Physics-Guided Machine Learning

Universities and Institutes of France


June 1, 2022


  • Organisation/Company: Laboratoire Hubert Curien
  • Research Field: Computer science › Informatics Engineering Physics
  • Researcher Profile: First Stage Researcher (R1) Recognised Researcher (R2) Established Researcher (R3) Leading Researcher (R4)
  • Application Deadline: 01/06/2022 00:00 - Europe/Brussels
  • Location: France › Saint-Etienne
  • Type Of Contract: Temporary
  • Job Status: Full-time
  • Offer Starting Date: 03/10/2022
  • The success of Machine Learning relies on the availability of a large amount of training examples. While most of vision and natural language processing tasks can benefit from massive data coming from the Internet, many real world applications still require to resort to physics-based models to be addressed. This is particularly the case when predicting complex dynamical phenomena (e.g. climate forecasting, self-organization of matter, fluid dynamics, evolution of biological structures) which are typically modeled by partial/ordinary differential equations (PDE/ODE). Considering that most differential equations are costly over-simplistic representation of the underlying real phenomenon, a recent trend emerged aiming at combining physical knowledge and data-driven approaches. This combination can be addressed in different ways: (i) Machine Learning can be used to train surrogate models of PDE solvers 1, 2. These latter are usually expensive (they can take weeks!) and therefore do not scale well in high dimensions. Therefore, learning a cheap approximation of PDEs might be of great interest in many real world applications; (ii) Machine Learning can be used to discover automatically the dynamics (i.e. the underlying PDE) that is hidden behind the data 3, 4; This can be done by pre-defining or learning the differential terms of PDEs and optimizing the parameters of a linear combination; (iii) More challenging, the physical knowledge can be integrated in some way during the learning process 5, 6, 7, 8, 9.

    The objective of this thesis is to develop new methodological contributions in physics-guided Machine Learning in the specific domain of laser-matter interaction. Although this field has received some attention during the past few years 10, 11, 12, 13, it is still an emerging and exciting topic. In particular, the optimization of inhomogeneous energy absorption of ultrafast laser light impinging a rough surface remains an ongoing issue for laser manufacturing 14. Indeed, 3D topography, defined by shape, size and concentration of surface nanoreliefs, determines in a complex manner the radiative and nonradiative contributions in light scattering and surface wave excitation 15.

    In this thesis, we plan to develop the three main following scientific axes:

  • One major issue that laser-matter interaction can face comes from its difficulty to acquire mas- sive data. On the other hand, models in optics and photonics are available in the form of partial knowledge of physical dynamics. The objective is to benefit from this background knowledge at dif- ferent possible levels of the learning process: (i) by physically informing the initialization of model's parameters; (ii) by incorporating physics-based guidance into the architecture design; (iii) by inte- grating physical constraints in well-shaped loss functions; (iv) by building hybrid physics-ML models where data-driven models are exploited to correct the errors made by simplistic physical models. A key challenge shared by the last two points is to find an appropriate integration of physical laws and equations that have good properties to allow learning (i.e. differentiability, continuity, controllable complexity, ...). For example, the impact of 3D topography can be modeled by computational electrodynamics through Finite Difference Time Domain approach to solve Maxwell's equations (coupled PDE) and enhanced with physics-informed Machine Learning. Machine learning can be used to predict complex extreme local field enhancement and collective effects that appear during light-surface coupling, while considering adequate energy and flux con- servation laws.

  • PDEs are usually specified through some initial conditions and parameters. Each time the domain of interest changes (the geographic area considered in climate forecasting, the matter used in laser interaction, the biological structure studied, etc.), one needs to retrain from scratch the surrogate- based model from a (sufficiently) large amount of data. The objective of this thesis will be to investigate domain adaptation 16 solutions to transfer the knowledge from one domain to another by only having access to a limited number of training samples.

  • The interpretability of machine learning models is a recurring challenge. Physics-informed models already offer the advantage of being physically grounded and thus more interpretable 17. When considering hybrid physics-ML models (where data is used to learn an additional, less constrained, model), care must be taken in order to keep the interpretability of the model 18. If made inter- pretable, and especially in low data contexts, hybrid models can not only allow for a validation by physicists but also help or guide the scientific discovery process.
  • Expected candidate profile

  • Master or engineering student graduated with a degree in Machine learning, Data Science or in Applied Mathematics, or, physics student with a strong interest and background in Machine learning.
  • A student who is eager to exploit his/her skills in machine learning to address physical problems.
  • A candidate who has at least a B2 level of English.
  • References

    1 Isaac E. Lagaris, Aristidis Likas, and Dimitrios I. Fotiadis. Artificial neural networks for solving ordinary and partial differential equations. IEEE Trans. Neural Networks, 9(5):987–1000, 1998.

