Nicolas Boullé

Nicolas Boullé

Assistant Professor at Imperial College London

Publications

  1. J. Bao, N. Boullé, T. J.B. Liu, R. Sarfati, and C. J. Earls, Text-Trained LLMs Can Zero-Shot Extrapolate PDE Dynamics, submitted, 2025. arxiv

  2. N. Boullé, M. Colbrook, and G. Conradie, Convergent Methods for Koopman Operators on Reproducing Kernel Hilbert Spaces, submitted, 2025. arxiv

  3. R. Sarfati, T. J.B. Liu, N. Boullé, and C. J. Earls, What's in a prompt? Language models encode literary style in prompt embeddings, EMNLP (2025). arxiv

  4. J. Rowbottom, S. Fresca, P. Lio, C.-B. Schönlieb, and N. Boullé, Multi-Level Monte Carlo Training of Neural Operators, submitted, 2025. arxiv

  5. O. Zekri and N. Boullé, Fine-Tuning Discrete Diffusion Models with Policy Gradient Methods, NeurIPS (2025). arxiv

  6. C. Runkel, S. Xiao, N. Boullé, and Y. Chen, Operator learning regularization for macroscopic permeability prediction in dual-scale flow problem, submitted, 2024. arxiv

  7. O. Zekri, A. Odonnat, A. Benechehab, L. Bleistein, N. Boullé, and I. Redko, Large Language Models as Markov Chains, submitted, 2024. arxiv

  8. T. J.B. Liu, N. Boullé, R. Sarfati, and C. J. Earls, Density estimation with LLMs: a geometric investigation of in-context learning trajectories, ICLR (2025). arxiv

  9. R. Sarfati, T. J.B. Liu, N. Boullé, and C. J. Earls, Lines of Thought in Large Language Models, ICLR (2025). arxiv

  10. N. Bouziani and N. Boullé, Structure-Preserving Operator Learning, submitted, 2024. arxiv

  11. N. Boullé and M. Colbrook, Multiplicative Dynamic Mode Decomposition, SIAM J. Appl. Dyn. Syst. 24(2) (2025), 1945-1968. arxiv

  12. D. Persson, N. Boullé, and D. Kressner, Randomized Nyström approximation of non-negative self-adjoint operators, SIAM J. Math. Data Sci. 7(2) (2025), 670-698. arxiv

  13. T. J.B. Liu, N. Boullé, R. Sarfati, and C. J. Earls, LLMs learn governing principles of dynamical systems, revealing an in-context neural scaling law, EMNLP - Oral (2024). arxiv

  14. N. Boullé, D. Halikias, S. E. Otto, and A. Townsend, Operator learning without the adjoint, J. Mach. Learn. Res. 25(364) (2024), 1-54. arxiv

  15. N. Boullé and M. Colbrook, On the Convergence of Hermitian Dynamic Mode Decomposition, Physica D 472 (2024), 134405. arxiv

  16. N. Boullé and A. Townsend, A Mathematical Guide to Operator Learning, Handbook of Numerical Analysis 25 (2024), 83-125. arxiv

  17. N. Boullé, A. Herremans, and D. Huybrechs, Multivariate rational approximation of functions with curves of singularities, SIAM J. Sci. Comput. 46(6) (2024), A3401-A3426. arxiv

  18. N. Boullé, D. Halikias, and A. Townsend, Elliptic PDE learning is provably data-efficient, PNAS 120(39) (2023), e2303904120. arxiv

  19. F. Laakmann and N. Boullé, Bifurcation analysis of a two-dimensional magnetic Rayleigh-Bénard problem, Physica D 467 (2024), 134270. arxiv

  20. H. Praveen, N. Boullé, and C. Earls, Principled interpolation of Green's functions learned from data, Comput. Methods Appl. Mech. Eng. 409 (2023), 115971. arxiv

  21. N. Boullé, I. Newell, P. E. Farrell, and P. G. Kevrekidis, Two-component three-dimensional atomic Bose-Einstein condensates supporting complex stable patterns, Phys. Rev. A 107 (2023), 012813. arxiv

  22. N. Boullé, S. Kim, T. Shi, and A. Townsend, Learning Green's functions associated with time-dependent partial differential equations, J. Mach. Learn. Res. 23(218) (2022), 1-34. arxiv

  23. N. Boullé, P. E. Farrell, and M. E. Rognes, Optimization of Hopf Bifurcation Points, SIAM J. Sci. Comput. 45(3) (2023), B390-B411. arxiv

  24. N. Boullé, P. E. Farrell, and A. Paganini, Control of bifurcation structures using shape optimization, SIAM J. Sci. Comput. 44(1) (2022), A57-A76. arxiv

  25. N. Boullé and A. Townsend, A generalization of the randomized singular value decomposition, ICLR (2022). arxiv

  26. N. Boullé, C. J. Earls, and A. Townsend, Data-driven discovery of Green's functions with human-understandable deep learning, Sci. Rep. 12 (2022), 4824. arxiv

  27. N. Boullé, J. Słomka, and A. Townsend, An optimal complexity spectral method for Navier-Stokes simulations in the ball, 2021. arxiv

  28. N. Boullé, V. Dallas, and P. E. Farrell, Bifurcation analysis of two-dimensional Rayleigh-Bénard convection using deflation, Phys. Rev. E 105(5) (2022), 055106. arxiv

  29. A. J. Ellingsrud, N. Boullé, P. E. Farrell, and M. E. Rognes, Accurate numerical simulation of electrodiffusion and osmotic water movement in brain tissue, Math. Med. Biol. 38(4) (2021), 516-551. arxiv

  30. N. Boullé and A. Townsend, Learning elliptic partial differential equations with randomized linear algebra, Found. Comput. Math. 23 (2023), 709-739. arxiv

  31. N. Boullé, E. G. Charalampidis, P. E. Farrell, and P. G. Kevrekidis, Deflation-based identification of nonlinear excitations of the three-dimensional Gross-Pitaevskii equation, Phys. Rev. A 102(5) (2020), 053307. arxiv

  32. N. Boullé, Y. Nakatsukasa, and A. Townsend, Rational neural networks, NeurIPS 33 (2020). arxiv

  33. E. G. Charalampidis, N. Boullé, P. E. Farrell, and P. G. Kevrekidis, Bifurcation analysis of stationary solutions of two-dimensional coupled Gross-Pitaevskii equations using deflated continuation, Commun. Nonlinear Sci. Numer. Simulat. 87 (2020), 105255. arxiv

  34. N. Boullé and A. Townsend, Computing with functions in the ball, SIAM J. Sci. Comput. 42(4) (2020), C169-C191. arxiv

  35. N. Boullé, V. Dallas, Y. Nakatsukasa, and D. Samaddar, Classification of chaotic time series with deep learning, Physica D 403 (2020), 132261. arxiv

    PhD Thesis (University of Oxford, 2022): Data-driven discovery of Green's functions