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Nvidia Modulus Symbolic(Modulus Sym) Workflow and Example

A typical workflow followed when developing in Modulus Sym.

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Hydra

This is a configuration package designed to empower users in configuring hyperparameters. These hyperparameters determine the structure and training behavior of neural networks. Users can conveniently set these hyperparameters using YAML configuration files, a human-readable text format. Hydra plays the role of the first component initiated when addressing a problem with Modulus Sym. It wields influence across all aspects of Modulus Sym.

Geometry and Data 

Modulus Sym offers a dual approach for solving physics simulation challenges – a blend of physics-based knowledge and data-driven machine learning. Both these approaches revolve around transforming the physics problem into a mathematical optimization puzzle. The core of this problem exists within a specific geometry and dataset. Modulus Sym provides a flexible geometry module, allowing users to either create a new geometry from scratch using basic shapes or import existing geometries from mesh. In scenarios involving data-driven solutions, Modulus Sym offers diverse ways to access data, including standard in-memory datasets and resource-efficient lazy-loading methods for handling extensive datasets.

Nodes

Within Modulus Sym, Nodes play a key role by representing components executed during the forward pass of training. A Node encapsulates a torch.nn.Module, providing  input and output details. This attribute enables Modulus Sym to construct execution graphs and automatically fill in missing elements, essential for computing necessary derivatives. Nodes can encompass various elements, such as PyTorch neural networks natively integrated into Modulus Sym, user-defined PyTorch networks, feature transformations, and even equations.

Domain

The Domain is a central role by encompassing not only all the Constraints but also supplementary elements essential for the training journey. These supplementary components consist of Inferencers, Validators, and Monitors. As developers engage with Modulus Sym, the Constraints defined by the user are seamlessly integrated into the training Domain. This combinated results in the formation of a comprehensive assembly of training objectives, laying the foundation for a cohesive and purposeful training process.

Constraints

Constraints serve as the training goals. Each Constraint encompasses the loss function and a collection of Nodes, which Modulus Sym utilizes to construct a computational graph for execution. Numerous physical challenges require multiple training objectives to comprehensively define the problem. Constraints play a pivotal role in structuring such scenarios, offering the mechanism to establish these intricate problem setups.

Inferencers

An Inferencer primarily performs the forward pass of a set of Nodes. During training, Inferencers can be employed to evaluate training metrics or obtain predictions for visualization or deployment purposes. The frequency at which Inferencers are invoked is governed by Hydra configuration settings.

Validators

Validators function similarly to Inferencers but also incorporate validation data. Their role involves quantifying the model's accuracy during training by comparing it against physical outcomes generated through alternative methods. This "validation" phase verifies whether Modulus Sym meets operational requirements by comparing its computed simulation results to established known result.

Monitors

Monitors function similarly to Inferencers but also calculate specific measures instead of fields. These measures may encompass global quantities like total energy or local measurements like pressure in front of a bluff body (a distinctive shape with unique fluid dynamics attributes). Monitors are seamlessly integrated into Tensorboard results for easy visualization. Furthermore, Monitor outcomes can be exported to a text file in comma-separated values (CSV) format.

Solver

A Solver stands as a core component within Modulus Sym, responsible for implementing the optimization loop and overseeing the training process. By taking a predefined Domain, the Solver orchestrates the execution of Constraints, Inferencers, Validators, and Monitors as needed. In each iteration, the Solver calculates the overall loss from all Constraints and then refines any trainable models within the Nodes associated with the Constraints.

Modulus Sym Development Workflow

The key steps of general workflow include:

  • "Load Hydra": Initialize Hydra using the Modulus Sym main decorator to read in the YAML configuration file.

  • "Load Datasets": Load data if needed.

  • "Define Geometry": Define the geometry of the system if needed.

  • "Create Nodes": Create any Nodes required, such as the neural network model.

  • "Create Domain": Create a training Domain object.

  • "Create Constraint" and "Add Constraint to Domain"

  • "Create {Validator, Inferencer, Monitor}" and "Add {Validator, Inferencer, Monitor} to Domain": Create any Inferencers, Validators or Monitors needed, and add them to the Domain.

  • "Create Solver": Initialize a Solver with the populated training Domain.

  • "Run Solver": Run the Solver. The resulting training process optimizes the neural network to solve the physics problem.

Modulus Training

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• Modulus enables the representation of complex problems using sets of constraints, serving as training objectives.
• In constraints, the integration of multiple nodes or models allows for the acquisition of diverse loss functions—ranging from data-driven to physics-driven in nature.
• Seamlessly exporting the outcomes of trained models to visualization software becomes effortlessly achievable with Modulus.

Example

In the following section, we will solve the "Fluid Flow", "Parameterized Problem" and "Inverse Problem" with same geometry conditions.




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