Raphaël Pestourie, MBA, PhD


I am a Postdoctoral Associate of Prof. Steven G. Johnson's group in the Mathematics Department of the Massachusetts Institute of Technology (MIT) and my research boils down to one word: HEDGing.

Over centuries, humans have been great at developing informative abstract knowledge using the scientific method. Unfortunately, when it comes to using that knowledge on specific engineering problems by formulating intuitions or educated guesses, the number of parameters and goals that our working memory can take into account simultaneously is limited to about four... (Cowan (2010))

Enter HEDGing: High-dimensional Educated Digital Guessing! HEDGing is a computing paradigm that I developed over the past decade. My research scales the number of parameters and goals to tackle problems with millions to billions of independent components, by teaching knowledge to computer programs and using their educated digital guesses.

For example, in artificial intelligence, I taught physics and uncertainty quantification to machine learning algorithms so that their predictions not only benefit from existing data, but also from existing human knowledge. Applications include optics, thermo-electrics, mechanics, and fluidics.

In optics in particular, I incorporated Maxwell's equations and relevant field knowledge such as common approximations into a computer program, and in return, the program could design billions of parameters simultaneously taking into account multiple complex goals.

HEDGing is a very exciting computing paradigm which takes advantage of the high-dimensional and parallel properties of computer memory and human knowledge, developed over centuries of scientific method, to achieve the best of both worlds. I am now looking into expanding it to other areas such as green technologies and bio-medical applications.

HEDGing is at the interface between numerical methods, (Bayesian and scientific) machine learning techniques, and end-to-end large-scale optimization. My work is multidisciplinary and experiment-driven on a wide range of applications. I thrive working on collaborative, interdisciplinary problems where research outcomes are larger than the mere sum of the contributions from each discipline. My philosophy is to develop tools through impactful applications rather than focusing on methods development alone.

Social media:

Follow me on Twitter @rpestouriePhD and on Google Scholar.


Peer-reviewed articles: (* these authors contributed equally)

[11] Z. Li, R. Pestourie, et al. "Empowering Metasurfaces with Inverse Design: Principles and Applications," ACS Photonics [DOI]

[10] Z. Li*, R. Pestourie*, et al. "Inverse design enables large-scale high-performance meta-optics reshaping virtual reality," Nat. Comm. [DOI] | Press: Nature blog

[9] Z. Lin, R. Pestourie, et al. "End-to-end metasurface inverse design for single-shot multi-channel imaging," Optics Express

[8] E. Bayati*, R. Pestourie*, et al. "Inverse Designed Extended Depth of Focus Meta-Optics for Broadband Imaging in the Visible," Nanophotonics [DOI]

[7] L. Lu, R. Pestourie, et al. "Physics-informed neural networks with hard constraints for inverse design," SIAM Journal on Scientific Computing [DOI]

[6] Z. Lin, C. Roques-Carmes, R. Pestourie, et al.. "End-to-end nanophotonic inverse design for imaging and polarimetry," Nanophotonics [DOI]

[5] R. Pestourie et al. "Active learning of deep surrogates for PDEs: Application to metasurface design," npj Computational Materials [DOI] | Press: IBM blog

[4] E. Bayati*, R. Pestourie*, et al., “Inverse designed metalenses with extended depth of focus,” ACS Photonics [DOI]

[3] Z. Lin, V. Liu, R. Pestourie, et al., “Topology optimization of freeform large-area metasurfaces,” Optics Express [DOI]

[2] R. Pestourie, et al., “Inverse design of large-area metasurfaces,” Optics Express [DOI] | > 150 citations | Press: MIT News

[1] C. Pérez-Arancibia, R. Pestourie, and S.G. Johnson, “Sideways adiabaticity: Beyond ray optics for slowly varying metasurfaces,” Optics Express [DOI]

Pre-prints under review:

[4] L. Lu, R. Pestourie, et al. "Multifidelity deep neural operators for efficient learning of partial differential equations with application to fast inverse design of nanoscale heat transport," 2022 [arXiv]

[3] C. Munley, ..., R. Pestourie, S.G. Johnson, and Arka Majumdar "Inverse-Designed Meta-Optics with Spectral-Spatial Engineered Response to Mimic Color Perception," 2022 [arXiv]

[2] S. Fisher, R. Pestourie, and S.G. Johnson "Efficient perturbative framework for coupling of radiative and guided modes in nearly periodic surfaces," (2022) [arXiv]

[1] R. Pestourie, et al. "Physics-enhanced deep surrogates for PDEs," (November 2021) [arXiv]

Patent: R. Pestourie, Y. Mroueh, P. Das, S. G. Johnson "Active learning of data models for scaled optimization" US Patent 17/405318

PhD thesis: "Assume Your Neighbor is Your Equal: Inverse Design in Nanophotonics" Harvard University Library website.

