Nicolas Boullé

Department of Mathematics
Imperial College London
London, SW7 2AZ, UKn.boulle@imperial.ac.uk

Research interests
Numerical analysis, machine learning, computational physics

Employment2024-date Assistant Professor in Applied Mathematics, Imperial College London, UK.
Department of Mathematics.

2022-2024 Research Fellow, University of Cambridge, UK.
Isaac Newton Institute and Department of Applied Maths and Theoretical Physics.

Education
2018-2022 DPhil in Numerical Analysis, University of Oxford, UK.
Supervised by Prof. Patrick Farrell and Prof. Alex Townsend.

2017-2018 Visiting Research Student, Cornell University, USA.
Supervised by Prof. Alex Townsend.

2015-2017 BSc and 1st year of MSc in Mathematics, ENS Rennes, France.
2013-2015 University foundation course in Mathematics, Lycée Saint-Louis, France.

Research prizes
2024
2023
2022
2021
2021

SIAM Activity Group on Linear Algebra Best Paper Prize
IMA Lighthill-Thwaites Prize, 2nd place.
STEM for Britain, finalist.
IMA Leslie Fox Prize for Numerical Analysis, 2nd prize.
G-Research PhD Prize, 2nd place (£5000).

Research grants and fellowships
2023-2028 Scientific Artificial Intelligence (SciAI) Center, Office of Naval Research, $11.3m,Imperial PI, personal support: $485k.

2022-2023 INI-Simons Postdoctoral Research Fellowship, Simons Foundation.

Research supervision
PhD students:○

Gustav Conradie (Cambridge, with Matt Colbrook), 2024-present.

○

Christina Runkel (Cambridge, with Carola Schönlieb), 2021-present.

Undergraduate and MSc students:○

Qile Jiang (Cornell REU summer project), 2023.

○

Emily Zhang (Cornell REU summer project), 2023.

○

Henry Smith (Yale undergraduate student), 2021-2022.

○

Franklin Deng (Cornell REU summer project), 2021.
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○Jack Krew (Cornell REU summer project), 2021.

○

Markus Dablander (Oxford PhD student mini-project), 2020.

Teaching
2021
2020
2019
2019

Tutor for Approximation of functions, Mathematical Institute, University of Oxford.
Tutor for Approximation of functions, Mathematical Institute, University of Oxford.
TA for Practical Numerical Analysis, Mathematical Institute, University of Oxford.
TA for Approximation of functions, Mathematical Institute, University of Oxford.

Professional activities
2024 Co-organizer of a minisymposium, SIAM Conference on Applied Linear Algebra
Title: Operator Learning and Linear Algebra.

2023-2024 Co-organizer of the Cambridge ACA seminar
2023 Co-organizer of a minisymposium, 93rd GAMM Annual Meeting
Title: Randomized algorithms in numerical linear algebra.

2022 Highlighted Reviewer of ICLR 2022
2021-date Referee for several journals and conferences, including NeurIPS, ICML, ICLR,JMLR, and SISC.
2021 Co-organizer of a minisymposium, SIAM Annual Meeting
Title: Approximation theory of neural networks.

Submitted papers
28. O. Zekri, A. Odonnat, A. Benechehab, L. Bleistein, N. Boullé, and I. Redko, Large Language Models
as Markov Chains, submitted.
27. T. J.B. Liu, N. Boullé, R. Sarfati, and C. J. Earls, Visualizing in-context probability trajectories ofLLMs, submitted.
26. R. Sarfati, T. J.B. Liu, N. Boullé, and C. J. Earls, Lines of Thought in Large Language Models,submitted.
25. N. Bouziani and N. Boullé, Structure-Preserving Operator Learning, submitted.
24. N. Boullé and M. Colbrook, Multiplicative Dynamic Mode Decomposition, submitted.
23. D. Persson, N. Boullé, and D. Kressner, Randomized Nyström approximation of non-negative
self-adjoint operators, submitted.
22. N. Boullé and M. Colbrook, On the Convergence of Hermitian Dynamic Mode Decomposition,submitted.

