Discovering the Unknowns: A First Step

TL;DR

This paper introduces a method to identify unknown variables in complex systems by analyzing data for gradual and sudden changes, utilizing Gaussian processes and sparse modeling, demonstrated on a fusion simulation dataset.

Contribution

It proposes a novel approach combining Gaussian process modeling with sparse change detection to uncover unknown system variables from data.

Findings

Successful identification of unknown variables in simulated fusion data

Efficient estimation of numerous parameters using sparse Gaussian process models

Encouraging results demonstrating the method's potential in complex systems

Abstract

This article aims at discovering the unknown variables in the system through data analysis. The main idea is to use the time of data collection as a surrogate variable and try to identify the unknown variables by modeling gradual and sudden changes in the data. We use Gaussian process modeling and a sparse representation of the sudden changes to efficiently estimate the large number of parameters in the proposed statistical model. The method is tested on a realistic dataset generated using a one-dimensional implementation of a Magnetized Liner Inertial Fusion (MagLIF) simulation model and encouraging results are obtained.