# NINNs: Nudging Induced Neural Networks

arXiv: https://arxiv.org/abs/2203.07947 · HTML: https://mlsanity.com/paper/2203.07947/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 28 references that are in the map.
- First posted on arXiv 15 Mar 2022.

## Builds on (most cited first, 8 of 8)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Stable Architectures for Deep Neural Networks](https://mlsanity.com/paper/1705.03341/) (2017)
- [Deep Neural Networks Motivated by Partial Differential Equations](https://mlsanity.com/paper/1804.04272/) (2018)
- [Robust Training and Initialization of Deep Neural Networks: An Adaptive Basis Viewpoint](https://mlsanity.com/paper/1912.04862/) (2019)
- [Fractional Deep Neural Network via Constrained Optimization](https://mlsanity.com/paper/2004.00719/) (2020)
- [Novel Deep neural networks for solving Bayesian statistical inverse](https://mlsanity.com/paper/2102.03974/) (2021)
- [Novel DNNs for Stiff ODEs with Applications to Chemically Reacting Flows](https://mlsanity.com/paper/2104.01914/) (2021)
- [Continuous data assimilation for the three-dimensional Brinkman-Forchheimer-extended Darcy model](https://mlsanity.com/paper/1502.00964/) (2015)

## Built on by (most cited first, 2 of 2)

- [Neural Network Representation of Time Integrators](https://mlsanity.com/paper/2211.17039/) (2022)
- [Neural Operator-Based Nonlinear Nudging for Chaotic Dynamical Systems](https://mlsanity.com/paper/2508.05778/) (2025)

## Abstract (arXiv)

New algorithms called nudging induced neural networks (NINNs), to control and improve the accuracy of deep neural networks (DNNs), are introduced. The NINNs framework can be applied to almost all pre-existing DNNs, with forward propagation, with costs comparable to existing DNNs. NINNs work by adding a feedback control term to the forward propagation of the network. The feedback term nudges the neural network towards a desired quantity of interest. NINNs offer multiple advantages, for instance, they lead to higher accuracy when compared with existing data assimilation algorithms such as nudging. Rigorous convergence analysis is established for NINNs. The algorithmic and theoretical findings are illustrated on examples from data assimilation and chemically reacting flows.