Videos of invited talks

Invited talk at SciMLCon on March 23rd 2022 Physics-enhanced deep surrogates trained end to end

Invited seminar at IBM on February 24th 2022 Scientific machine learning: from optics to deep surrogates

Invited seminar at MERL on February 8th 2022 Extreme optics design as a large-scale optimization problem

Invited seminar at IEEE Photonics Society (Boston) on May 13th 2021 Inverse design of complex meta-optics

About Me

Like my scientific ML models, I am highly educated. I earned five masters, a PhD, and a postdoc:

  1. Diplôme grande école from ESSEC

  2. Ingénieur des Arts et Manufactures specialized in Physics from École Centrale Paris (now CentraleSupelec)

  3. Master of research in Nanosciences from Université Paris Saclay

  4. MBA from ESSEC

  5. AM in Statistics from Harvard University

  6. PhD in Applied Mathematics with a secondary field in Computational Science and Engineering from Harvard John A. Paulson School of Engineering and Applied Sciences

  7. Postdoctoral studies in the Mathematics department at MIT (3 years).

During my PhD, I was an Arthur Sachs Fellow selected by the French Fulbright Commission, and a Jean Gaillard fellow selected by the Board of Directors of the École Centrale des Arts et Manufactures in Paris. In addition, I was awarded membership into the Harvard Graduate School Leadership Institute through the Harvard Kennedy School’s Center for Public Leadership.

I am a strong believer that research should result in innovation and commercialization. I have working experience in a hedge fund (a not so different kind of hedging) and in startups both as an employee and as a founder. I have published many peer-reviewed articles (my Google Scholar page) and am a patent inventor.

I come from France and am an advocate of bilingualism. I love learning languages and have lived in three different continents. Outside work, I play music with/for my kids, and build stuff digitally or in real-life.

Contact me at rpestour ατ mit δøτ edu


Please check out my résumé.


News (archived)

Please follow my Twitter account for the latest news: @rpestouriePhD

November 2021: I was invited to present at OPTICSMEET2021 on Saturday November 6th. My virtual presentation will be about a new paradigm for surrogate-based inverse design in nanophotonics, leveraging AI to go beyond the locally periodic approximation.

November 2021: Surrogate-based inverse design meets end-to-end optimization. We discovered spontaneous multiplexing when combining large-scale metasurface design and Tikhonov regularization for multi-channel imaging (spectral, polarization and depth), end-to-end. Check it out on arXiv.

September 2021: Excited to talk about "Extreme Optics: Inverse Design and Experimental Realizations of Ultra-Large-Area Complex Meta-Optics" at the 15th International Congress on Artificial Materials for Novel Wave Phenomena - Metamaterials 2021

September 2021: Our paper Inverse Designed Extended Depth of Focus Meta-Optics for Broadband Imaging in the Visible was accepted in the journal Nanophotonics.

August 2021: Our paper "Physics-informed neural networks with hard constraints for inverse design" was accepted in SIAM Journal on Scientific Computing.

August 2021: Excited to talk at SPIE Optics and Photonics in the session on Deep Learning in Photonics in San Diego, CA!

July 2021: I just pushed the supporting code of my active learning article in npj Computational Materials. It is part of the IBM open source project on uncertainty quantification called UQ360.

June 2021: Excited to talk at the OSA Optical Design and Fabrication Congress about complex design of metasurfaces.

May 2021: Our work on surrogate models for PDEs was features on IBM blog AI boosts the discovery of metamaterials vital for next-gen gadgets.

May 2021: I will be presenting on "Inverse Design of Complex Meta-Optics" on May 13th at the Boston Chapter of the IEEE Photonic Society. Thank you for the invitation!

May 2021: We put on arXiv our latest work on lenses with Extended Depth of Field. Check it out! Inverse Designed Extended Depth of Focus Meta-Optics for Broadband Imaging in the Visible.

April 2021: We put on arXiv the fruit of a multiple year collaboration culminating in the larger metasurface in the visible to date (cm diameter)! Check it out Inverse design enables large-scale high-performance meta-optics reshaping virtual reality.

