LADE Seminar

Abstract

Differential equations serve as foundational tools across various scientific domains, allowing us to forecast system behavior. While many of these equations defy analytical solutions, necessitating the use of computationally intensive numerical solvers, recent strides within the Deep Learning community have targeted this challenge. However, when training data is scarce, Deep Learning models often struggle to generalize or converge effectively. One promising approach to mitigate the data scarcity involves incorporating inductive bias, such as system-specific knowledge, during model training. In this presentation, we’ll explore the latest advancements in leveraging Deep Learning techniques for solving differential equations. This includes innovative methodologies like physics-informed machine learning, imposition of orthogonality constraints, and augmentation techniques for both data and equations. Finally, we’ll delve into recent software developments designed for solving differential equations via deep learning, while also addressing the ongoing challenges within this evolving field.