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Scientific Machine Learning for Modeling and Computer Simulations

Description et justification du domaine

There has recently been a great interest and a growing enthusiasm in the development of Machine Learning-based approaches for applications in science and engineering. This new field of research has actually been coined Scientific Machine Learning, in short SciML, and has the potential to make innovative breakthroughs in scientific discovery and knowledge. The keen interest in SciML is soaring due to the combination of several factors: the availability of massive amounts of data from scientific instruments, computational models, or other sources; the development and use of efficient data analysis algorithms; constant advances in high-performance computing; and some recent successes reported by industry, research laboratories, and academia (see e.g., DOE report on “Basic Research Needs Workshop for Scientific Machine Learning Core Technologies for Artificial Intelligence”, 2019). Despite the pervasive spread and effort to integrate Machine Learning techniques into PDE-based computer simulations, there are still numerous challenges and opportunities for developing new SciML methodologies and improving the accuracy, robustness, reliability, and the theory of SciML required for routine use in science and engineering applications.

Generations of scientists have worked to identify and characterize the basic laws underlying the current engineering challenges involving multi-scale and multi-physics models, and computational science has worked to develop tools and methodologies to turn these mathematical models into effective predictive models. Yet, there remain a large number of computational bottlenecks that will require new paradigms of computation, of which SciML is the most promising. Among these obstacles, we mention the ‘curse of dimensionality’ which is particularly acute in PDE-based optimization, fine parameter tuning for complex algorithms, and an effective theory of reduced-order modeling. Furthermore, SciML offers the possibility of developing data-driven subscale models for complex phenomena out of reach of numerical models, such as for crack propagation, composite materials, and fluid-structure interactions. Yet, the field of SciML also imposes new requirements to Machine Learning tools, namely about accuracy and robustness, which will surely help to clarify the theoretical foundations of those tools, which are too often the result of ad-hoc development.

The idea of taking into account prior scientific knowledge expressed from first principles has the advantage of reducing the amount of data necessary for training and prediction and the potential to improve the fidelity of phenomenological models in solid and fluid mechanics. Scientific machine learning can also help develop new surrogates for complex forward models, optimize parameter tuning within multi-scale and multi-physics simulations, and enhance the predictive capabilities of scientific computing. SciML has been used to extract from data, the interaction terms in models of differential equations, thereby providing new means of developing and validating traditional scientific models. By combining traditional finite-element solvers to Neural Networks, researchers have constructed new classes of solvers that are not entirely beholden to the geometry (i.e., the mesh) of the domain and can thereby overcome the curse of dimensionality. There are also several computational problems that have been traditionally overlooked because only ad-hoc algorithms were available, such as the broad-phase search in a contact detection problem, but for which one has hope to obtain accurate and fast algorithms based on image recognition.

SciML is by nature an interdisciplinary domain of research, which requires expertise from applied and computational mathematics, computer and data science, engineering, and physical and natural sciences. The proposed research theme is therefore the bridge between Machine Learning and traditional modeling in engineering, and therefore should be represented in IVADO’s long-term vision. SciML will undoubtedly have a significant impact for a wide range of applications in solid mechanics, fluid mechanics, heat transfer, wave propagation, material sciences, subsurface modeling, health sciences, etc. It will also assist in conceptualizing new paradigms for the development of digital twins and cyber-physical systems for use in the field of Industry 4.0.

Ajout 14/07 : C’est un thème qui vise à structurer les échanges entre le sujet contemporain de l’apprentissage automatique et celui de la modélisation numérique. Cette interface regroupe des chercheurs de plusieurs disciplines d’ingénierie qui ne se retrouveront pas dans la majorité des thèmes proposés, car ceux-ci sont en grande majorité axés sur des champs d’applications. L’apprentissage automatique est fondamentalement un développement informatique et mathématique, donc abstrait, et il est pertinent de formuler les axes de recherche en termes méthodologiques, plutôt qu’en termes d’expertises spécifiques au champ d’application. De plus, l’échange entre l’apprentissage automatique et les méthodes traditionnelles d’approximation ont le potentiel d’aider les deux domaines. En particulier, les questions entourant les notions de convergence, de précision et de stabilité sont mal définies en apprentissage automatique. Finalement, j’aimerais insister sur le fait que la majorité des numériciens et numériciennes, ceux de Polytechnique qui utilisent le calcul de haute performance quotidiennement pour la modélisation, utilisent déjà les techniques d’apprentissage automatique dans certains de leurs projets.

Contexte

Mots-clefs : Predictive scientific modeling, Physics-informed neural network (PINN), Domain-aware and physics-informed learning, Adaptive algorithms for enhanced accuracy, A posteriori error analysis , Enhanced modeling and simulation with machine learning , Verification and robustness, Model validation, Reduced-order modeling, Digital twin, internet of things, cyber-physical systems

Organisations pertinentes :

  • Hydro-Québec, Maya HTT, Altair Engineering, Ansys, Julia, Simutech Group, Bombardier, Aéro Montréal, MDA Ltd, Centre de Recherches Mathématiques, MITACS, Compute Canada and Calcul Québec, Centre de Technologies Avancées, CANMET Materials, IACM – International Association for Computational Mechanics, USACM – United States Association for Computational Mechanics, CACSE – Canadian Association for computational Mechanics
  • (Ajout 22/07) Safran R&T Center, The Oden Institute at UT Austin, ETS, Canadian Statistical Sciences Institute

Personnes pertinentes suggérées durant la consultation :

Les noms suivants ont été proposés par la communauté et les personnes mentionnées ci-dessous ont accepté d’afficher publiquement leur nom. Notez cependant que tous les noms des professeur.e.s (qu’ils soient affichés publiquement ou non sur notre site web) seront transmis au comité conseil pour l’étape d’identification et de sélection des thèmes stratégiques. Notez également que les personnes identifiées durant l’étape de consultation n’ont pas la garantie de recevoir une partie du financement. Cette étape sert avant tout à présenter un panorama du domaine, incluant les personnes pertinentes et non à monter des équipes pour les programmes-cadres.

  • David Vidal
  • Marc Laforest
  • Serge Prudhomme
  • Steven Dufour
  • Frederick Gosselin
  • Jerome Vetel
  • Julie Carreau

Programmes-cadres potentiels

Foundational topics of research interest would be:

  1. Development of physics-informed neural network (PINN) algorithms for the solution of initial and boundary-value problems involving systems of ordinary or partial differential equations. These systems of equations are virtually present in all fields of science and engineering.
  2. Mathematical analysis of neural network structures and their performance, convergence and stability, well-posed formulations, approximation properties of deep neural networks, initialization of networks, a posteriori error estimation of neural network solutions and adaptive methods, a priori estimation of the number of data points for training and testing, etc.
  3. Development of data-driven subscale models.
  4. Development of data-driven methods to optimize traditional numerical models, through the optimization of the discretization parameters such as the order of the elements or the underlying mesh.
  5. Development of uncertainty quantification methodologies for machine learning predictions as data from observations or model input parameters are typically noisy and uncertain.
  6. Verification and validation of machine learning-based models.

Documentation complémentaire

(pas de documentation complémentaire pour le moment)

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Historique

13 juillet 2021 : Première version

15 juillet 2021 : Ajout d’informations complémentaires, d’organisations et personnes pertinentes

22 juillet 2021 : Complément d’information dans la section “Contexte”