Nicolas Boullé

Nicolas Boullé

Assistant Professor at Imperial College London

Publications

  1. G. Conradie, N. Boullé, J-C Loiseau, S. L. Brunton, and M. J. Colbrook, Trustworthy Koopman Operator Learning: Invariance Diagnostics and Error Bounds, submitted, 2026. arxiv

  2. O. Zekri, T. Uscidda, N. Boullé, and A. Korba, Generalized Discrete Diffusion from Snapshots, submitted, 2026. arxiv

  3. T. J.B. Liu, B. Zadeoglu, R. Sarfati, N. Boullé, and C. J. Earls, Jacobian Scopes: token-level causal attributions in LLMs, submitted, 2026. arxiv

  4. J. Bao, N. Boullé, T. J.B. Liu, R. Sarfati, and C. J. Earls, Text-Trained LLMs Can Zero-Shot Extrapolate PDE Dynamics, ICLR Workshop on AI & PDE - Oral (2026). arxiv

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

  6. 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

  7. J. Rowbottom, S. Fresca, P. Lio, C.-B. Schönlieb, and N. Boullé, Multi-Level Monte Carlo Training of Neural Operators, Comput. Methods Appl. Mech. Eng. 453 (2026), 118800. arxiv

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

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

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

  11. 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

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

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

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

  15. 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

  16. 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

  17. 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

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

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

  20. 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

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

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

  23. 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

  24. 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

  25. 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

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

  27. 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

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

  29. 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

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

  31. 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

  32. 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

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

  34. 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

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

  36. 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

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

  38. 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