133 citations · 160 across the 8 of their papers we have counts for
9 papers
Schur-Neural KF: Learned Schur-Consistent Corrections to the Extended Kalman Filter
Min Kim, Lianghao Cao, Soon-Jo Chung +1
We present Schur-Neural KF (SN-KF), a learning-based correction to the extended Kalman filter (EKF) that preserves the probabilistic conditioning interpretation of the EKF. The met…
Enforcing Dirichlet Boundary Conditions in Operator Learning
Andrew M. Stuart, Margaret Trautner
Operator learning in scientific machine learning is concerned with approximation of maps between infinite-dimensional function spaces; such maps frequently arise as the solution op…
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…
Energy-based Transport for Amortized Bayesian Inference
Ricardo Baptista, Hojjat Kaveh, 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…
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…
Operator Learning Using Random Features: A Tool for Scientific Computing
Nicholas H. Nelsen, Andrew M. Stuart
Supervised operator learning centers on the use of training data, in the form of input-output pairs, to estimate maps between infinite-dimensional spaces. It is emerging as a power…
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…
Operator Learning: Algorithms and Analysis
Nikola B. Kovachki, Samuel Lanthaler, Andrew M. Stuart
Operator learning refers to the application of ideas from machine learning to approximate (typically nonlinear) operators mapping between Banach spaces of functions. Such operators…
The Random Feature Model for Input-Output Maps between Banach Spaces
Nicholas H. Nelsen, Andrew M. Stuart
Well known to the machine learning community, the random feature model is a parametric approximation to kernel interpolation or regression methods. It is typically used to approxim…