A PyTorch and SymPy based library for the use of symbolic neural differential equations.
While neural network-based function approximation is incredible for its ability to approximate any function, where we know the exact function, symtorch can be useful.
This repository is currently more of a model zoo but will provide some domain-specific utilities in the future.
Until the pull request for sympy goes through, the updated version of sympy can be installed like so:
pip install git+https://github.com/synthetic-tensors/sympy.git
This should be fixed shortly.
- CUDA: This implementation currently only runs on CPU ⬜️
- Stochastic Neural ODE solver: torchSDE ⬜️
- neural CDE ⬜️
- symbolic GDE systems: Graph differential equations ⬜️
- Stable API ⬜️
- Incorporation into torchdyn: so that pytorch differential equation work can live in one place ⬜️
Please see the examples directory for how to use this within the context of a pytorch Model
from sympy import symbols, lambdify, Matrix
import torch
import inspect
from matplotlib import pyplot as plt
from torchdiffeq import odeint
K_ = symbols('k1 k2 k3 k4')
S_ = symbols('S1 S2 S3 S4')
t_ = symbols('t')
k1, k2, k3, k4 = K_
S1, S2, S3, S4 = S_
sys = Matrix([[-S1*k1], [S1*k1 - S2*k2 + S3*k3], [S2*k2 - S3*k3 - S3*k4], [S3*k4]])
array2mat = [{'ImmutableDenseMatrix': torch.tensor}, 'torch']
f = lambdify([t_, S_, K_], sys, modules=array2mat)
def lambda_f(t, s):
k = torch.tensor([0.1, 0.5, 0.5, 0.5])
return f(t, s, k)
init = torch.tensor([100.0, 0.0, 0.0, 0.0]).view(-1, 1)
t = torch.linspace(0, 50, 101)
sola = odeint(func=lambda_f, y0=init, t=t, method='rk4')
this yields:
