Notes on NVIDIA Modulus

[YunchaoYang]

What is modulus?

From its official website, NVIDIA Modulus is a neural network framework that blends the power of physics (in the form of governing partial differential equations (PDEs)) with data to build high-fidelity, parameterized surrogate models with near-real-time latency. Whether you’re looking to get started with AI-driven physics problems or designing digital twin models for complex non-linear, multi-physics systems, NVIDIA Modulus can support your work.

keywords:

1. what: a neural network framework
2. why: support AI-driven physics problems and digital twin models
3. how: blend physics (PDE) with data in NN
4. Where: Modulus tutorial NGC image
5. when: latest version 22.07

How to install NVIDIA Modulus container:

singularity build modulus:22.07.sif docker://nvcr.io/nvidia/modulus/modulus:22.07

Key Components

• Geometry and Data: self-explanary
• Nodes (wrapper of as torch.nn.Module)
• Constraint : training objectives
• Domain: hold all constraints as well as additional components in training
• Solver: Solvers are the are instances of the core Modulus trainer, which contains the optimization loop and manages the training process. A solver takes a defined domain and calls the constraints, inferencers, monitors and validators when required. During one iteration, the solver will compute the global loss from all constraints and then optimize any trainable models present in the Nodes provided to the constraints.
• Hydra: configuration of tuning parameters using YAML format
• Inferencers: forward pass
• Validators: validation data
• Monitors: similarly to inferencers, but calculating specific measures as oppose to fields

Workflow

Initialize Hydra using the Modulus main decorator to read in the configuration YAML.

1. Load necessary data if needed.
2. Define the geometry of the system if needed.
3. Create any Nodes required, such as your neural network model.
4. Create a training Domain object.
5. Create constraints and add each to the domain.
6. Create any inferencers, validators or monitors needed.
7. Initialize a solver with the populated training domain.
8. Run the solver, beginning optimization.

Theories and Algorithms

PINN

• Method
  • build neural network to approximate a given PDE and boundary conditions by minimizing loss function.
  • Integral Equations losses significantly speeds up convergence.
• Parameterized Geometries
  • solve parameterized differential equation
• Inverse Problems
• Weak solution of PDEs using PINNs

Examples:

• Lid Driven Cavity link

MultiGPU runs

[farrate]

The examples at:

https://gitlab.com/nvidia/modulus/examples

Are unavailable. Do you have any idea why?

Thanks