# Learning Reduced-Order Dynamics with Singularity via Latent-Augmented Neural Ordinary Differential Equations

arXiv: https://arxiv.org/abs/2608.22142 · HTML: https://mlsanity.com/paper/2608.22142/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 27 references that are in the map.
- First posted on arXiv 22 Aug 2026.

## Builds on (most cited first, 13 of 13)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Augmented Neural ODEs](https://mlsanity.com/paper/1904.01681/) (2019)
- [On Second Order Behaviour in Augmented Neural ODEs](https://mlsanity.com/paper/2006.07220/) (2020)
- [Deep networks for system identification: a Survey](https://mlsanity.com/paper/2301.12832/) (2023)
- [ODE Transformer: An Ordinary Differential Equation-Inspired Model for Sequence Generation](https://mlsanity.com/paper/2203.09176/) (2022)
- [Learning Nonlinear Projections for Reduced-Order Modeling of Dynamical Systems using Constrained Autoencoders](https://mlsanity.com/paper/2307.15288/) (2023)
- [Data-Driven Learning-Based Optimization for Distribution System State Estimation](https://mlsanity.com/paper/1807.01671/) (2018)
- [Signed Graph Neural Ordinary Differential Equation for Modeling Continuous-time Dynamics](https://mlsanity.com/paper/2312.11198/) (2023)
- [ControlSynth Neural ODEs: Modeling Dynamical Systems with Guaranteed Convergence](https://mlsanity.com/paper/2411.02292/) (2024)
- [Continuous-time Graph Representation with Sequential Survival Process](https://mlsanity.com/paper/2312.13068/) (2023)
- [Online Reduced-Order Data-Enabled Predictive Control](https://mlsanity.com/paper/2407.16066/) (2024)
- [Learning and Current Prediction of PMSM Drive via Differential Neural Networks](https://mlsanity.com/paper/2412.09028/) (2024)

## Abstract (arXiv)

This paper addresses the issue of self-intersecting trajectories (in phase space) in industrial reduced-order modeling and proposes the Latent-Augmented Neural Ordinary Differential Equations (LA-NODEs) framework. From the perspective of artificial intelligence, the proposed method augments conventional neural ordinary differential equations to enhance model expressiveness, enabling the representation of conflicting vector fields that may arise in reduced-order systems, thereby improving learning accuracy. Through theoretical analysis, the underlying mechanism of the framework is established, and a condition for determining the minimum required augmentation dimension is derived. From the perspective of engineering applications, the effectiveness of the proposed method is validated on the reduced-order system of two representative industrial models, namely an interior permanent magnet synchronous motor (IPMSM) drive and a distributed energy system (DES). Experimental results demonstrate that the proposed method can recover system features that are difficult to capture using conventional approaches and achieve superior performance in terms of prediction accuracy and modeling fidelity, thereby providing an effective approach for high-precision data-driven modeling of complex industrial systems.