Inverse problem instabilities in large-scale modeling of matter in extreme conditions

M F Kasim,S M Vinko,T P Galligan,G Gregori,J Topp-Mugglestone

doi:10.1063/1.5125979

Abstract

Our understanding of physical systems often depends on our ability to match complex computational modeling with the measured experimental outcomes. However, simulations with large parameter spaces suffer from inverse problem instabilities, where similar simulated outputs can map back to very different sets of input parameters. While of fundamental importance, such instabilities are seldom resolved due to the intractably large number of simulations required to comprehensively explore parameter space. Here, we show how Bayesian inference can be used to address inverse problem instabilities in the interpretation of x-ray emission spectroscopy and inelastic x-ray scattering diagnostics. We find that the extraction of information from measurements on the basis of agreement with simulations alone is unreliable and leads to a significant underestimation of uncertainties. We describe how to statistically quantify the effect of unstable inverse models and describe an approach to experimental design that mitigates its impact.

Highlights

Our understanding of physical systems closely depends on our ability to predictively model their behavior in controlled experimental settings
Some difficulties with this approach for inertial fusion energy research have been discussed within the context of insufficiently accurate models and diagnostics,[1,2] but little attention has been paid to the intrinsic limitation of integrated experiments in their own right and to the systematic uncertainties introduced by correlated physical parameters in both experiment and simulation
Inelastic x-ray Thomson scattering (XRTS) is a widely used tool in high energy density physics to determine the conditions of warmdense matter via direct probing of the electron response function.[10,11,12]

Summary

Introduction

Our understanding of physical systems closely depends on our ability to predictively model their behavior in controlled experimental settings. An example of such research is the study of matter at high energy densities, i.e., systems at temperatures exceeding $10 000 K at the typical density of a solid or at pressures exceeding 1 Mbar Matter in these conditions is of great interest to astrophysical and inertial confinement fusion (ICF) investigations and tends to be highly transient, inhomogeneous, and challenging to controllably create and difficult to probe. Research here relies strongly on complex computational modeling that needs to account for a wide range of processes and interactions, which, critically, depend on a large number of variable parameters Some difficulties with this approach for inertial fusion energy research have been discussed within the context of insufficiently accurate models and diagnostics,[1,2] but little attention has been paid to the intrinsic limitation of integrated experiments in their own right and to the systematic uncertainties introduced by correlated physical parameters in both experiment and simulation

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Conclusion