ldc_pinns

Lid Driven Cavity Flow using Purely Physics Driven Neural Networks (PINNs)

This example demonstrates how to set up a purely physics-driven model for solving a Lid Driven Cavity (LDC) flow using PINNs. The goal of this example is to demonstrate the interoperability of PhysicsNeMo, physicsnemo.sym and PyTorch. This example adopts a workflow where appropriate utilities are imported from physicsnemo, physicsnemo.sym and torch to define the training pipeline.

Specifically, this example demonstrates how the geometry and physics utilities from physicsnemo.sym can be used in custom training pipelines to handle geometry objects (typically found in Computer Aided Engineering (CAE)) workflows and introduce physics residual and boundary condition losses.

This example takes a non-abstracted way to define the problem. The boundary condition constraints, residual constraints, and the subsequent physics loss computation are defined explicitly. If you previously used the (now archived) physicsnemo-sym repository, where the Solver / Domain / Constraint abstractions handled these steps implicitly, see the PhysicsNeMo v2.0 Migration Guide for how the equivalent pieces look in this newer, explicit style.

Getting Started

Prerequisites

If you are running this example outside of the PhysicsNeMo container, install PhysicsNeMo with the sym extra: pip install "nvidia-physicsnemo[sym]"

Training

To train the model, run

python train.py

This should start training the model. Since this is training in a purely Physics based fashion, there is no dataset required.

Instead, we generate the geometry using the physicsnemo.mesh module and sample the point cloud using the GeometryDatapipe utility. The PhysicsNeMo v2.0 Migration Guide shows how this maps from the older physicsnemo-sym geometry primitives.

For computing the physics losses, we will use the PhysicsInformer utility from physicsnemo.sym. The PhysicsNeMo v2.0 Migration Guide shows how this maps from the older physicsnemo-sym PDE / make_nodes workflow.

The results would get saved in the ./outputs/ directory.

Additional Reading

This example demonstrates computing physics losses on point clouds. For more examples on physics informing different type of models and model outputs, refer to:

• Point clouds: Darcy Flow (DeepONet), Stokes Flow (MLP)
• Regular grid: Darcy Flow (FNO)
• Unstructured meshes: Stokes Flow (MeshGraphNet)