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Learning, Computation, and Control:
Learning, Computation, and Control:
My research revolves around computational mathematics for optimisation and control, nonlinear PDEs, high-dimensional approximation (a.k.a. learning), and agent-based models across scales. Some relevant keywords below.
Foundations: Dynamic optimization with ODE/PDE constraints; large-scale and sparse optimization; mathematical control theory; high-dimensional approximation; numerical methods for Hamilton-Jacobi PDEs and dynamic programming; optimal transport, mean-field control/games.
Applications. Scientific Machine Learning: data-driven control design in trajectory optimization, epidemiology, and large-scale dynamics. Agent-based models: nonlocal PDES, collective behaviour, consensus control. Nonlinear control design: power electronics, swarm robotics, reinforcement learning. Control of PDEs: fluid flow and vibration control, optimal actuator design.
Please have a look at Research , Publications and CV for more details. I'm always happy to discuss about any of these topics for projects and supervision, so please feel free to get in touch!
Prospective PhD/postdoc applicants, please read before contacting me. I'm always interested in hearing about candidates with a keen and demonstrable interest on applied and computational mathematics, understood in a wide sense. Being that said, please be aware of the following:
In practice, all my students have a maths BSc/MSc, this is essential for our day-to-day communication and PhD research. This is not about gatekeeping, it's about whether I'm the right person to supervise you. Exceptional candidates with engineering degrees can be considered in the frame of a multidisciplinary project, but I advertise these separately.
PhD studentships for international students are extremely competitive at Imperial. I don't want to waste your time unless I'm certain there's a reasonable chance that you will be funded.
Please do not contact me with last minute requests for sponsorship. And please, do not send me a LLM wall of text, it's noticeable.
Being able to read and follow the instructions above is a skill that I value very highly :)
Short Bio
Short Bio
I'm Reader in Computational Optimisation and Control at Department of Mathematics, Imperial College London. Prior joining Imperial in 2021, my criminal record includes: Assistant Professor in Applied Mathematics, University of Nottingham (2019-2021), Imperial College Research Fellow (Maths, 2017-2019), Research Scientist (Optimization and Control Group, 2013-2017), RICAM Linz, Austrian Academy of Sciences, and Postdoctoral Researcher (Maths, EU ITN-SADCO, 2011-2013), Sapienza University of Rome.
I'm originally from Chile and grew up in front of the Pacific, in Viña del Mar. I received a B.Sc. in Mathematical Engineering and a M.Sc. in Electronic Engineering from the Federico Santa María Technical University in Valparaíso. In 2008 I moved to Norway, where I got a Ph.D. in Mathematics in 2012 from the University of Bergen (with some periods away from the rain in Oslo and Trento).
News (2025-)
News (2025-)
Alexander Vladimirsky is starting a sabbatical with us at Imperial, supported by a Royal Society Wolfson Visiting Fellowship.
Together with Elisa Calzola, Iain Smears, and Max Jensen we are organizing the ICMS workshop Numerical methods for Hamilton-Jacobi and mean field PDEs.
José Carrillo, Matías Delgadino, and your truly are organizing a minisymposium on Mean Field PDEs at Scale: Computation, Control, and Gradient Flows, at LACIAM 2026. It's in my hometown!
Sara Bicego passed her viva in June 2026. She did an outstanding thesis on optimal control of agent-based dynamics across different scales. Congrats Sara!
With Mathieu Lauriere we are orgazining a minisymposium on Learning and Computation for Mean Field Games and Control at SIAM CT25.
We are organizing a 1 day workshop (Feb. 6) on New Technologies for Conservation Science as part of our Turner Kirk Trust project on Understanding collective animal behaviour under extreme climatic events.
Starting from 2025, we are starting a new EPSRC Centre for Doctoral Training in Collaborative Computational Modelling at the Interface (CCMI) (I'm Co-Director for Training :))! There will be openings for PhDs every fall for a number of years. If you are interested with me, please send me a non-generic (LLM-generated) email as soon as possible.
I'm the SIAM News Liaison for the Activity Group on Control and Systems Theory, please get in touch if you'd like to discuss a control-related piece for sinews.
We've restarted the series on Learning, Computation, and Control (LC2) at Imperial. Past talks are hosted here.
