Publications

Preprints

M. Raj, L. Cao, A. Stuart, K. Bhattacharya; A Neural-Network Framework to Learn History-Dependent Constitutive Laws and Identifiability of Internal Variables
[Preprint]

A. Vadeboncoeur, M. Girolami, K. Bhattacharya, A. M. Stuart; Distributional Inverse Homogenization
[Preprint]

E. Calvello, E. Carlson, N. Kovachki, M. N. Manta, A. M. Stuart; Operator Learning for Smoothing and Forecasting
[Preprint]

K. Bhattacharya, L. Cao, A. Stuart; Optimal Experimental Design for Reliable Learning of History-Dependent Constitutive Laws
[Preprint]

R. Baptista, A. Stuart, S. Tran; Large Language Models: A Mathematical Formulation
[Preprint]

X.-H. Zhou, L. Beronilla, M. K. Sleeman, H. Hu, M. Morzfeld, A. M. Stuart, T. A. Zaki; Neural ensemble Kalman filter: Data assimilation for compressible flows with shocks
[Preprint]

N. H. Nelsen, H. Owhadi, A. M. Stuart, X. Yang, Z. Zou; Bilevel Optimization for Learning Hyperparameters: Application to Solving PDEs and Inverse Problems with Gaussian Processes.
[Preprint]

R. Baptista, A. M. Stuart, S. Tran; A Mathematical Perspective On Contrastive Learning.
[Preprint]

E. Bach, R. Baptista, E. Luk and AM Stuart; Learning Optimal Filters Using Variational Inference.
[Preprint]

K. Bhattacharya, L. Cao, G. Stepaniants, A. Stuart, M. Trautner; Learning Memory and Material Dependent Constitutive Laws
[Preprint]

R. Baptista, A. Dasgupta, N. B. Kovachki, A. Oberai, A. M. Stuart; Memorization and Regularization in Generative Diffusion Models
[Preprint]

E. Bach, R. Baptista, D. Sanz-Alonso, A. Stuart; Machine Learning for Inverse Problems and Data Assimilation
[Preprint]

S. Lanthaler, A. M. Stuart, M. Trautner; Discretization Error of Fourier Neural Operators
[Preprint]