Reconstructing the system coefficients for coupled harmonic oscillators

TL;DR

This paper introduces an iterative optimization method using Tikhonov regularization to reconstruct coupling and damping coefficients in coupled harmonic oscillators, reducing the need for laboratory experiments.

Contribution

It presents a novel, experiment-free iterative strategy for inverse problem solving in physical systems, specifically for identifying system coefficients.

Findings

Significant reduction in laboratory experiments needed

Method accurately identifies coupling and damping coefficients

Compared favorably with purely experimental approaches

Abstract

Physical models often contain unknown functions and relations. In order to gain more insights into the nature of physical processes, these unknown functions have to be identified or reconstructed. Mathematically, we can formulate this research question within the framework of inverse problems. In this work, we consider optimization techniques to solve the inverse problem using Tikhonov regularization and data from laboratory experiments. We propose an iterative strategy that eliminates the need for further laboratory experiments. Our method is applied to identify the coupling and damping coefficients in a system of oscillators, ensuring an efficient and experiment-free approach. We present our results and compare them with those obtained from an alternative, purely experimental approach. By employing our proposed strategy, we demonstrate a significant reduction in the number of laboratory experiments required.