Publications
21. T. J.B. Liu, N. Boullé, R. Sarfati, and C. J. Earls, LLMs learn governing principles of dynamicalsystems, revealing an in-context neural scaling law, EMNLP (2024).
20. N. Boullé, D. Halikias, S. E. Otto, and A. Townsend, Operator learning without the adjoint, J.
Mach. Learn. Res. (2024).
19. N. Boullé and A. Townsend, A Mathematical Guide to Operator Learning, Handbook of Numerical
Analysis (2024).

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18. N. Boullé, A. Herremans, and D. Huybrechs, Multivariate rational approximation of functions withcurves of singularities, SIAM J. Sci. Comput. (2024).
17. N. Boullé, D. Halikias, and A. Townsend, Elliptic PDE learning is provably data-efficient, PNAS
(2023).
16. F. Laakmann and N. Boullé, Bifurcation analysis of a two-dimensional magnetic Rayleigh-Bénard
problem, Physica D (2024).
15. H. Praveen, N. Boullé, and C. Earls, Principled interpolation of Green’s functions learned from data,
Comput. Methods Appl. Mech. Eng. (2023).
14. N. Boullé, I. Newell, P. E. Farrell, and P. G. Kevrekidis, Two-Component 3D Atomic Bose-Einstein
Condensates Supporting Complex Stable Patterns, Phys. Rev. A (2023).
13. N. Boullé, S. Kim, T. Shi, and A. Townsend, Learning Green’s functions associated with parabolic
partial differential equations, J. Mach. Learn. Res. (2022).
12. N. Boullé, P. E. Farrell, and M. E. Rognes, Optimal control of Hopf bifurcations, SIAM J. Sci.
Comput. (2023).
11. N. Boullé, P. E. Farrell, and A. Paganini, Control of bifurcation structures using shape optimization,
SIAM J. Sci. Comput. (2022).
10. N. Boullé and A. Townsend, A generalization of the randomized singular value decomposition, ICLR
(2022).
9. N. Boullé, C. J. Earls, and A. Townsend, Data-driven discovery of Green’s functions with humanunderstandable deep learning, Sci. Rep. (2022).
8. N. Boullé, V. Dallas, and P. E. Farrell, Bifurcation analysis of two-dimensional Rayleigh–Bénard
convection using deflation, Phys. Rev. E (2022).
7. A. Ellingsrud, N. Boullé, P. E. Farrell, and M. E. Rognes, Accurate numerical simulation ofelectrodiffusion and osmotic water movement in brain tissue, Math. Med. Biol. (2021).
6. N. Boullé and A. Townsend, Learning elliptic partial differential equations with randomized linear
algebra, Found. Comput. Math. (2022).
5. 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 (2020).
4. N. Boullé, Y. Nakatsukasa, and A. Townsend, Rational neural networks, NeurIPS (2020).
3. 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. (2020).
2. N. Boullé and A. Townsend, Computing with functions in the ball, SIAM J. Sci. Comput. (2020).
1. N. Boullé, V. Dallas, Y. Nakatsukasa, and D. Samaddar, Classification of chaotic time series withdeep learning, Physica D (2020).

Technical reports
3. N. Boullé, J. Słomka, and A. Townsend, An optimal complexity spectral method for Navier–Stokes
simulations in the ball, arXiv:2103.16638, 2021.
2. D. Barton, N. Boullé, E. Campillo-Funollet, C. Hall, S. Ruangdech, and Y. Zhou, Compressing
aerodynamic hazard data (with Zenotech), ESGI 162, 2020.
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1. E. Campillo-Funollet, N. Boullé, M. Ebeling-Rump, A. Pichler, A. Farid, M. P. Goodridge, H. Lee,B. Lyu, and M. Sejeso, Uncertainty in seismic inverse problems (with BP), ESGI 145, 2019.

