Microsoft Research · AI for Science

Structured machine learning across scales of atomistic modeling.

I am a machine-learning researcher at Microsoft Research. My work spans electronic structure, molecular simulation, reactions, proteins, and materials.

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01 / Overview

I study how mathematical and physical structure can make learned models tractable, scalable, and useful.

I develop generative models and architectures that encode geometry and physical constraints. The goal is not only to fit complex scientific data, but to build models whose structure supports the computation the science requires.

I completed my PhD at Université de Montréal and Mila with Aaron Courville. My thesis, Probability flows in deep learning, developed likelihood-based generative models through deterministic and stochastic transformations of probability distributions.

02 / Current work

Learning across scientific scales

Current projects apply structured machine learning at different levels of atomistic description, from electron densities to proteins and crystalline materials.

Electronic structure

Skala

Accurate and scalable exchange-correlation with deep learning

Density functional theory makes electronic-structure calculations tractable by working with the electron density, but its accuracy depends on approximating the unknown exchange-correlation functional.

Skala learns this non-local functional directly from electron densities. Inspired by the multipole expansion, its architecture routes information between fine integration grids and atom-centered coarse representations, building on equivariant processing and physical constraints to make non-local density modeling scalable.

Trained on an unprecedented volume of high-accuracy chemistry data, Skala establishes a new state of the art for exchange-correlation functionals: it surpasses the accuracy of leading hybrid functionals while retaining computational cost closer to semi-local DFT.

Accurate and scalable exchange-correlation with deep learning arXiv, 2025 · revised 2026

Paper Code

Molecular simulation

Two for One

Diffusion models that are also force fields

Coarse-graining makes molecular simulation less expensive by replacing groups of atoms with a smaller set of variables, but it also requires recovering the effective interactions lost in that reduction.

Two for One trains a diffusion model on equilibrium structures. Its conservative score serves two purposes: it generates independent equilibrium samples and defines a force field for molecular dynamics. The same model reproduces equilibrium distributions, free-energy landscapes, and folding behavior on benchmark proteins.

Two for One: Diffusion Models and Force Fields for Coarse-Grained Molecular Dynamics JCTC, 2023

Paper

Materials design

MatterGen

Generative modeling for inorganic materials

Materials discovery is an inverse-design problem: rather than evaluating a known crystal, the goal is to generate stable structures with desired properties.

MatterGen is an equivariant diffusion model for periodic crystals. It can generate diverse, stable, and novel materials, or condition generation on chemical, mechanical, electronic, and magnetic properties. Candidate materials from the model were synthesized experimentally, connecting generative design to physical validation.

A generative model for inorganic materials design Nature, 2025

Paper Code

03 / Foundations

Probability flows in deep learning

My PhD studied likelihood-based generative modeling through change of variables. The central question was how the structure of a probability transformation controls the tradeoff between flexibility and scalable computation.

Deterministic transport

Structure makes expressive maps tractable.

Neural Autoregressive Flows parameterize the triangular structure of the Knothe-Rosenblatt rearrangement with monotonic neural networks. Convex Potential Flows instead represent the gradient of a convex potential, following Brenier's optimal-transport map. Augmented Normalizing Flows lift transport into a larger space, connecting auxiliary variables with phase-space and Hamiltonian dynamics.

Neural Autoregressive FlowsICML, 2018 Oral
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Augmented Normalizing FlowsarXiv, 2020
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Convex Potential FlowsICLR, 2021 Spotlight
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Stochastic transport

Diffusion extends probability flows to noisy dynamics.

Score-based models formulated through stochastic differential equations emerged as a promising approach to generative modeling, but initially lacked a likelihood-based theoretical treatment. We derived a continuous-time variational framework connecting score matching to likelihood. We then extended diffusion models to Riemannian manifolds, enabling generative modeling on constrained spaces such as the torus of protein dihedral angles.

A Variational Perspective on Diffusion-Based Generative Models and Score MatchingNeurIPS, 2021 Spotlight
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Riemannian Diffusion ModelsNeurIPS, 2022
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Read the doctoral thesis Probability flows in deep learning