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Presenter:
Ilias Bilionis, Purdue University
Abstract:
Can you make a neural network satisfy a physical law? There are two main types of these laws: symmetries and ordinary/partial differential equations. This webinar will focus on differential equations in this short presentation. The simplest way to bake information about a differential equation with neural networks is to create a regularization term for the loss function used in training. The presenter will explain the mathematics of this idea and will also talk about applying physics-informed neural networks to a plethora of applications spanning the range from solving differential equations for all possible parameters in one sweep (e.g., solve for all boundary conditions) to calibrating differential equations using data to design optimization. Then, attendees will work on a hands-on activity that shows you to implement the ideas in PyTorch. Some familiarity with how conventional neural networks are trained (stochastic gradient descent) is assumed. Also, attendees need to know the basics of PyTorch to follow along. Going over this tutorial should be sufficient: https://pytorch.org/tutorials/beginner/pytorch_with_examples.html.
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