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Director of Research (if dissertation) or Advisor (if thesis)
Z, Y
Doctoral Committee Chair(s)
Z, Y
Committee Member(s)
Raginsky, Maxim
Belabbas, Mohamed
Kim, Joohyung
Department of Study
Electrical & Computer Eng
Discipline
Electrical & Computer Engr
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Physics Informed Neural Networks
Machine Learning
Abstract
One of the core functions of computers has been their ability to perform modeling tasks that predict and explain the world. One of the most common approaches for doing this has been the finite element method. However, this approach is computationally costly and can be slow. In more recent years, parallel computing strategies have become a popular alternative. These approaches use neural networks or other machine learning methods to model and predict the behavior of systems. One of these techniques that is especially promising is the Physics-Informed Neural Network, or PINN. PINN uses a neural network to efficiently and accurately solve partial differential equations or PDEs. In this work, we introduce an improvement to the PINN method. This new approach is called the ``Drift Correcting Multiphysics Informed Neural Network”, or DCMPINN. DCMPINN has three novel enhancements that improve its ability to solve complex systems of PDEs.
The first of these improvements is the ability to model nonlinear hyperelastic deformations. This functionality is critical for modeling the behavior of biological systems or soft robots. The second improvement is a novel system of solving PDEs over long timescales. First, the input domain is decomposed into several subdomains which allows for more efficient training on each subdomain. Then, an additional ``Drift Correcting" network is trained to maintain continuity between different subdomains while ensuring that quantities of interest such as energy do not drift from their target values over the course of the simulation. The final improvement is the ability to solve coupled systems of PDEs. By assigning one or more terms of the neural network’s loss function to each type of physics that is to be modeled, coupled systems of PDEs can be efficiently solved.
The improvements developed in DCMPINN represent a significant improvement over existing methods for solving coupled PDEs. This will allow computational resources to be more efficiently utilized in the creation of more complex and comprehensive models of real-world processes.
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