    2 Maziar Raissi, Paris Perdikaris, and George E. Karniadakis. Physics- informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. J. Comput. Phys., 378:686–707, 2019.

    3 Zichao Long, Yiping Lu, Xianzhong Ma, and Bin Dong. PDE-net: Learning PDEs from data. In Jennifer Dy and Andreas Krause, editors, Proceedings of the 35th International Conference on Machine Learning, volume 80 of Proceedings of Machine Learning Research, pages 3208–3216. PMLR, 10–15 Jul 2018.

    4 Joseph Bakarji, Kathleen P. Champion, J. Nathan Kutz, and Steven L. Brunton. Discovering governing equations from partial measurements with deep delay autoencoders. CoRR, abs/2201.05136, 2022.

    5 Alireza Yazdani, Lu Lu, Maziar Raissi, and George Em Karniadakis. Systems biology informed deep learning for inferring parameters and hidden dynamics. PLoS Comput. Biol., 16(11), 2020.

    6 Yuan Yin, Vincent Le Guen, J´er´emie Don`a, Emmanuel de B´ezenac, Ibrahim Ayed, Nicolas Thome, and Patrick Gallinari. Augmenting physical models with deep networks for complex dynamics forecasting. In 9th International Conference on Learning Representations, ICLR 2021, Virtual Event, Austria, May 3-7, 2021., 2021.

    7 Emmanuel de B´ezenac, Arthur Pajot, and Patrick Gallinari. Deep learning for physical processes: Incorpo- rating prior scientific knowledge. In 6th International Conference on Learning Representations, ICLR 2018, Vancouver, BC, Canada, April 30 - May 3, 2018, Conference Track Proceedings., 2018.

    8 Daniel L. Marino and Milos Manic. Combining physics-based domain knowledge and machine learning using variational gaussian processes with explicit linear prior. CoRR, abs/1906.02160, 2019.

    9 Jared Willard, Xiaowei Jia, Shaoming Xu, Michael Steinbach, and Vipin Kumar. Integrating scientific knowl- edge with machine learning for engineering and environmental systems. 2020.

    10 Kan Yao, Rohit Unni, and Yuebing Zheng. Intelligent nanophotonics: merging photonics and artificial intelli- gence at the nanoscale. Nanophotonics, 8(3):339–366, Jan 2019.

    11 B. Mills, D.J. Heath, J.A. Grant-Jacob, and W.R. Eason. Predictive capabilities for laser machining via a neural network. Optics Express, 26, 2018.

    12 B. Mills, D.J. Heath, J.A. Grant-Jacob, Y. Xie, and W.R. Eason. Image- based monitoring of femtosecond laser machining via a neural network. Journal of Physics: Photonics, 1, 2019.

    13 I. Malkiel, M. Mrejen, A. Nagler, U. Arieli, L. Wolf, and H. Suchowski. Plasmonic nanostructure design and characterization via deep learning. Light: Science & Applications, 7, 2018.

    14 Razvan Stoian and Jean-Philippe Colombier. Advances in ultrafast laser structuring of materials at the nanoscale. Nanophotonics, 9(16):4665–4688, 2020.

    15 Anton Rudenko, Cyril Mauclair, Florence Garrelie, Razvan Stoian, and Jean-Philippe Colombier. Self- organization of surfaces on the nanoscale by topography-mediated selection of quasi-cylindrical and plasmonic waves. Nanophotonics, 8(3):459–465, 2019.

    16 Ievgen Redko, Emilie Morvant, Amaury Habrard, Marc Sebban, and Youn`es Bennani. Advances in Domain Adaptation Theory. Elsevier, August 2019.

    17 Jared Willard, Xiaowei Jia, Shaoming Xu, Michael Steinbach, and Vipin Kumar. Integrating physics-based modeling with machine learning: A survey. arXiv preprint arXiv:2003.04919, 1(1):1–34, 2020.

    18 Amuthan A Ramabathiran and Prabhu Ramachandran. Spinn: Sparse, physics- based, and partially inter- pretable neural networks for pdes. Journal of Computational Physics, 445:110600, 2021.

    Funding category: Contrat doctoral

    A 3-year fellowship is available in Laboratory Hubert Curien at University Jean Monnet of Saint-Etienne, (member of Lyon University) France.

    PHD Country: France

    Offer Requirements Specific Requirements
  • Master or engineering student graduated with a degree in Machine learning, Data Science or in Applied Mathematics, or, physics student with a strong interest and background in Machine learning.
  • A student who is eager to exploit his/her skills in machine learning to address physical problems.
  • A candidate who has at least a B2 level of English.
  • Contact Information
  • Organisation/Company: Laboratoire Hubert Curien
  • Organisation Type: Public Research Institution
  • Website: https://
  • Country: France
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