Physics-Informed Neural Networks (PINNS) Microcredential Course

Recently, Machine Learning (ML) approaches to data assimilation and modelling have been very successful in interpreting large amounts of data, such as human behavior prediction, marketing, etc. However, direct applications of machine learning methods without understanding the underlying engineering and physics can be challenging. This happens because, on the one hand, the datasets may be too small for the application of ML methods suitable for large data, while, on the other hand, the reliability of the ML output may not be acceptable for high-responsibility industries such as utilities. To address some of these problems, the Physics Informed Neural Networks (PINNs) have been developed. PINNs incorporate learning on the data as well as matching the differential equations and boundary conditions describing the system. PINNs may be superior to standard ML methods in constructing digital twins of engineering problems and operating on small datasets. 

The use of PINNs relies on the knowledge of mathematics, physics, and engineering underlying the particular problem and the understanding of how to implement PINNs successfully. The students will start with the basics of neural networks and develop the knowledge of how to build PINNs for particular applications. PINNs have been successfully used for various scientific and industrial applications, including weather/climate predictions, fluid flow in industrial machinery, renewable energy, geophysics and others. 

The emphasis of this course is on the hands-on implementation of PINNs for particular problems of science and engineering and the analysis of advantages and potential difficulties in using PINNs in practice. Examples in the course will include topics from math biology, geophysics, wave propagation and other fields.