Featured Publications

A Graph Signal Processing Perspective on Numerical Sequence Representations in LLM In-Context Learning

J. Bao, Z. Qi, T. J.B. Liu, G. Arora, R. Sarfati, N. Boullé, and C. J. Earls

arXiv preprint

A zero-one law for one-shot system identification

N. Boullé, D. Halikias, S. E. Otto, and A. Townsend

arXiv preprint

Deep Embedded Multiplicative DMD for Algebra-Preserving Koopman Learning

K. Gray, F. Brown, N. Boullé, and M. J. Colbrook

arXiv preprint

Physics-guided correction for operator learning under model misspecification

L. Ma, N. Boullé, Y.-S. Yang, H. Wu, and L. Guo

arXiv preprint

Gibbs Gradient Descent: A Langevin Approach to Optimization

O. Zekri, A. Korba, and N. Boullé

arXiv preprint

Trustworthy Koopman Operator Learning: Invariance Diagnostics and Error Bounds

G. Conradie, N. Boullé, J.-C. Loiseau, S. L. Brunton, and M. J. Colbrook

arXiv preprint

Generalized Discrete Diffusion from Snapshots

O. Zekri, T. Uscidda, N. Boullé, and A. Korba

arXiv preprint

Jacobian Scopes: token-level causal attributions in LLMs

T. J.B. Liu, B. Zadeoglu, R. Sarfati, N. Boullé, and C. J. Earls

arXiv preprint

Text-Trained LLMs Can Zero-Shot Extrapolate PDE Dynamics

J. Bao, N. Boullé, T. J.B. Liu, R. Sarfati, and C. J. Earls

ICLR Workshop on AI & PDE - Oral (2026)

Multi-Level Monte Carlo Training of Neural Operators

J. Rowbottom, S. Fresca, P. Lio, C.-B. Schonlieb, and N. Boullé

Comput. Methods Appl. Mech. Eng. 453 (2026), 118800

Convergent Methods for Koopman Operators on Reproducing Kernel Hilbert Spaces

N. Boullé, M. Colbrook, and G. Conradie

arXiv preprint

What's in a prompt? Language models encode literary style in prompt embeddings

R. Sarfati, T. J.B. Liu, N. Boullé, and C. J. Earls

EMNLP (2025)

Fine-Tuning Discrete Diffusion Models with Policy Gradient Methods

O. Zekri and N. Boullé

NeurIPS (2025)

Density estimation with LLMs: a geometric investigation of in-context learning trajectories

T. J.B. Liu, N. Boullé, R. Sarfati, and C. J. Earls

ICLR (2025)

Lines of Thought in Large Language Models

R. Sarfati, T. J.B. Liu, N. Boullé, and C. J. Earls

ICLR (2025)

Multiplicative Dynamic Mode Decomposition

N. Boullé and M. Colbrook

SIAM J. Appl. Dyn. Syst. 24(2) (2025), 1945-1968

Randomized Nystrom approximation of non-negative self-adjoint operators

D. Persson, N. Boullé, and D. Kressner

SIAM J. Math. Data Sci. 7(2) (2025), 670-698

Operator learning regularization for macroscopic permeability prediction in dual-scale flow problem

C. Runkel, S. Xiao, N. Boullé, and Y. Chen

arXiv preprint

Large Language Models as Markov Chains

O. Zekri, A. Odonnat, A. Benechehab, L. Bleistein, N. Boullé, and I. Redko

arXiv preprint

Structure-Preserving Operator Learning

N. Bouziani and N. Boullé

arXiv preprint

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

T. J.B. Liu, N. Boullé, R. Sarfati, and C. J. Earls

EMNLP - Oral (2024)

Operator learning without the adjoint

N. Boullé, D. Halikias, S. E. Otto, and A. Townsend

J. Mach. Learn. Res. 25(364) (2024), 1-54

On the Convergence of Hermitian Dynamic Mode Decomposition

N. Boullé and M. Colbrook

Physica D 472 (2024), 134405

A Mathematical Guide to Operator Learning

N. Boullé and A. Townsend

Handbook of Numerical Analysis 25 (2024), 83-125

Multivariate rational approximation of functions with curves of singularities

N. Boullé, A. Herremans, and D. Huybrechs

SIAM J. Sci. Comput. 46(6) (2024), A3401-A3426

Bifurcation analysis of a two-dimensional magnetic Rayleigh-Benard problem

F. Laakmann and N. Boullé

Physica D 467 (2024), 134270

Elliptic PDE learning is provably data-efficient

N. Boullé, D. Halikias, and A. Townsend

PNAS 120(39) (2023), e2303904120

Principled interpolation of Green's functions learned from data

H. Praveen, N. Boullé, and C. Earls

Comput. Methods Appl. Mech. Eng. 409 (2023), 115971

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

N. Boullé, I. Newell, P. E. Farrell, and P. G. Kevrekidis

Phys. Rev. A 107 (2023), 012813

Optimization of Hopf Bifurcation Points

N. Boullé, P. E. Farrell, and M. E. Rognes

SIAM J. Sci. Comput. 45(3) (2023), B390-B411

Learning elliptic partial differential equations with randomized linear algebra

N. Boullé and A. Townsend

Found. Comput. Math. 23 (2023), 709-739

Learning Green's functions associated with time-dependent partial differential equations

N. Boullé, S. Kim, T. Shi, and A. Townsend

J. Mach. Learn. Res. 23(218) (2022), 1-34

Control of bifurcation structures using shape optimization

N. Boullé, P. E. Farrell, and A. Paganini

SIAM J. Sci. Comput. 44(1) (2022), A57-A76

A generalization of the randomized singular value decomposition

N. Boullé and A. Townsend

ICLR (2022)

Data-driven discovery of Green's functions with human-understandable deep learning

N. Boullé, C. J. Earls, and A. Townsend

Sci. Rep. 12 (2022), 4824

Bifurcation analysis of two-dimensional Rayleigh-Benard convection using deflation

N. Boullé, V. Dallas, and P. E. Farrell

Phys. Rev. E 105(5) (2022), 055106

An optimal complexity spectral method for Navier-Stokes simulations in the ball

N. Boullé, J. Slomka, and A. Townsend

arXiv preprint

Accurate numerical simulation of electrodiffusion and osmotic water movement in brain tissue

A. J. Ellingsrud, N. Boullé, P. E. Farrell, and M. E. Rognes

Math. Med. Biol. 38(4) (2021), 516-551

Deflation-based identification of nonlinear excitations of the three-dimensional Gross-Pitaevskii equation

N. Boullé, E. G. Charalampidis, P. E. Farrell, and P. G. Kevrekidis

Phys. Rev. A 102(5) (2020), 053307

Rational neural networks

N. Boullé, Y. Nakatsukasa, and A. Townsend

NeurIPS 33 (2020)

Bifurcation analysis of stationary solutions of two-dimensional coupled Gross-Pitaevskii equations using deflated continuation

E. G. Charalampidis, N. Boullé, P. E. Farrell, and P. G. Kevrekidis

Commun. Nonlinear Sci. Numer. Simulat. 87 (2020), 105255

Computing with functions in the ball

N. Boullé and A. Townsend

SIAM J. Sci. Comput. 42(4) (2020), C169-C191

Classification of chaotic time series with deep learning

N. Boullé, V. Dallas, Y. Nakatsukasa, and D. Samaddar

Physica D 403 (2020), 132261