PIMS Lunchbox Lecture - Vakhtang Putkaradze

Abstract: Recently, Machine Learning (ML) approaches to data assimilation and modeling 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 and accuracy of the pure ML-based prediction may not be acceptable in high-responsibility industrial settings. To address some of these problems, the Physics Informed Neural Networks (PINNs) have been developed. PINNs incorporate learning on the data and match 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. PINNs have been used successfully in many industrial and scientific applications due to their unmatched computational speed and efficiency.

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. We discuss some of the successes of PINNs, together with some of the cautionary tales regarding their applications.