# ANODEV2: A Coupled Neural ODE Evolution Framework

arXiv: https://arxiv.org/abs/1906.04596 · HTML: https://mlsanity.com/paper/1906.04596/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Jun 2019.

## Built on by (most cited first, 12 of 12)

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- [An Over Complete Deep Learning Method for Inverse Problems](https://mlsanity.com/paper/2402.04653/) (2024)
- [Accelerating Dynamical System Simulations with Contracting and Physics-Projected Neural-Newton Solvers](https://mlsanity.com/paper/2106.02543/) (2021)
- [Characteristic Neural Ordinary Differential Equations](https://mlsanity.com/paper/2111.13207/) (2021)
- [Parameter-varying neural ordinary differential equations with partition-of-unity networks](https://mlsanity.com/paper/2210.00368/) (2022)

## Abstract (arXiv)

It has been observed that residual networks can be viewed as the explicit Euler discretization of an Ordinary Differential Equation (ODE). This observation motivated the introduction of so-called Neural ODEs, which allow more general discretization schemes with adaptive time stepping. Here, we propose ANODEV2, which is an extension of this approach that also allows evolution of the neural network parameters, in a coupled ODE-based formulation. The Neural ODE method introduced earlier is in fact a special case of this new more general framework. We present the formulation of ANODEV2, derive optimality conditions, and implement a coupled reaction-diffusion-advection version of this framework in PyTorch. We present empirical results using several different configurations of ANODEV2, testing them on multiple models on CIFAR-10. We report results showing that this coupled ODE-based framework is indeed trainable, and that it achieves higher accuracy, as compared to the baseline models as well as the recently-proposed Neural ODE approach.