# Neural Conjugate Flows: Physics-informed architectures with flow structure

arXiv: https://arxiv.org/abs/2411.08326 · HTML: https://mlsanity.com/paper/2411.08326/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 38 references that are in the map.
- First posted on arXiv 13 Nov 2024.

## Builds on (most cited first, 9 of 9)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Lagrangian Neural Networks](https://mlsanity.com/paper/2003.04630/) (2020)
- [Augmented Neural ODEs](https://mlsanity.com/paper/1904.01681/) (2019)
- [On Neural Differential Equations](https://mlsanity.com/paper/2202.02435/) (2022)
- [Respecting causality is all you need for training physics-informed neural networks](https://mlsanity.com/paper/2203.07404/) (2022)
- [An Expert's Guide to Training Physics-informed Neural Networks](https://mlsanity.com/paper/2308.08468/) (2023)
- [On weight initialization in deep neural networks](https://mlsanity.com/paper/1704.08863/) (2017)
- [On the Universality of Volume-Preserving and Coupling-Based Normalizing Flows](https://mlsanity.com/paper/2402.06578/) (2024)

## Built on by (most cited first, 1 of 1)

- [PINNverse: Accurate parameter estimation in differential equations from noisy data with constrained physics-informed neural networks](https://mlsanity.com/paper/2504.05248/) (2025)

## Abstract (arXiv)

We introduce Neural Conjugate Flows (NCF), a class of neural network architectures equipped with exact flow structure. By leveraging topological conjugation, we prove that these networks are not only naturally isomorphic to a continuous group, but are also universal approximators for flows of ordinary differential equation (ODEs). Furthermore, topological properties of these flows can be enforced by the architecture in an interpretable manner. We demonstrate in numerical experiments how this topological group structure leads to concrete computational gains over other physics informed neural networks in estimating and extrapolating latent dynamics of ODEs, while training up to five times faster than other flow-based architectures.