DeepXDE 0.1.0

Deep learning library for solving differential equations

DeepXDE ℒ

DeepXDE is a deep learning library for solving differential equations on top of TensorFlow.

Use DeepXDE if you need a deep learning library that

• solves partial differential equations (PDEs),
• solves integro-differential equations (IDEs),
• solves fractional partial differential equations (fPDEs),
• solves inverse problems for differential equations,
• approximates functions from a dataset with/without constraints,
• approximates functions from multi-fidelity data.

DeepXDE is extensible to solve other problems in scientific computing.

Features

DeepXDE supports

• complex domain geometries without tyranny mesh generation. The basic geometries are interval, triangle, rectangle, polygon, disk, cuboid, and sphere. Other geometries can be constructed as constructive solid geometry (CSG) by operations: union, difference, and intersection;
• multi-physics, i.e., coupled PDEs;
• 4 types of boundary conditions: Dirichlet, Neumann, Robin, and periodic;
• time-dependent PDEs are solved as easily as time-independent ones by only adding initial conditions;
• residue-based adaptive training points;
• uncertainty quantification using dropout;
• four domain geometries: interval, disk, hyercube and hypersphere;
• two types of neural networks: fully connected neural network, and residual neural network;
• many different losses, metrics, optimizers, learning rate schedules, initializations, regularizations, etc.;
• useful techniques, such as dropout and batch normalization;
• callbacks to monitor the internal states and statistics of the model during training;
• compact and nice code, very close to the mathematical formulation.

All the components of DeepXDE are loosely coupled, and thus DeepXDE is well-structured and highly configurable. It is easy to add new functions to each modules to satisfy new requirements.

Installation

DeepXDE requires TensorFlow to be installed. Then, you can install DeepXDE itself.

• Install the stable version:

pip install deepxde

• For developers, you should clone the folder to your local machine and put it along with your project scripts.

git clone https://github.com/lululxvi/deepxde.git

• Dependencies

  • Matplotlib
  • NumPy
  • SALib
  • scikit-learn
  • SciPy
  • TensorFlow

Why this logo, ℒ?

The art of scientific computing with deep learning is to design Loss ℒ.

License

Apache license 2.0