TorchPhysics

TorchPhysics is a Python library of deep learning methods for solving differential equations. You can use TorchPhysics to:

solve ordinary and partial differential equations via physics-informed neural networks (PINN) [1] or the Deep Ritz method [2]
train a neural network to approximate solutions for different parameters
solve inverse problems and interpolate external data via the above methods

TorchPhysics is build upon the machine learning library PyTorch.

Features

The Goal of this library is to create a basic framework that can be used in many different applications and with different deep learning methods. To this end, TorchPhysics aims at a:

modular and expandable structure
easy to understand code and clean documentation
intuitive and compact way to transfer the mathematical problem into code
reliable and well tested code basis

Some build in features are:

mesh free domain generation. With pre implemented domain types: Point, Interval, Parallelogram, Circle, Triangle and Sphere
loading external created objects, thanks to a soft dependency on Trimesh and Shapely
creating complex domains with the boolean operators Union, Cut and Intersection and higher dimensional objects over the Cartesian product
allowing interdependence of different domains, e.g. creating moving domains
different point sampling methods for every domain: RandomUniform, Grid, Gaussian, Latin hypercube, Adaptive and some more for specific domains
different operators to easily define a differential equation
pre implemented fully connected neural network and easy implementation of additional model structures
sequentially or parallel evaluation/training of different neural networks
normalization layers and adaptive weights [3] to speed up the training process
powerful and versatile training thanks to PyTorch Lightning
- many options for optimizers and learning rate control
- monitoring the loss of individual conditions while training

Getting Started

To learn the functionality and usage of TorchPhysics we recommend to have a look at the following sections:

Installation

TorchPhysics can be installed by using:

pip install git+https://github.com/boschresearch/torchphysics

If you want to change or add something to the code. You should first copy the repository and install it locally:

git clone https://github.com/boschresearch/torchphysics
pip install .

About

TorchPhysics was originally developed by Nick Heilenkötter and Tom Freudenberg, as part of a seminar project at the University of Bremen, in cooperation with the Robert Bosch GmbH. Special thanks belong to Felix Hildebrand, Uwe Iben, Daniel Christopher Kreuter and Johannes Mueller, at the Robert Bosch GmbH, for support and supervision while creating this library.

License

TorchPhysics uses a Apache License, see the LICENSE file.

Bibliography

[1]	Raissi, Perdikaris und Karniadakis, “Physics-informed neuralnetworks: A deep learning framework for solving forward and inverseproblems involving nonlinear partial differential equations”, 2019.

[2]	E and Yu, "The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problems", 2017

[3]	McClenny und Braga-Neto, “Self-Adaptive Physics-Informed NeuralNetworks using a Soft Attention Mechanism”, 2020