Nicolas Boullé

Nicolas Boullé

Assistant Professor at Imperial College London

Publications

  1. K. Gray, F. Brown, N. Boullé, and M.J. Colbrook, Deep Embedded Multiplicative DMD for Algebra-Preserving Koopman Learning, submitted, 2026.

  2. L. Ma, N. Boullé, Y.-S. Yang, H. Wu, and L. Guo, Physics-guided correction for operator learning under model misspecification, submitted, 2026. arxiv

  3. O. Zekri, A. Korba, and N. Boullé, Gibbs Gradient Descent: A Langevin Approach to Optimization, submitted, 2026.

  4. 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

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

  6. 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

  7. 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

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

  9. 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

  10. 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

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

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

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

  14. 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

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

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

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

  18. 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

  19. 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

  20. 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

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

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

  23. 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

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

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

  26. 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

  27. 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

  28. 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

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

  30. 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

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

  32. 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

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

  34. 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

  35. 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

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

  37. 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

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

  39. 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

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

  41. 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