A Parallel ODE Solver for PyTorch

torchode is a suite of single-step ODE solvers such as dopri5 or tsit5 that are compatible with PyTorch's JIT compiler and parallelized across a batch. JIT compilation often gives a performance boost, especially for code with many small operations such as an ODE solver, while batch-parallelization means that the solver can take a step of 0.1 for one sample and 0.33 for another, depending on each sample's difficulty. This can avoid performance traps for models of varying stiffness and ensures that the model's predictions are independent from the compisition of the batch. See the paper for details.

Documentation

If you get stuck at some point, you think the library should have an example on x or you want to suggest some other type of improvement, please open an issue on github.

Installation

You can get the latest released version from PyPI with

pip install torchode

To install a development version, clone the repository and install in editable mode:

git clone https://github.com/martenlienen/torchode
cd torchode
pip install -e .

Usage

import matplotlib.pyplot as pp
import torch
import torchode as to

def f(t, y):
    return -0.5 * y

y0 = torch.tensor([[1.2], [5.0]])
n_steps = 10
t_eval = torch.stack((torch.linspace(0, 5, n_steps), torch.linspace(3, 4, n_steps)))

term = to.ODETerm(f)
step_method = to.Dopri5(term=term)
step_size_controller = to.IntegralController(atol=1e-6, rtol=1e-3, term=term)
solver = to.AutoDiffAdjoint(step_method, step_size_controller)
jit_solver = torch.compile(solver)

sol = jit_solver.solve(to.InitialValueProblem(y0=y0, t_eval=t_eval))
print(sol.stats)
# => {'n_f_evals': tensor([26, 26]), 'n_steps': tensor([4, 2]),
# =>  'n_accepted': tensor([4, 2]), 'n_initialized': tensor([10, 10])}

pp.plot(sol.ts[0], sol.ys[0])
pp.plot(sol.ts[1], sol.ys[1])

Citation

If you build upon this work, please cite the following paper.

@inproceedings{lienen2022torchode,
  title = {torchode: A Parallel {ODE} Solver for PyTorch},
  author = {Marten Lienen and Stephan G{\"u}nnemann},
  booktitle = {The Symbiosis of Deep Learning and Differential Equations II, NeurIPS},
  year = {2022},
  url = {https://openreview.net/forum?id=uiKVKTiUYB0}
}