Current and recent research projects:
Current and recent research projects:
Toyota Central R&D Labs Exchange Agreement, 9/2025-9/2027.
EPSRC CDT Collaborative Computational Modelling at the Interface (CCMI), 6/2024-9/2033.
Turner Kirk Trust, Towards a quantitative understanding of collective animal behaviour under climatic events, 8/2024-2/2025.
EPSRC Grant, Project: Elastic Manufacturing Systems, 9/2020-9/2025.
EPSRC New Horizons Award, Project: Overcoming the Curse of Dimensionality with Tensor Decompositions, 3/2021-5/2023.
UKRI-EPSRC COVID-19 Fund, Project: Optimal Lockdown, 8/2020-2/2021.
Gaspard Monge Program for Optimization, Operations Research and Data Science, Project TIDAL: Taming the Curse of Dimensionality in Dynamic Programming Equations, 7/2019-7/2022.
Editorial duties:
Editorial duties:
Upcoming talks:
Upcoming talks:
2026:
2026:
Numerical methods for Hamilton-Jacobi and mean field PDEs, ICMS Edinburgh, UK, 9/26.
Mathematical Foundations of Digital Twins, Oberwolfach, DE, 6/26.
II Latin American Congress on Industrial and Applied Mathematics LACIAM, UTFSM, Valparaíso, CL, 1/26.
2025:
2025:
Round Meanfield IV: N-body sul Canal Grande, Iuav University of Venice, IT, 9/25.
Brazilian National Congress on Computational and Applied Mathematics (plenary), FGV Rio, BR, 9/25.
SIAM Control and Its Applications 2025, Québec, CA, 7/25.
X Journées Franco-Chiliennes d’Optimisation, Rouen, FR, 7/25.
Biennial Numerical Analysis Conference, University of Strathclyde, UK, 6/25.
SIAM Applications of Dynamical Systems, Denver, US, 5/25.
Mathematics for Machine Learning: Applications to PDEs and Related Fields, University of Ferrara, IT, 3/25.
Computational Mathematics and Applications Seminar, University of Oxford, UK, 2/25.
Finance and Stochastics Seminar, Imperial, UK, 1/25.
Past news and miscellanea
Past news and miscellanea
2024:
2024:
I've led the design of a new stream on Scientific Computing & Machine Learning for our Applied Maths MSc. You can read the press release here!
2023:
2023:
Together with Claudia Totzeck we are organizing a focus session on ``Optimization and Applications'' at the 6th European Conference on Computational Optimization (September 25-27, 2023).
Together with John Pearson we are organizing a mini-symposium on ``Modern Numerical Methods for PDE-constrained Optimization and Control'' at the International Congress on Industrial and Applied Mathematics (August 20-25, 2023).
Together with Susana Gomes we are organizing a session on ``Optimization and Control for Nonlinear Dynamics'' at the 2023 British Applied Mathematics Colloquium (April 3-5, 2023).
2022:
2022:
The PhD project of Cathie Wells, co-supervised with Paul Williams, Nancy Nichols, and Ian Poll, has been awarded the 2022 Times Higher Education Award to Best STEM Project :)
2021:
2021:
Our work on optimised lockdown strategies for the COVID-19 pandemic has been featured by PLOS.
I joined the Editorial Board of Advances in Continuous and Discrete Models (Springer) , submissions on optimal control are particularly welcome!
Our work on reducing transatlantic flight emissions by fuel-optimised routing has been covered in different media: The Independent (UK), Repubblica (IT), Science Magazine.
Together with Sergey Dolgov we have been awarded an EPSRC New Horizons Award to develop the project Overcoming the curse of dimensionality in dynamic programming by tensor decompositions.
2020:
2020:
Together with Ritrabata Dutta and Susana Gomes we have been awarded UKRI-EPSRC funding to develop the project COVID19: Optimal Lockdown.
Together with Timm Faulwasser and Emmanuel Trélat we are organizing two MCSS special issues on "Machine Learning for Control Systems and Optimal Control” and “Optimal Control and Dynamic Games: Large Time Behavior and Geometry”. If you are interested in contributing, please get in touch.
Our MTNS short course on Modelling, Simulation, and Control of Social Dynamics Across Scales with Greg Pavliotis and our session on Optimal Actuator/Sensor Design with Kirsten Morris have been accepted but postponed to 2021.
