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SC17-003: Machine Learning for Solid Mechanics

WaiChing Sun, Columbia University
JS Chen, University of California, San Diego
Lab Instructors: Nikolas Vlassis & Bahado Bahmani, Columbia University, Karan Taneja & Kristen Susuki, UC San Diego
This course will be offered to graduate students and researchers to introduce the practical data analytics, dimension reduction, and machine learning techniques, for a variety of science and engineering applications in materials, structures, and systems. This course is designed for the audience with a background in mechanics and/or applied physics. The course will provide an overview of four major categories of machine learning techniques (dimensional reduction of manifold data, geometric learning of graphs, manifold embedding, and deep reinforcement learning) and a data-driven model-free framework. Case studies will be used to demonstrate how these learning techniques have enhanced research and technology advancements. These application problems will include a data-driven model-free paradigm for complex material systems, reduced-order modeling of fracture and thermal fatigue analysis, geometric learning for polycrystal and granular systems, and reinforcement learning-enabled multiscale modeling for decision-making for design-of-experiments. Lecture materials and lab handouts will be provided before the short course.
Target Groups:
Graduate students, researchers with an understanding of continuum mechanics. A course website will be set up for course materials and sample codes repository before the short course date.
Scientific/Technical areas covered:
  1. Manifold learning enhanced data-driven modeling of nonlinear materials
  2. Dimension reduction by manifold learning and autoencoders
  3. Geometric learning for predicting path-dependent constitutive responses
  4. Representation learning for high-dimensional data with physics constraints
  5. Reduced-order modeling for fracture and thermal fatigue problems

Provisional schedule



8 weeks before USNCCM

Short course webpage

4 weeks before USNCCM

Code repository

Offline lecture

Overview (Instructor: Chen & Sun)

Offline lecture

Practical tutorial: TensorFlow, PyTorch, Jupiter notebook, cloud computing, code binding

(Instructor: Vlassis & Sun)

8:30am -9:30 am

Deep geometric learning 1: graph embeddings for constitutive modeling and reduced-order modeling with limited data

(Instructor: Sun)

9:30am -9:45am

Coffee Break

9:45am - 10:45am

Manifold Based Learning and Data-Driven Computing for Nonlinear Solid Mechanics: Dimension Reduction and Thermodynamics (Instructor: Chen)


Coffee break


Jupiter Lab 1

noon - 1:00pm

Lunch break


Neural Network Enhanced Computational Mechanics for Localization Problems

(Instructor: Chen)


Coffee break


Deep geometric learning 2: Geometric autoencoder and optimal transport for de-noising of data for elasticity

(Instructor: Bahmani, & Sun)


Coffee break


Jupiter Lab 2

Expected and the minimal number of participants: Expected = 20.