Mathematical Sciences Department
Virtual Colloquium
Speaker: Ameya Jagtap, Brown University
Friday, April 12, 2024
11am - 12pm
Zoom Meeting ID: 938 8407 5985
Title: Physics-Informed Neural Networks and Neural Operators: Advancements and Applications
Abstract: Traditional scientific computing faces limitations, such as needing detailed knowledge of physical laws and conditions, and the burdensome processes of mesh generation and extensive simulations. These methods also struggle with complex, high-dimensional problems governed by parameterized partial differential equations (PDEs), limiting their practicality. Physics-informed machine learning (PIML), especially through physics-informed neural networks (PINNs), offers a robust alternative. This presentation explores PINNs, showcasing their advantages in various applications over traditional approaches. We also examine advancements in PINNs, including conservative and extended versions for large-scale data and model management, and adaptive activation functions that enhance the efficiency of deep, physics-informed networks. Additionally, we discuss deep operator networks, a neural operator that excels in mapping between infinite-dimensional function spaces, presenting a significant leap over traditional PDE solvers by delivering higher accuracy with less computational effort. These networks, particularly effective in complex scenarios like stiff chemical kinetics, employ novel architectures for learning data-driven basis functions, facilitating the mapping between discontinuous solutions.