Lecturer: Yaohua Zang & Scholz Vincent

Objectives

• Understand deep learning fundamentals and learn to build/train neural networks in PyTorch.
• Develop familiarity with deep learning approaches for solving PDEs.
• Gain hands-on experience implementing deep learning algorithms for PDEs.
• Apply these methods to real-world engineering physics problems.

Contents

• Deep Learning Basics: Introduction to artificial neural networks (ANNs) and implementing and training ANNs with PyTorch
• Classical PDE Methods: PDE fundamentals and classical numerical methods, such as FEM and FDM.
• Physics-informed deep learning methods: Popular physics-informed deep learning methods, such as:
  • Physics-Informed Neural Networks (PINNs)
  • Deep Ritz Method (DeepRitz)
• Data-driven Deep Neural Operators: Popular deep neural operator methods based on supervised learning, such as:
  • Deep Neural Operator Network (DeepONet)
  • Fourier Neural Operator (FNO)

Resources

• Course Page