torchSODE

CUDA solver callable from PyTorch. Optimized for independent ordinary differential equations (ODEs) that can be represented as a sparse block diagonal matrix.

The solver itself is designed to be used during neural network training and thus accepts an additional argument grad

Installation

In your terminal of choice:

git clone https://github.com/Zymrael/torchODE.git

cd torchSODE/src

python setup.py install

In your python files or notebooks:

import torchSODE

API

torchSODE.solve(F, x0, grad, dt, steps, method='Euler') performs steps integration cycles with dt step size.

For problems where the size of x0 is too large allocating a matrix of dimensions size * size is not always possible. In these cases we assume a compressed representation of F which exposes only its diagonal values.

The following convention is used (regardless of problem size):

1. For diagonal F allocate a torch.Tensor of shape (1).
2. For 4 block-diagonal F, allocate a torch.Tensor of shape (2,2) with values of upper-left diagonal in position [0,0], upper-right diagonal [0,1], lower-left diagonal [1,0], lower-right diagonal [1,1].

In any other scenario torchSODE.solve requires x0.size(0) to match F.size(0) and F.size(1), with F assumed to be 4 block-diagonal.

Methods

'Euler' = Euler

'RK4' = Runge-Kutta 4