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Modulus Symbolic (Modulus Sym) repository is part of Modulus SDK and it provides algorithms and utilities to be used with Modulus core, to explicitly physics inform the model training. This includes utilities for explicitly integrating symbolic PDEs, domain sampling and computing PDE-based residuals using various gradient computing schemes.

It also provides higher level abstraction to compose a training loop from specification of the geometry, PDEs and constraints like boundary conditions using simple symbolic APIs. Please refer to the Lid Driven cavity that illustrates the concept.

Additional information can be found in the Modulus documentation.

Please refer to the Modulus SDK to learn more about the full stack.

You can run below example to start using the geometry module from Modulus-Sym as shown below:

>>> import numpy as np
>>> from modulus.sym.geometry.primitives_3d import Box
>>> from modulus.sym.utils.io.vtk import var_to_polyvtk
>>> nr_points = 100000
>>> box = Box(point_1=(-1, -1, -1), point_2=(1, 1, 1))
>>> s = box.sample_boundary(nr_points=nr_points)
>>> var_to_polyvtk(s, "boundary")
>>> print("Surface Area: {:.3f}".format(np.sum(s["area"])))
Surface Area: 24.000

To use the PDE module from Modulus-Sym, you can run the below example:

>>> from modulus.sym.eq.pdes.navier_stokes import NavierStokes
>>> ns = NavierStokes(nu=0.01, rho=1, dim=2)
>>> ns.pprint()
continuity: u__x + v__y
momentum_x: u*u__x + v*u__y + p__x + u__t - 0.01*u__x__x - 0.01*u__y__y
momentum_y: u*v__x + v*v__y + p__y + v__t - 0.01*v__x__x - 0.01*v__y__y

To use the computational graph builder from Modulus Sym:

>>> import torch
>>> from sympy import Symbol
>>> from modulus.sym.graph import Graph
>>> from modulus.sym.node import Node
>>> from modulus.sym.key import Key
>>> from modulus.sym.eq.pdes.diffusion import Diffusion
>>> from modulus.sym.models.fully_connected import FullyConnectedArch
>>> net = FullyConnectedArch(input_keys=[Key("x")], output_keys=[Key("u")], nr_layers=3, layer_size=32)
>>> diff = Diffusion(T="u", time=False, dim=1, D=0.1, Q=1.0)
>>> nodes = [net.make_node(name="net")] + diffusion.make_nodes()
>>> graph = Graph(nodes, [Key("x")], [Key("diffusion_u")])
>>> graph.forward({"x": torch.tensor([1.0, 2.0]).requires_grad_(True).reshape(-1, 1)})
{'diffusion_u': tensor([[-0.9956],
        [-1.0161]], grad_fn=<SubBackward0>)}

Please refer Introductory Example for usage of the physics utils in custom training loops and Lid Driven cavity for an end-to-end PINN workflow.

Users of Modulus versions older than 23.05 can refer to the migration guide for updating to the latest version.

The following resources will help you in learning how to use Modulus. The best way is to start with a reference sample and then update it for your own use case.

• Using Modulus Sym with your PyTorch model
• Using Modulus Sym to construct computational graph
• Reference Samples
• User guide Documentation

• Getting started Webinar
• AI4Science Modulus Bootcamp

The recommended method for installing the latest version of Modulus Symbolic is using PyPi:

pip install nvidia-modulus.sym

Note, the above method only works for x86/amd64 based architectures. For installing Modulus Sym on Arm based systems using pip, Install VTK from source as shown here and then install Modulus-Sym and other dependencies.

pip install nvidia-modulus.sym --no-deps
pip install "hydra-core>=1.2.0" "termcolor>=2.1.1" "chaospy>=4.3.7" "Cython==0.29.28" "numpy-stl==2.16.3" "opencv-python==4.5.5.64" \
    "scikit-learn==1.0.2" "symengine>=0.10.0" "sympy==1.12" "timm>=1.0.3" "torch-optimizer==0.3.0" "transforms3d==0.3.1" \
    "typing==3.7.4.3" "pillow==10.0.1" "notebook==6.4.12" "mistune==2.0.3" "pint==0.19.2" "tensorboard>=2.8.0"

The recommended Modulus docker image can be pulled from the NVIDIA Container Registry:

docker pull nvcr.io/nvidia/modulus/modulus:24.04

For a local build of the Modulus Symbolic Python package from source use:

git clone [email protected]:NVIDIA/modulus-sym.git && cd modulus-sym

pip install --upgrade pip
pip install .

To build release image insert next tag and run below:

docker build -t modulus-sym:deploy \
    --build-arg TARGETPLATFORM=linux/amd64 --target deploy -f Dockerfile .

Currently only linux/amd64 and linux/arm64 platforms are supported.

Modulus is an open source collaboration and its success is rooted in community contribution to further the field of Physics-ML. Thank you for contributing to the project so others can build on top of your contribution.

For guidance on contributing to Modulus, please refer to the contributing guidelines.

If Modulus helped your research and you would like to cite it, please refer to the guidelines

• Github Discussions: Discuss new architectures, implementations, Physics-ML research, etc.
• GitHub Issues: Bug reports, feature requests, install issues, etc.
• Modulus Forum: The Modulus Forum hosts an audience of new to moderate-level users and developers for general chat, online discussions, collaboration, etc.

Want to suggest some improvements to Modulus? Use our feedback form here.

Modulus is provided under the Apache License 2.0, please see LICENSE.txt for full license text.