Nicolas Boullé

Nicolas Boullé

Assistant Professor at Imperial College London

Publications

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

  2. T. J.B. Liu, N. Boullé, R. Sarfati, and C. J. Earls, Density estimation with LLMs: a geometric investigation of in-context learning trajectories, submitted, 2024. arxiv

  3. R. Sarfati, T. J.B. Liu, N. Boullé, and C. J. Earls, Lines of Thought in Large Language Models, submitted, 2024. arxiv

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

  5. N. Boullé and M. Colbrook, Multiplicative Dynamic Mode Decomposition, submitted, 2024. arxiv

  6. D. Persson, N. Boullé, and D. Kressner, Randomized Nyström approximation of non-negative self-adjoint operators, submitted, 2024. arxiv

  7. 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 (2024). arxiv

  8. N. Boullé, D. Halikias, S. E. Otto, and A. Townsend, Operator learning without the adjoint, to appear in J. Mach. Learn. Res., 2024. arxiv

  9. N. Boullé and M. Colbrook, On the Convergence of Hermitian Dynamic Mode Decomposition, submitted, 2023. arxiv

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

  11. N. Boullé, A. Herremans, and D. Huybrechs, Multivariate rational approximation of functions with curves of singularities, to appear in SIAM J. Sci. Comput., 2024. arxiv

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

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

  14. 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

  15. 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

  16. 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

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

  18. 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

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

  20. 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

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

  22. 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

  23. 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

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

  25. 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

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

  27. 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

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

  29. 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