PirateNets - Physics-Informed Deep Learning with Residual Adaptive Networks

Explore the innovative approach of Physics-Informed Residual Adaptive Networks (PirateNets) in this comprehensive lecture. Delve into the limitations of traditional physics-informed neural networks (PINNs) when scaling to larger and deeper architectures. Understand the root cause of performance degradation in multi-layer perceptron (MLP) architectures with unsuitable initialization schemes. Discover how PirateNets address these challenges through a novel adaptive residual connection, allowing networks to initialize as shallow and progressively deepen during training. Learn about the benefits of encoding appropriate inductive biases for specific PDE systems into the network architecture. Examine empirical evidence demonstrating PirateNets' superior optimization and accuracy gains from increased depth, ultimately achieving state-of-the-art results across various benchmarks in forward and inverse problems governed by partial differential equations.