NINNs: Nudging Induced Neural Networks
This addresses the problem of controlling and enhancing neural network accuracy for applications such as data assimilation and chemically reacting flows, though it appears incremental as it builds on existing DNNs.
The paper introduces Nudging Induced Neural Networks (NINNs), a framework that adds feedback control to deep neural networks to improve accuracy, achieving higher accuracy compared to existing data assimilation algorithms like nudging.
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.