Solving Inverse Problems With Physics-Informed DeepONet: A Practical Guide With Code Implementation
<p>In my <a href="https://medium.com/towards-data-science/operator-learning-via-physics-informed-deeponet-lets-implement-it-from-scratch-6659f3179887" rel="noopener">previous blog</a>, we delved into the concept of physics-informed DeepONet (PI-DeepONet) and explored why it is particularly suitable for operator learning, i.e., learning mappings from an input function to an output function. We also turned theory into code and implemented a PI-DeepONet that can accurately solve an ordinary differential equation (ODE) even with unseen input forcing profiles.</p>
<p><img alt="" src="https://miro.medium.com/v2/resize:fit:560/1*gJvrNuXwd2LK7DI_Y-Ft4g.png" style="height:256px; width:700px" /></p>
<p>Figure 1. Operators transform one function into another, which is a concept frequently encountered in real-world dynamical systems. <strong>Operator learning</strong> essentially involves training a neural network model to approximate this underlying operator. A promising method to achieve that is <strong>DeepONet</strong>. (Image by author)</p>
<p>The ability to solve these <strong><em>forward </em></strong>problems with PI-DeepONet is certainly valuable. But is that all PI-DeepONet can do? Well, definitely not!</p>
<p>Another important problem category we frequently encountered in computational science and engineering is the so-called <strong><em>inverse problem</em></strong>. In essence, this type of problem <strong>reverses the flow of information from output to input</strong>: the input is unknown and the output is observable, and the task is to estimate the unknown input from the observed output.</p>
<p><a href="https://towardsdatascience.com/solving-inverse-problems-with-physics-informed-deeponet-a-practical-guide-with-code-implementation-27795eb4f502">Website</a></p>