Modulus Sym Overview

• Geometry and Data

  Modulus Sym provides both physics-informed and data-driven machine learning solutions for physics simulation problems. All these solutions depend on expressing the physics problem as a mathematical optimization problem. The mathematical optimization problem is, in turn, posed on a particular geometry and/or set of data. Modulus Sym’ geometry module lets users either build a geometry from scratch using primitives, or import an existing geometry from a mesh. For data-driven problems, Modulus Sym has multiple methods for accessing data, including standard in-memory datasets as well as lazy loading methods for large-scale datasets.

• Nodes

  In Modulus Sym, Nodes represent components that will be executed in the forward pass during training. A Node may wrap a torch.nn.Module and provides additional information regarding its needed input and output variables. This lets Modulus Sym build execution graphs and automatically fill in missing components to compute required derivatives. Nodes may contain models or functions such as PyTorch neural networks that are built into Modulus Sym, user-defined PyTorch networks, feature transformations, or even equations.

• Constraints

  Constraints are the training objectives in Modulus Sym. A Constraint contains the loss function, and a set of Nodes from which Modulus Sym builds a computational graph for execution. Many physical problems need multiple training objectives in order for the problem to be well defined. Constraints provide the means for setting up such problems.

• Domain

  The Domain holds all Constraints as well as additional components needed in the training process. These additional components include Inferencers, Validators, and Monitors. When developing in Modulus Sym, Constraints that the user defines are then added to the training Domain to create a collection of training objectives.

• Solver

  A Solver is an instance of the core Modulus Sym trainer. It implements the optimization loop and manages the training process. A Solver takes a defined Domain and calls the Constraints, Inferencers, Validators, and Monitors 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

  Hydra is a configuration package built into Modulus Sym. It lets users set hyperparameters (parameters that determine the neural network’s structure and govern its training) using configuration files in YAML (a standard human-readable text format). Hydra is the first component to be initialized when solving a problem using Modulus Sym. It directly influences all Modulus Sym components.

• Inferencers

  An Inferencer executes just the forward pass of a set of Nodes. Inferencers may be used during training to assess training quantities or get predictions for visualization or deployment. Hydra configuration settings control the frequency at which Inferencers are called.

• Validators

  Validators work like Inferencers, but also take validation data. They quantify the accuracy of the model during training, by validating it against physical results produced by some other method. (“Validation” here means the part of “verification and validation” that checks whether Modulus Sym meets its operational requirements, by comparing the simulation results that Modulus Sym computes against some “known good” result.)

• Monitors

  Monitors also work like Inferencers, but calculate specific measures instead of fields. These measures may be global quantities such as total energy, or local probes such as pressure in front of a bluff body. (A “bluff body” is a kind of shape with special fluid dynamics properties.) Monitors are automatically added to Tensorboard results for viewing. Monitor results can also be exported to a text file in comma-separated values (CSV) format.

The figure below illustrates a typical workflow when developing in Modulus Sym. Not all problems will call for exactly this workflow, but it serves as a general guide. The key steps of this process 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 each of the \(N_{c}\) Constraints in turn, and add it to the 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.

More details of each step can be found in the Introductory Example chapter which provides a hands-on introduction to Modulus Sym.

Fig. 1 A typical workflow followed when developing in Modulus Sym.

Fig. 2 Modulus Sym’ training algorithm.