April 2021: Our paper "Active learning of deep surrogates for PDEs", where we extend our work previous in active learning to mechanical elasticity equations, was accepted at ICLR 2021 Workshop on Deep Learning for Simulation! I am looking forward to sharing this work with the community on May 7th!

March 2021: Excited to give a seminar "Efficient inverse design for extreme applications in optics" in the Instituto de Ingeniería Matemática y Computacional at Pontificia Universidad Católica de Chile!

February 2021: Our paper "Physics-informed neural networks (PINN) with hard constraints for inverse design" is now available on arXiv. It presents PINN used in inverse design, especially enforcing the PDE constraint via an augmented Lagrangian method. The advantage of this approach is that the resulting designs are smoother.

December 2020: Our paper "End-to-end nanophotonic inverse design for imaging and polarimetry." is available ahead of print in Nanophotonics .

December 2020: Excited to have been invited to present my research "Inverse design and deep learning for optical metasurfaces" for the groups of Prof. Boubacar Kanté and Prof. Eli Yablonovitch at UC Berkeley.

October 2020: npj Computation Materials published my collaboration with MIT-IBM Watson AI lab Active learning of deep surrogates for PDEs: application to metasurface design on October 29, 2020.

October 2020: I presented the poster "Active learning of deep surrogates for PDEs: Application to metasurface design" at the AI for Materials: From Discovery to Production symposium organised by the New York Academy of Sciences, on October 6, 2020.

August 2020: I just put on arXiv this fantastic work on active learning for PDE surrogate models done in collaboration with MIT-IBM lab. Using our active-learning algorithm, we can find the training points that make the biggest difference with respect to model accuracy improvement, thus reducing the need for data by more than an order of magnitude! The surrogate model is 100x faster than solving the PDE directly. Active learning of deep surrogates for PDEs: Application to metasurface design

June 2020: We just pushed an exciting ground-breaking article on arXiv about new usage of large-scale optimization for inverse design in nanophotonics "End-to-End Inverse Design for Inverse Scattering via Freeform Metastructures"

March 2020: ACS Photonics published my collaboration with Elyas Bayati and Arka Majumdar from UW of an inverse-designed lens with extended depth of field in 2D. Inverse designed metalenses with extended depth of focus

March 2020: L'Essentiel du Sup published an interview of me about the impact that multidisciplinarity has played in my student career as a dual degree student at ESSEC and École Centrale Paris (CentraleSupelec). Oser l'hybridation, de la théorie à la pratique

February 2020: I published a repository called fdfd_local_field on GitHub with julia code for embarassingly parallel simulations of Maxwell's equation in two dimensions. Github/rpestourie

January 2020: the 3rd Physics Informed Machine Learning Workshop in Santa Fe accepted my abstract "Active neural networks for electromagnetic surrogate models" about my current collaborative work with IBM Research. PIML 2020

December 2019: I defended my PhD in Applied Mathematics from Harvard John A. Paulson School of Engineering and Applied Sciences: "Assume Your Neighbor is Your Equal: Inverse Design in Nanophotonics" (available at Harvard University Library systems).

October 2019: Elyas Bayati and I pushed the first experimental application designed by my optimization framework-–a 2D lens with extended depth of field on arXiv. Inverse designed metalenses with extended depth of focus

May 2019: I presented an extension of my large-scale optimization framework to three dimensional applications at 2019 IEEE MTT-S International Conference on Numerical Electromagnetic and Multiphysics Modeling and Optimization. NEMO 2019

May 2019: I was interviewed by Jennifer Chu from MIT News Office to vulgarize my research. Mathematical technique quickly tunes next-generation lenses

May 2019: Optics Express published the extension of my optimization framework to topology optimization. Topology optimization of freeform large-area metasurfaces

March 2019: I defended my PhD secondary field in Computational Science and Engineering: "Hybrid Maxwell’s equations solver and inverse design tool for metasurfaces".

January 2019: I was invited to present my paper "Inverse design of large-area metasurfaces" at the Workshop on Numerical Analysis of Partial Differential Equations in Concepción, Chile. WONAPDE 2019

December 2018: Optics Express published my seminal paper about large-scale optimization of metasurfaces based on the local periodic approximation. Inverse design of large-area metasurfaces

November 2018: Optics Express published a study that my colleague Carlos Pérez-Arancibia conducted with me and Prof Steven G. Johnson about a locally periodic approximation for continuous surfaces. Sideways adiabaticity: beyond ray optics for slowly varying metasurfaces