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Learning Neural Constitutive Laws from Motion Observations for Generalizable PDE Dynamics
Pingchuan Ma · Peter Yichen Chen · Bolei Deng · Josh Tenenbaum · Tao Du · Chuang Gan · Wojciech Matusik

Tue Jul 25 02:00 PM -- 04:30 PM (PDT) @ Exhibit Hall 1 #813

We propose a hybrid neural network (NN) and PDE approach for learning generalizable PDE dynamics from motion observations. Many NN approaches learn an end-to-end model that implicitly models both the governing PDE and constitutive models (or material models). Without explicit PDE knowledge, these approaches cannot guarantee physical correctness and have limited generalizability. We argue that the governing PDEs are often well-known and should be explicitly enforced rather than learned. Instead, constitutive models are particularly suitable for learning due to their data-fitting nature. To this end, we introduce a new framework termed "Neural Constitutive Laws" (NCLaw), which utilizes a network architecture that strictly guarantees standard constitutive priors, including rotation equivariance and undeformed state equilibrium. We embed this network inside a differentiable simulation and train the model by minimizing a loss function based on the difference between the simulation and the motion observation. We validate NCLaw on various large-deformation dynamical systems, ranging from solids to fluids. After training on a single motion trajectory, our method generalizes to new geometries, initial/boundary conditions, temporal ranges, and even multi-physics systems. On these extremely out-of-distribution generalization tasks, NCLaw is orders-of-magnitude more accurate than previous NN approaches. Real-world experiments demonstrate our method's ability to learn constitutive laws from videos.

Author Information

Pingchuan Ma (MIT CSAIL)
Peter Yichen Chen (MIT CSAIL)
Bolei Deng (Computer Science and Artificial Intelligence Laboratory, Electrical Engineering & Computer Science)
Josh Tenenbaum (MIT)

Joshua Brett Tenenbaum is Professor of Cognitive Science and Computation at the Massachusetts Institute of Technology. He is known for contributions to mathematical psychology and Bayesian cognitive science. He previously taught at Stanford University, where he was the Wasow Visiting Fellow from October 2010 to January 2011. Tenenbaum received his undergraduate degree in physics from Yale University in 1993, and his Ph.D. from MIT in 1999. His work primarily focuses on analyzing probabilistic inference as the engine of human cognition and as a means to develop machine learning.

Tao Du (Tsinghua University)
Chuang Gan (Umass Amherst/ IBM)
Wojciech Matusik (MIT)

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