Dr Nicolas Boulle | Department of Applied Mathematics and Theoretical Physics

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I am a Research Fellow in Numerical Analysis.

My research interests lie at the intersection between numerical analysis and deep learning. I primarily focus on the mathematical foundations of deep learning to discover mathematical models (partial differential equations) from data, and the development of novel and theoretically justified numerical techniques.

I am a member of the Scientific Artificial Intelligence (SciAI) Center supported by the Office of Naval Research (ONR).

Publications

Randomized Nyström approximation of non-negative self-adjoint operators

D Persson, N Boullé, D Kressner

(2024)

(link to publication)

LLMs learn governing principles of dynamical systems, revealing an in-context neural scaling law

TJB Liu, N Boullé, R Sarfati, CJ Earls

(2024)

(link to publication)

Operator learning without the adjoint

N Boullé, D Halikias, SE Otto, A Townsend

(2024)

(link to publication)

On the Convergence of Hermitian Dynamic Mode Decomposition

N Boullé, MJ Colbrook

(2024)

(doi: 10.48550/arxiv.2401.03192)

(link to publication)

A Mathematical Guide to Operator Learning

N Boullé, A Townsend

(2023)

(link to publication)

Multivariate rational approximation of functions with curves of singularities

N Boullé, A Herremans, D Huybrechs

(2023)

(link to publication)

Elliptic PDE learning is provably data-efficient

N Boullé, D Halikias, A Townsend

– Proceedings of the National Academy of Sciences

(2023)

120,

e2303904120

(doi: 10.1073/pnas.2303904120)

Principled interpolation of Green's functions learned from data

H Praveen, N Boullé, C Earls

– Computer Methods in Applied Mechanics and Engineering

(2023)

409,

115971

(doi: 10.1016/j.cma.2023.115971)

Elliptic PDE learning is provably data-efficient

N Boullé, D Halikias, A Townsend

(2023)

(link to publication)

Two-component three-dimensional atomic Bose-Einstein condensates supporting complex stable patterns

N Boullé, I Newell, PE Farrell, PG Kevrekidis

– Physical Review A

(2023)

107,

012813

(doi: 10.1103/PhysRevA.107.012813)