SiNDAE - SiNDAE

SiNDAE (Simultaneous Neural Differential-Algebraic Equation) is a Python package for learning unknown nonlinear terms in ODE/DAE systems from noisy time-series observations.

Rather than training a neural network in isolation and plugging it into a simulator afterward, SiNDAE embeds the network directly inside the physics-based model and trains it by solving a single nonlinear program (NLP). This simultaneous approach preserves the DAE structure, allows exact second-order derivatives, and is robust to index-2 constraints.

SiNDAE is the companion code to Lueg et al. (2025).

Training algorithms¶

Algorithm	Description
Simultaneous	NN weights and DAE states are all decision variables in one large NLP. Solved with POUNCE (exact Hessian, or L-BFGS for the grey-box variant).
Decomposition	Outer Adam loop updates NN weights; inner NLP (POUNCE + GBM) solves the DAE at each step. Gradients via KKT implicit differentiation. Supports MPI.

Both algorithms use Pyomo DAE for symbolic model building and Lagrange–Radau collocation for time discretization.

Quickstart¶

import numpy as np
import sindae as sd

problem = sd.LeslieGowerProblem(nfe=40, ncp=3)
sd.generate_data(problem, noise_std=[0.05, 0.05])

mlp = sd.SimpleMLP(in_size=2, out_size=1, widths=[16, 16],
                   activations=[jax.nn.softplus] * 2)

model = sd.HybridDAE(
    method="simultaneous",              # or "decomposition"
    net=mlp,
    train=sd.SimultaneousConfig(reg_coef=1e-3),
)
model.fit(problem)                      # smoother -> pretrain -> train

new_problem = sd.LeslieGowerProblem(ics=np.array([[1.2, 0.15]]), nfe=40, ncp=3)
pred = model.predict(new_problem, slack_coef=1e-5)

See Quickstart Guide for the full walkthrough, including the stage-level functions behind the wrapper.

Contents¶

References¶

Lueg, L. R., Alves, V., Schicksnus, D., Kitchin, J. R., Laird, C. D., & Biegler, L. T. (2025). A simultaneous approach for training neural differential-algebraic systems of equations. arXiv Preprint arXiv:2504.04665. https://arxiv.org/abs/2504.04665