I joined the Editorial Board of Mathematics of Control, Signals, and Systems (Springer) , submissions on optimal control are particularly welcome!
2019:
2019:
Together with Karl Kunisch we organized a workshop on Feedback Control as part of the Special Semester on Optimization at RICAM.
Together with Giacomo Albi, Michael Herty and Giuseppe Visconti we organized a 4-session minisymposium at ICIAM 2019 on Novel Concepts in Model-driven Optimization and Control of Agent-based Systems.
Together with Mattia Zanella we organized a minisymposium at the 28th Biennial Numerical Analysis Conference on Computational methods for model-driven optimization and control under uncertainty.
The book on Numerical Methods for Hamilton-Jacobi-Bellman equations is finally available!
2018 and before:
2018 and before:
Starting from October 12th 2018, I'll be teaching a TCC course at Imperial on Mathematical Foundations of Reinforcement Learning, please don't hesitate to get in touch if you are interested in attending in person or holographically!.
Since April 2018 I am also affiliated to the Data Science Institute at Imperial.
The book on Optimal Control and Applications is finally out!.
An article by the Austrian Press Agency about our research on computational approaches to the control of social dynamics and collective behavior is available here.
The Workshop on Numerical methods for Hamilton-Jacobi equations in optimal control and related fields, November 21th-25th 2016 at RICAM was a great success. We had more than 30 international speakers who presented the state of the art concerning the numerical approximation of HJB eqns. and related topics. Thanks to all of them for their participation!
You can find here a talk that I gave in August in Jyväskylä about our current research on high-dimensional HJB equations. I wish I would have known the camera was recording the center of the classroom.
Emiliano Cristiani did a press release about our paper "Invisible control of self-organizing agents leaving unknown environments", which is now available in several Italian media.
I'll just leave this here.
Past conferences and talks
Past conferences and talks
2024:
2024:
High-Dimensional Control Problems and Mean-Field Equations with Applications in Machine Learning, Oberwolfach, DE, 12/24
Mathematics and Algorithms for Data, University of Bath, UK, 11/24.
MDay II (a celebration of M. Falcone's legacy), Sapienza University of Rome, IT, 11/24.
Applied Mathematics Seminar, University of Warwick, UK, 11/24.
MTNS 2024, Cambridge, UK, 8/24.
French-German-Spanish Conference on Optimization, Gijón, ES, 6/24.
New Trends in Optimal Control, Warwick/Venice, IT, 5/24.
Interacting Particle Systems: Analysis, Control, Learning and Computation, ICERM, US, 5/24.
27th Annual Conference of the Tunisian Mathematical Society, Monastir, TN, 4/24.
Control and Optimization Seminar, Louisiana State University, online, 3/24.
Imperial-UCL Numerics Seminar, ICL, UK, 2/24.
Modeling, analysis, and control of multi-agent systems across scales, CRM Pisa, IT, 1/24.
Numerical Methods for Optimal Transport Problems and Mean Field Games, UTFSM, CL, 1/24.
2023:
2023:
UCSB Applied Math/PDE/Data Science Seminar, online, 12/23.
Control Methods in Hyperbolic Partial Differential Equations, Oberwolfach, DE, 11/23.
6th European Conference on Computational Optimization, Heidelberg, 9/23.
International Congress on Industrial and Applied Mathematics, Tokyo, JP, 8/23.
Numerical Analysis and Scientific Computing seminar, University of Waterloo, CA, 8/23.
SIAM Conference on Control and its Applications, Philadelphia, US, 7/23.
Numerical Methods for Mean Field Games and Related Problems, UCL, UK, 7/23.
Numerical Optimization Seminar, University of Konstanz, DE, 7/23.
Numerical Aspects of Hyperbolic Balance Laws and Related Problems, Cortona, IT, 6/23.
Nonlinear Partial Differential Equations, Sapienza University of Rome, IT, 5/23.
Third AFOSR-Monterey Workshop on Computational Issues in Nonlinear Control, US, 5/23.
Applied and Computational Analysis Seminar, University of Cambridge, UK, 5/23.
British Applied Mathematics Colloquium, University of Bristol, UK, 4/23.
