NINNs: Nudging Induced Neural Networks

TL;DR

NINNs are a new class of neural networks that incorporate feedback control during forward propagation to enhance accuracy and convergence, applicable to most existing DNNs with minimal additional computational cost.

Contribution

The paper introduces NINNs, a novel framework that integrates nudging feedback into neural networks, providing improved accuracy and convergence guarantees.

Findings

NINNs achieve higher accuracy than traditional nudging algorithms.

Rigorous convergence analysis confirms stability of NINNs.

Applications demonstrated in data assimilation and chemical flow modeling.

Abstract

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.