# Learning Neural Differential Algebraic Equations via Operator Splitting

arXiv: https://arxiv.org/abs/2403.12938 · HTML: https://mlsanity.com/paper/2403.12938/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 42 references that are in the map.
- First posted on arXiv 19 Mar 2024.

## Builds on (most cited first, 17 of 17)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Neural Controlled Differential Equations for Irregular Time Series](https://mlsanity.com/paper/2005.08926/) (2020)
- [Augmented Neural ODEs](https://mlsanity.com/paper/1904.01681/) (2019)
- [Universal Differential Equations for Scientific Machine Learning](https://mlsanity.com/paper/2001.04385/) (2020)
- [Stiff Neural Ordinary Differential Equations](https://mlsanity.com/paper/2103.15341/) (2021)
- [Hierarchical Deep Learning of Multiscale Differential Equation Time-Steppers](https://mlsanity.com/paper/2008.09768/) (2020)
- [Extending Lagrangian and Hamiltonian Neural Networks with Differentiable Contact Models](https://mlsanity.com/paper/2102.06794/) (2021)
- [Constructing Neural Network-Based Models for Simulating Dynamical Systems](https://mlsanity.com/paper/2111.01495/) (2021)
- [DAE-PINN: A Physics-Informed Neural Network Model for Simulating Differential-Algebraic Equations with Application to Power Networks](https://mlsanity.com/paper/2109.04304/) (2021)
- [Physics-Informed Machine Learning for Modeling and Control of Dynamical Systems](https://mlsanity.com/paper/2306.13867/) (2023)
- [Stochastic Physics-Informed Neural Ordinary Differential Equations](https://mlsanity.com/paper/2109.01621/) (2021)
- [Meta-Learning of Neural State-Space Models Using Data From Similar Systems](https://mlsanity.com/paper/2211.07768/) (2022)
- [MINN: Learning the dynamics of differential-algebraic equations and application to battery modeling](https://mlsanity.com/paper/2304.14422/) (2023)
- [Constrained Block Nonlinear Neural Dynamical Models](https://mlsanity.com/paper/2101.01864/) (2021)
- [Structural Inference of Networked Dynamical Systems with Universal Differential Equations](https://mlsanity.com/paper/2207.04962/) (2022)

## Built on by (most cited first, 6 of 6)

- [A Simultaneous Approach for Training Neural Differential-Algebraic Systems of Equations](https://mlsanity.com/paper/2504.04665/) (2025)
- [CHyLL: Learning Continuous Neural Representations of Hybrid Systems](https://mlsanity.com/paper/2512.10117/) (2025)
- [Learning Physical Operators using Neural Operators](https://mlsanity.com/paper/2602.23113/) (2026)
- [HyCOP: Hybrid Composition Operators for Interpretable Learning of PDEs](https://mlsanity.com/paper/2605.00820/) (2026)
- [Physics-Guided Dimension Reduction for Simulation-Free Operator Learning of Stiff Differential-Algebraic Systems](https://mlsanity.com/paper/2604.19930/) (2026)
- [Learning to Test: Latent Representation Learning for Dynamic Instability Detection](https://mlsanity.com/paper/2604.10967/) (2026)

## Abstract (arXiv)

Differential algebraic equations (DAEs) describe the temporal evolution of systems that obey both differential and algebraic constraints. Of particular interest are systems that contain implicit relationships between their components, such as conservation laws. Here, we present an Operator Splitting (OS) numerical integration scheme for learning unknown components of DAEs from time-series data. In this work, we show that the proposed OS-based time-stepping scheme is suitable for relevant system-theoretic data-driven modeling tasks. Presented examples include (i) the inverse problem of tank-manifold dynamics and (ii) discrepancy modeling of a network of pumps, tanks, and pipes. Our experiments demonstrate the proposed method's robustness to noise and extrapolation ability to (i) learn the behaviors of the system components and their interaction physics and (ii) disambiguate between data trends and mechanistic relationships contained in the system.