) is one of the main mode…