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

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.