Center for Mathematics and Artificial Intelligence Colloquium, online, 3/23.
20 Years of the Johann Radon Institute (RICAM), Linz, AT, 3/23.
Deep-dive session on Optimal Control and Inference, Isaac Newton Institute, UK, 2/23.
Oden Institute Seminar, US, 2/23.
2022:
2022:
Chengdu Winter School on Numerical Methods for Evolution PDEs, online, 12/22.
Kinetic equations: Recent Developments and Novel Applications, BIRS-CMO Oaxaca, MX, 11/22.
MMSC 2022: Workshop on Mathematical Modeling and Scientific Computing, TU Munich (online), DE, 10/22.
Mathematical Data Science, Control and Optimization, KFU Graz, AT, 9/22.
Mathematical Theory of Networks and Systems MTNS22, Bayreuth, DE, 9/22 (semi-plenary).
SciCADE22 Scientific Computation and Differential Equations, University of Iceland, IS, 7/22.
Theory and numerics of Mean Field Games and Hamilton-Jacobi equations, Rome, IT, 6/22.
From Individual to Collective Behaviour in Biological and Robotic Systems, ICMS, UK, 6/22.
French Society for Industrial and Applied Mathematics Conference, Limoges, FR, 5/22.
SIAM Conference on Analysis of Partial Differential Equations, TU Berlin, DE, 3/22.
Numerical Analysis Seminar, The University of Hong Kong, HK, 3/22.
2021:
2021:
60th Conference on Decision and Control IEEE CDC21, December 13th-15th, Austin, Texas, US.
Deep Learning and Partial Differential Equations, INI Cambridge, UK, 11/21.
2021 SIAM Conference on Control and Its Applications, July 19th - 21st 2021, Spokane, Washington, US.
Ghana Numerical Analysis Seminar, July 2021, GH.
Analysis of Data-driven Optimal Control, May 9th-15th 2021, MFO Oberwolfach, DE.
Control in Times of Crisis Seminar, April 27th 2021, online.
PDEs and Numerical Methods Seminar, March 23rd 2021, Mathematical Laboratory INSA Rouen, FR (online).
Numerical Analysis Seminar, March 5th 2021, University of Bath, UK (online).
Third Multidisciplinary Workshop in Science and Engineering, January 18th-19th 2021, UTEM, CL (online).
2020:
2020:
DMV Annual Meeting 2020, September 14th-18th 2020, Online/Chemnitz, DE (online).
Seminario di Modellistica Differenziale Numerica, June 30th 2020, Online/Rome, IT (online).
Inverse Problems and Optimisation for PDEs, May 29th 2020, Scottish Numerical Methods Network (online).
Edinbugh Research Group in Optimization Seminar, January 22nd 2020, Edinburgh, UK.
2019:
2019:
Special Semester on Optimization, September 30th-December 11th 2019, RICAM Linz, AT.
Workshop on Optimal Control and Mean Field Games, October 14th-18th 2019, Rio de Janeiro, BR.
Third Monterey Workshop on Computational Issues in Nonlinear Control, October 7th-9th 2019, Naval Postgraduate School, US.
Control Methods in Hyperbolic Partial Differential Equations, November 1st-7th 2020, Oberwolfach, DE.
Numerical Aspects of Hyperbolic Balance Laws and Related Problems, Aug 31st -Sep 4th 2020, Alba di Canazei, IT.
MTNS 2020, August 24th-28th 2020, University of Cambridge, UK.
Kinetic Equations: Recent Developments and Novel Applications, May 3rd - 8th 2020, Casa Matemática Oaxaca, MX.
January 22nd 2020, University of Edinbugrh, UK.
Special Semester on Optimization, September 30th-December 11th 2019, RICAM Linz, AT.
Workshop on Optimal Control and Mean Field Games, October 14th-18th 2019, Rio de Janeiro, BR.
Third Monterey Workshop on Computational Issues in Nonlinear Control, October 7th-9th 2019, Naval Postgraduate School, US.
Algebraic Spline Geometry Meeting, August 21st-23rd 2019, Swansea University, UK.
International Conference on Continuous Optimization, August 5th-8th 2019, Berlin, DE.
International Congress on Industrial and Applied Mathematics, July 15th-19th 2019, Valencia, ES.
