This repository provides sample applications demonstrating use of specific Physics-ML model architectures that are easy to train and deploy. These examples aim to show how such models can help solve real world problems.
| Use case | Concepts covered |
|---|---|
| Darcy Flow | Introductory example for learning basics of data-driven models on Physics-ML datasets |
| Darcy Flow (Data + Physics) | Data-driven training with physics-based constraints |
| Lid Driven Cavity Flow | Purely physics-driven (no external simulation/experimental data) training |
| Vortex Shedding | Introductory example for learning the basics of MeshGraphNets in Modulus |
| Medium-range global weather forecast using FCN-AFNO | Introductory example on training data-driven models for global weather forecasting (auto-regressive model) |
| Lagrangian Fluid Flow | Introductory example for data-driven training on Lagrangian meshes |
| Stokes Flow (Physics Informed Fine-Tuning) | Data-driven training followed by physics-based fine-tuning |
The several examples inside Modulus can be classified based on their domains as below:
NOTE: The below classification is not exhaustive by any means! One can classify single example into multiple domains and we encourage the users to review the entire list.
NOTE: * Indicates externally contributed examples.
| Use case | Model | Transient |
|---|---|---|
| Vortex Shedding | MeshGraphNet | YES |
| Drag prediction - External Aero | MeshGraphNet, UNet, DoMINO, FigConvNet | NO |
| Navier-Stokes Flow | RNN | YES |
| Gray-Scott System | RNN | YES |
| Lagrangian Fluid Flow | MeshGraphNet | YES |
| Darcy Flow using Nested-FNOs | Nested-FNO | NO |
| Darcy Flow using Transolver* | Transolver (Transformer-based) | NO |
| Darcy Flow (Data + Physics Driven) using DeepONet approach | FNO (branch) and MLP (trunk) | NO |
| Darcy Flow (Data + Physics Driven) using PINO approach (Numerical gradients) | FNO | NO |
| Stokes Flow (Physics Informed Fine-Tuning) | MeshGraphNet and MLP | NO |
| Lid Driven Cavity Flow | MLP | NO |
| Magnetohydrodynamics using PINO (Data + Physics Driven)* | FNO | YES |
| Shallow Water Equations using PINO (Data + Physics Driven)* | FNO | YES |
| Shallow Water Equations using Distributed GNNs | GraphCast | YES |
| Vortex Shedding with Temporal Attention | MeshGraphNet | YES |
| Use case | Model |
|---|---|
| Fluid Super-resolution* | Diffusion |
| Use case | Model |
|---|---|
| Cardiovascular Simulations* | MeshGraphNet |
| Brain Anomaly Detection | FNO |
| Use case | Model |
|---|---|
| Metal Sintering Simulation* | MeshGraphNet |
| Use case | Model |
|---|---|
| Force Prediciton for Lennard Jones system | MeshGraphNet |
In addition to the examples in this repo, more Physics-ML usecases and examples can be referenced from the Modulus-Sym examples.
In each of the example READMEs, we indicate the level of support that will be provided. Some examples are under active development/improvement and might involve rapid changes. For stable examples, please refer the tagged versions.
We're posting these examples on GitHub to better support the community, facilitate feedback, as well as collect and implement contributions using GitHub issues and pull requests. We welcome all contributions!