Machine Learning for Solid Mechanics

JS Chen, WaiChing Steve Sun, Qizhi He and Nick Vlassis

Department of Mechanical and Aerospace Engineering, Rutgers University

Relevance to WCCM–ECCOMAS

This short course will introduce practical and scientific machine learning methods for solid mechanics, with an emphasis on how modern data-driven methods can be formulated, interpreted, and deployed in mechanics problems.

Course description

This short course is intended for graduate students, researchers, and practitioners with a background in continuum mechanics, computational mechanics, materials, and applied physics. The course will introduce practical and scientific machine learning methods for solid mechanics, with an emphasis on how modern data-driven methods can be formulated, interpreted, and deployed in mechanics problems. It will also highlight how these methods can be used to integrate and automate AI-enabled workflows in both research and engineering practice.

The course will cover four main methodological directions: data-driven and neural network-augmented computing for nonlinear solid mechanics; thermodynamics-based data-driven methods for elastic and inelastic modeling; latent-space generative artificial intelligence for the inverse design of structures with target functionalities; and automatic engineering workflows with agentic AI.

The objective is to expose participants to recent advances across these four directions and to pair that overview with hands-on practical implementation. The course will therefore emphasize both the fundamentals of using advanced AI tools and their deployment in these specific mechanics and engineering applications. Case studies will demonstrate how these methods support data-driven computational solid mechanics, generative design of material systems and structures, and agentic AI workflows in which natural-language commands are used to automate data processing, modeling tasks, and parts of the engineering design process.

The course content is also informed by the organizers’ forthcoming book, Machine Learning for Solid Mechanics, currently in preparation for publication by Wiley.

Objectives and target groups

This short course is intended for graduate students, researchers, and practitioners with a background in continuum mechanics, computational mechanics, materials, and applied physics.

  • Data-driven and neural network-augmented computing for nonlinear solid mechanics
  • Thermodynamics-based data-driven methods for elastic and inelastic modeling
  • Latent-space generative artificial intelligence for the inverse design of structures with target functionalities
  • Automatic engineering workflows with agentic AI

Participants will be expected to bring their own laptops for the hands-on sessions, and course materials and sample code will be shared via a course website and an online repository before the event.

Scientific and technical areas covered

  • Computational and methodological foundations for machine learning in solid mechanics
  • Data-driven formulations and constitutive modeling
  • Generative design of materials and structures
  • AI-assisted engineering workflows
  • Manifold-based representations of high-dimensional mechanical response data
  • Neural operator frameworks for nonlinear, elastic, and inelastic solids
  • Diffusion-based and latent space generative models
  • Foundation models for engineering reasoning and workflow support
  • Agentic AI systems in engineering computation

Bio-sketch

J. S. Chen is currently the Inaugural William Prager Chair Professor and Distinguished Professor of Structural Engineering Department, Professor of Mechanical and Aerospace Engineering Department, and the Founding Director of Center for Extreme Events Research at UC San Diego. Before joining UCSD in October 2013, he was the Chancellor’s Professor of UCLA Civil & Environmental Engineering Department where he served as the Department Chair during 2007-2012. J. S. Chen’s research is in computational mechanics, meshfree method, multiscale materials modeling, machine-learning-enhanced computational mechanics, and physics-informed data-driven computing. He is the Past President of USACM and EMI. He has received numerous awards, including the John von Neumann Medal from USACM, the Belytschko Medal from USACM, the Raymond D. Mindlin Medal from EMI, the Computational Mechanics Award from IACM, the Grand Prize from Japan Society for Computational Engineering and Science (JSCES), the Ted Belytschko Applied Mechanics Award from ASME Applied Mechanics Division, the Computational Mechanics Award from Japan Association for Computational Mechanics (JACM), among others.

WaiChing Sun is an associate professor in the Department of Civil Engineering and Engineering Mechanics at Columbia University. Sun obtained his B.S. from UC Davis (2005); M.S. in civil engineering (geomechanics) from Stanford (2007); M.A. degree from Princeton (2008); and Ph.D. in theoretical and applied mechanics from Northwestern (2011). Prior to joining Columbia, he was a senior member of technical staff in the mechanics of materials department at Sandia National Laboratories (Livermore, CA). He is the recipient of the John Argyris Award (2020), NSF CAREER Faculty Development Award in 2019, ASCE EMI Leonardo da Vinci Award in 2018, the Zienkiewicz Numerical Methods in Engineering Prize in 2017, US Air Force Young Investigator Program Award in 2017, the Dresden Fellowship in 2016, US Army Young Investigator Program Award in 2015, and the Caterpillar Best Paper Prize in 2013, among others.

Qizhi (“KaiChi") is an Assistant Professor in the Department of Civil, Environmental, and Geo-Engineering at the University of Minnesota (UMN). He received his Ph.D. in Structural Engineering and Computational Science from the University of California, San Diego. Before joining UMN in 2022, he was a Postdoctoral Research Associate in Scientific Machine Learning at Pacific Northwest National Laboratory. Dr. He’s research focuses on the development of next-generation numerical algorithms and physics-integrated machine learning methods for multiphysics and multiscale modeling of materials and geosystems under extreme conditions. His work also advances model reduction, inverse analysis and digital twin frameworks for large-scale applications in solid mechanics, material design, and geosciences. Dr. He is a member of the ASCE Engineering Mechanics Institute (EMI) technical committees on Computational Mechanics and Machine Learning in Mechanics, and he also serves on the editorial boards of Computers and Geotechnics and Acta Mechanica Sinica.

Nikolaos Napoleon Vlassis is an Assistant Professor in the Department of Mechanical and Aerospace Engineering at Rutgers University, where he is the Principal Investigator of the Computational Mechanics and Artificial Intelligence (MechAI) Group. He received his Ph.D. in Civil Engineering and Engineering Mechanics from Columbia University in 2021, where he was a Mindlin Scholar, and his Diploma in Civil Engineering from the National Technical University of Athens in 2017. Before joining Rutgers in 2023, he was a Postdoctoral Research Scientist in the Department of Civil Engineering and Engineering Mechanics at Columbia University. Dr. Vlassis’s research focuses on computational mechanics, artificial intelligence for material modeling and design, geometric deep learning, interpretable machine learning for elastoplasticity, generative AI for inverse design, and multiscale computational solid mechanics. Dr. Vlassis is a member of ASME, ASCE, USACM, and the EMI technical committees on Computational Mechanics and Machine Learning in Mechanics. He also serves as the New Jersey Liaison for the SIAM New York–New Jersey–Pennsylvania Section.