Скачать или смотреть Model Discovery with Physics-Informed Machine Learning - Data-Driven Dynamics | Lecture 21

In the previous lecture, we were introduced to the powerful and versatile method of physics-informed neural networks (PINNs). In this lecture, we continue exploring PINNs, focusing on their use for model discovery. Similar to methods like EDMD and SINDy, we show how a dictionary of candidate functions can be introduced to describe the solution of a partial differential equation (PDE). The PINN is then trained to fit the PDE solution within the span of this dictionary, effectively learning the underlying model from data. We demonstrate this approach using the heat equation, showing how the network can recover the diffusion coefficient from synthetic temperature data. This lecture highlights how PINNs can uncover hidden physical laws directly from observations, bridging data and theory in a powerful way.

Jupyter notebook comes from Diffusion_Discovery.ipynb here: https://github.com/jbramburger/DataDr...

PyTorch version: https://github.com/jbramburger/DataDr...

Original PINNs paper: https://www.sciencedirect.com/science...

Get the book here: https://epubs.siam.org/doi/10.1137/1....

Scripts and notebooks to reproduce all examples: https://github.com/jbramburger/DataDr...

This book provides readers with:

methods not found in other texts as well as novel ones developed just for this book;

an example-driven presentation that provides background material and descriptions of methods without getting bogged down in technicalities;

examples that demonstrate the applicability of a method and introduce the features and drawbacks of their application; and

a code repository in the online supplementary material that can be used to reproduce every example and that can be repurposed to fit a variety of applications not found in the book.

More information on the instructor: https://hybrid.concordia.ca/jbrambur/

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