Adjoint-based Fourier Neural Operators and conservation-preserving Fourier Neural Operators. Worked done during the Moncrief Program at the Oden Institute (UT Austin) in 2022 summer.

Numerical Methods for Stochastic Simulations of Scientific Problems. Include algorithms for Sampling, Forward Uncertainty Propagation, Filtering, and Rare Event Simulations. Demonstrated with noteb…

Codes for the paper "Reducing Operator Complexity of Galerkin Coarse-Grid Operators with Machine Learning". Baseline included.

A Suite of Numerical Linear Algebra Algorithms: Krylov Subspace Methods and Variants, Preconditioning Methods, Smoothing Methods, and Golub-Kahan

A Suite of Numerical Optimization Algorithms: Variants of Newton's Methods, Proximal Methods, Non-negative Matrix Factorization, etc.

Comparing Stochastic Interpolants and Score-Based Generative Models via Entropic Optimal Transport

Sampling Methods Based on the Langevin Dynamics