Enhancing Scientific Computing Through Physics-Informed Neural Networks

Explore the potential of physics-informed deep learning (PIDL) in scientific computing through this comprehensive lecture. Delve into physics-informed neural networks (PINNs) and their capabilities in addressing challenges faced by traditional computational approaches. Discover how PINNs can efficiently handle high-dimensional problems governed by parameterized partial differential equations (PDEs) and incorporate noisy data in inverse problems. Learn about extensions such as conservative PINNs (cPINNs) and eXtended PINNs (XPINNs) designed for big data and large models. Examine various adaptive activation functions that enhance convergence in deep and physics-informed neural networks. Gain insights into diverse applications where PINNs outperform traditional methods, and understand their current limitations and future potential in advancing scientific computing.