Academic visits and talks
I-X Imperial College London Seminar, London, UK.
October 2024
Firedrake 2024 Conference, Oxford, UK.
September 2024
Huawei Workshop, invited speaker, Bordeaux, France.
September 2024
Workshop on ML in infinite dimensions, invited speaker, Bath, UK.
August 2024
4th Symposium on ML and Dynamical Systems, invited speaker, Canada.
July 2024
Cornell University, USA.
June 2024
Grenoble AI for Sciences Workshop, keynote speaker, France.
May 2024
SIAM Conference on Applied Linear Algebra, Prize Lecture, France.
May 2024
Alan Turing Institute, online seminar.
May 2024
University of Bath, Numerical Analysis seminar, UK.
April 2024
One World Mathematics of Machine Learning, online seminar.
April 2024
Dynamics, Data and Deep learning workshop, invited speaker, UK.
March 2024
SCML2024 Conference, invited speaker, Japan.
March 2024
Inria Strasbourg, invited by Victor Michel-Dansac, France.
February 2024
University of Cambridge, M4DL Workshop.
January 2024
University of Birmingham, Applied Mathematics Seminar.
January 2024
Lawrence Livermore National Laboratory, DDPS Webinar.
December 2023
UCLouvain, invited by Estelle Massart, Belgium.
October 2023
Johns Hopkins University, online Postdoc Seminar.
September 2023
Maths4DL Conference, invited speaker, UK.
July 2023
29th Biennial Numerical Analysis Conference, UK.
June 2023
Brown University, invited by Brendan Keith, USA.
June 2023
British Applied Mathematics Colloquium, UK.
April 2023
UCL, Math4DL workshop.
March 2023
SIAM Conference on Computational Science and Engineering, Netherlands.
February 2023
KU Leuven, invited by Daan Huybrechs, Belgium.
February 2023
The Alan Turing Institute, Oden-Turing workshop.
January 2023
University of Cambridge, CIA seminar.
November 2022
The Alan Turing Institute, UK.
November 2022
University of Leicester, CMS Mathematics seminar.
November 2022
EPFL, invited by Daniel Kressner, Switzerland.
October 2022
Imperial College, Numerics & Acoustics Workshop.
September 2022
BIFD conference, Netherlands.
August 2022
Equadiff 15 conference, Czech Republic.
July 2022
University of Cambridge, invited by Carola Schönlieb.
June 2022
IMA Conference on Numerical Linear Algebra and Optimization, Birmingham.
June 2022
Householder Symposium on Numerical Linear Algebra, Italy.
June 2022
University of Oxford, Numerical Analysis seminar.
May 2022
ICLR 2022 conference, online.
April 2022
SIAM Conference on Uncertainty Quantification, online.
April 2022
Virtual study group, V-KEMS.
March 2022
STEM for Britain, UK House of Commons.
March 2022
Cornell University, invited by Alex Townsend, USA.
February 2022
PRISM Residential workshop, UK.
January 2022
SIAM UKIE Annual Meeting, online.
January 2022
University of Oxford, Junior Applied Mathematics Seminar.
October 2021
11th Montreal Industrial Problem Solving Workshop, online.
August 2021
SIAM Annual Meeting, online.
July 2021
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British Early Career Mathematicians’ Colloquium, online.
20th IMA Leslie Fox Prize Event, online.
21st Geilo Winter School, online.
NeurIPS 2020 conference, online.
University of Oxford, Numerical Analysis seminar.
European Study Group with Industry 162, University of Leeds.
Simula Research Laboratory, visiting Marie Rognes, Norway.
European Study Group with Industry 145, University of Cambridge.
University of Oxford, Numerical Analysis seminar.
MIT, visiting Jonasz Słomka, USA.
Cornell University, SCAN seminar, USA.
Memorial University of Newfoundland, visiting Alex Bihlo, Canada.

July 2021
June 2021
January 2021
December 2020
November 2020
July 2020
August-September 2019
April 2019
October 2018
April 2018
November 2017
September 2017

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