  Our understanding of physical systems generally depends on our ability to
match complex computational modelling with 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 machine
learning can be used to address inverse problem instabilities, and apply it to
two popular experimental diagnostics in plasma physics. We find that the
extraction of information from measurements simply on the basis of agreement
with simulations 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.
