Nicolas Boullé

Nicolas Boullé

Research Fellow at the University of Cambridge

Publications

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

  2. 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, submitted, 2024. arxiv

  3. N. Boullé, D. Halikias, S. E. Otto, and A. Townsend, Operator learning without the adjoint, submitted, 2024. arxiv

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

  5. N. Boullé and A. Townsend, A Mathematical Guide to Operator Learning, to appear in the Handbook of Numerical Analysis, 2023. arxiv

  6. N. Boullé, A. Herremans, and D. Huybrechs, Multivariate rational approximation of functions with curves of singularities, submitted, 2023. arxiv

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

  8. F. Laakmann and N. Boullé, Bifurcation analysis of a two-dimensional magnetic Rayleigh-Bénard problem, submitted, 2022. arxiv

  9. 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

  10. 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

  11. 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

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

  13. 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

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

  15. 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

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

  17. 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

  18. 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

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

  20. 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

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

  22. 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

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

  24. 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