28th Biennial Numerical Analysis Conference, June 25th-28th 2019, University of Strathclyde, UK.
The British Applied Mathematics Colloquium 2019, April 24th-26th 2019, University of Bath, UK.
Seminario Cruz del Sur, March 13 2019, Universidad de la Frontera, Temuco, CL
The 90th(!) GAMM Annual Meeting, February 18th-22nd 2019, TU Wien, AT.
Scientific Machine Learning, January 28th-30th 2019, ICERM Brown, US.
2018:
2018:
Frontier Technologies for High-Dimensional Problems and Uncertainty Quantification, December 17th-21st 2018, RICAM Linz, AT.
From interacting particle systems to kinetic equations: modelling, control and numerical methods, November 26th-30th 2018, University of Verona, IT.
Algorithms and Applications of High Dimensional Approximation, November 22nd-23rd 2018, University of Bath, UK.
Mathematics and Applications Sussex Seminar, November 15th 2018, University of Sussex, UK.
Numerical Analysis and Scientific Computing Seminar, October 2nd 2018, University of Strathclyde, UK.
Research Program on Mathematical Biology , September 27th - October 7th 2018, Mittag-Leffler Insitut, SE.
LMS Applied Algebra and Geometry Meeting, September 10th 2018, Swansea University, UK.
IFIP TC 7 Conference on System Modelling and Optimization, July 23rd-27th 2018, Essen, DE.
The 12th AIMS Conference on Dynamical Systems, Differential Equations and Applications, July 5th-9th 2018, Taipei, TW.
Max Ent 2018, July 2nd-6th 2018, The Alan Turing Institute, London, UK.
Curves and Surfaces, June 28th-July 4th 2018, Arcachon, FR.
The 14th IEEE International Conference on Control and Automation, June 12th-15th 2018, Anchorage, Alaska, USA.
Oxford NA Seminar, May 22nd 2018, University of Oxford, UK.
UK-Japan Workshop on Analysis of Nonlinear PDEs, May 16th-18th 2018, Swansea, UK.
Data-Driven Modelling of Complex Systems, May 8th-10th 2018, The Alan Turing Institute, London, UK.
IFAC Workshop Lagrangian and Hamiltonian Methods for Nonlinear Control, May 1st-4th 2018, UTFSM, Valparaíso, CL.
XXXI Jornada de Matemática de la Zona Sur, April 26th-28th 2018, Universidad Austral de Chile, Valdivia, CL.
Challenges in Optimal Control of Nonlinear PDE-Systems, April 8th-14th 2018, Oberwolfach, DE.
Computational and Geometric Design, Optimization, and Optimal control, April 3rd 2018, Universidad del Rosario, Bogotá, CO.
The 89th(!) GAMM Annual Meeting, March 19th-23rd 2018, TU Munich, DE.
Applied Algebra and Combinatorics, March 9th 2018, Swansea University, UK.
2017:
2017:
Applied Mathematics Seminar November 24th 2017, University of Warwick, UK.
Control and Optimization Conference November 15th -17th 2017, Palaiseau, FR.
Applied and Numerical Analysis Seminar October 17th 2017, Imperial College London, UK.
19th Congress of the Austrian Mathematical Society September 11-15 2017, Paris-Lodron University of Salzburg, AT.
Pedestrian Dynamics: Modeling, Validation and Calibration, August 21st-25th 2017, Brown University, US.
Numerical methods for stochastic models: control, uncertainty quantification, mean-field, August 10th,16th 2017, CIRM Marseille, FR.
IFAC 2017 World Congress, July 9th-14th 2017, Toulouse, FR.
27th Biennial Numerical Analysis Conference, June 27th-30th 2017, University of Strathclyde, UK.
Numerical methods for optimal control problems: algorithms, analysis and applications, June 19th-23rd 2017, IndAM, Rome, IT.
International Workshop on Optimal Control of Dynamical Systems, May 15th-19th 2017, Graz, Austria.
SIAM Conference on Computational Science and Engineering, February 27th -March 3rd 2017, Atlanta, Georgia, US.
Workshop on Mathematical Medicine and Mathematical Pharmacology, February 2nd-3rd 2017, Swansea University, UK.
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