Retrospective Cost Parameter Estimation with Application to Space Weather Modeling

TL;DR

This paper introduces a novel gradient-, ensemble-, and adjoint-free data-driven parameter estimation method called RCPE, applicable to complex large-scale models like space weather, demonstrated through three diverse examples.

Contribution

The paper presents RCPE, a new parameter estimation technique suitable for high-dimensional nonlinear models, expanding the toolkit beyond traditional methods.

Findings

RCPE effectively estimates parameters in nonlinear systems.

It successfully estimates physical parameters in space weather models.

The method is versatile across different types of complex models.

Abstract

This chapter reviews standard parameter-estimation techniques and presents a novel gradient-, ensemble-, adjoint-free data-driven parameter estimation technique in the DDDAS framework. This technique, called retrospective cost parameter estimation (RCPE), is motivated by large-scale complex estimation models characterized by high-dimensional nonlinear dynamics, nonlinear parameterizations, and representational models. RCPE is illustrated by estimating unknown parameters in three examples. In the first example, salient features of RCPE are investigated by considering parameter estimation problem in a low-order nonlinear system. In the second example, RCPE is used to estimate the convective coefficient and the viscosity in the generalized Burgers equation by using a scalar measurement. In the final example, RCPE is used to estimate thermal conductivity coefficients that relate temporal temperature variation with the vertical gradient of the temperature in the atmosphere.