Research

I work at the interface of scientific computing, numerical analysis, and machine learning. My training is in classical numerical methods; I am interested in how modern ML can be used reliably in science and engineering—where predictions must be accurate, efficient, and interpretable beyond the training set.

AI for Science and Engineering

Scientific machine learning is reshaping how we model complex physical systems. In weather and climate, learned models now compete with operational forecast systems; in other domains, neural operators learn maps between function spaces from data or hybrid data–physics setups. Much of my work aims to develop AI-for-science methods from first principles: architectures and training objectives that respect geometry, stability, and uncertainty, rather than treating these as afterthoughts at deployment time.

Representative examples include Spherical Fourier Neural Operators (SFNO) for stable dynamics on the sphere, neural operators with localized integral and differential kernels for multiscale structure, principled approaches for extending neural architectures to function spaces, and FourCastNet 3, which combines spherical signal-processing primitives with end-to-end probabilistic ensemble training. These ideas connect to classical numerical analysis—resolution invariance, controlled spectra, calibrated uncertainty—and to high-performance computing for scalable training and inference. In practice they are supported by libraries such as torch-harmonics, Makani, and NeuralOperator.

Much of this work has been applied to learned global weather and climate systems, including ACE for climate prediction, the Huge Ensembles hindcast studies (Part 1, Part 2), and FourCastNet 3 for fast, skillful probabilistic medium-range forecasting. The video below shows 15 FourCastNet 3 ensemble members from a rollout trained with Makani; in the paper, each 15-day global forecast is generated in about 60 seconds on a single NVIDIA H100 GPU, so an ensemble of this size is feasible on one GPU in minutes rather than the hours required by conventional systems.

Numerical Methods

My background is in numerical methods, with a focus on partial differential equations and numerical linear algebra. That training remains a source of inspiration for my ML work: stability, preconditioning, and multiscale structure show up in learned models, and ideas from ML feed back into how we build solvers and discretizations. I believe numerical methods and machine learning will ultimately form one cohesive field that integrates methods from both domains.

During my PhD, I worked on approximate fast direct solvers for Helmholtz-type problems (SIAM paper) and discontinuous Galerkin methods for global tsunami modeling (Ocean Modelling). Here are some interesting examples: