TorchDAE

Numerical Differential-Algebraic Equation solvers in PyTorch. Autodifferentiable and GPU-capable.

TorchDAE is a PyTorch-based library providing numerical Differential-Algebraic Equation (DAE) solvers.

Features include:

• Implicit Solvers: Multiple stiff solvers (including BDF1, BDF2, SDIRK TR-BDF2, and 5th-order Radau IIA);
• Automatic Index Reduction: lowering high-index DAEs to Index-1 using Pantelides' algorithm and Mattsson-Söderlind Dummy Derivatives;
• Manifold Stabilization: Coordinate Projection Method (CPM) and Baumgarte feedback to eliminate numerical constraint drift;
• Events & Resets: Vectorized, differentiable event handling with continuous-time Hermite state interpolation and resets;
• Adjoint Methods: Continuous adjoint sensitivity backward-in-time for constant-memory backpropagation;
• Vmap support: Full support for PyTorch vmap and batched input on GPU and CPU pipelines.

Installation

pip install torchdae

Requires Python 3.8+ and PyTorch 2.0+.

Documentation

Available at https://yousef-rafat.github.io/torchdae/.

Quick Example

A simple example of how to solve an Index-1 DAE with BDF2.

import torch
from torchdae import solve_bdf2

# Define a simple Index-1 DAE: F(t, y, yp) = 0
def physics(t, y, yp):
    # supporting batching
    y1, y2 = y[..., 0], y[..., 1]
    y1p, _ = yp[..., 0], yp[..., 1]
    
    # f1 (differential): y1' + y1 - y2 = 0
    f1 = y1p + y1 - y2
    
    # f2 (algebraic): y1 + y2 - sin(t) = 0
    t_tensor = torch.as_tensor(t, dtype=y.dtype, device=y.device)
    f2 = y1 + y2 - torch.sin(t_tensor)
    
    return torch.stack([f1, f2], dim=-1)

y0 = torch.tensor([[0.5, -0.5]])

sol = solve_bdf2(physics, t_span=(0.0, 1.0), y0=y0, h=0.01)

print("Solved states at t=1.0:", sol.ys[-1, 0].numpy())