Nicolas Boullé

Nicolas Boullé

Assistant Professor at Imperial College London

Publications

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

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

  3. 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

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

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

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

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

  8. 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

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

  10. N. Boullé and M. Colbrook, On the Convergence of Hermitian Dynamic Mode Decomposition, to appear in Physica D, 2024. arxiv

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

  12. 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

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

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

  15. 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

  16. 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

  17. 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

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

  19. 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

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

  21. 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

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

  23. 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

  24. 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

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

  26. 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

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

  28. 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

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

  30. 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