Nonlinear Reduced DNN Models for State Estimation

TL;DR

This paper introduces a data-driven approach using deep neural networks to create nonlinear reduced models for parametric PDEs, enabling efficient state estimation with improved robustness.

Contribution

It presents a novel neural network-based state estimation scheme with sensor-induced decomposition for parametric PDEs, enhancing model accuracy and robustness.

Findings

Effective neural network models for PDE state estimation

Sensor-induced decomposition improves approximation accuracy

Numerical tests demonstrate robustness and performance improvements

Abstract

We propose in this paper a data driven state estimation scheme for generating nonlinear reduced models for parametric families of PDEs, directly providing data-to-state maps, represented in terms of Deep Neural Networks. A major constituent is a sensor-induced decomposition of a model-compliant Hilbert space warranting approximation in problem relevant metrics. It plays a similar role as in a Parametric Background Data Weak framework for state estimators based on Reduced Basis concepts. Extensive numerical tests shed light on several optimization strategies that are to improve robustness and performance of such estimators.