hydropml/paml_piml

PiML is a widely used approaches to incorporate physical constraints, which can be trained from additional information obtained by enforcing the physical laws (for example, designing loss functions (regularization))

Physics-informed Machine Learning

In scientific computing, physical phenomena are often described using a strong mathematical form consisting of governing differential equations as well as initial and boundary conditions. PiML is a widely-used approach that integrates physical laws into ML models (for example, designing loss functions or regularization), facilitates the accurate capture of dynamic patterns and concomitantly diminishes the search space for model parameters. This approach is sometimes referred to as imposing differentiable constraints in loss functions. It integrates (noisy) data and mathematical models, and implements them through neural networks (physics-informed neural networks) or kernel-based neural operators (physics-informed neural operators).

Challenges of vanilla PINNs

Model Zoo

Physics-informed Neural Networks

Physics-informed Neural Operators

Continuously updating
More information can be found in the PAPER