Infrared and nebular lines provide some of our best probes of the physics regulating the properties of the interstellar medium (ISM) at high-redshift. However, interpreting the physical conditions of high-redshift galaxies directly from emission lines remains complicated due to inhomogeneities in temperature, density, metallicity, ionisation parameter, and spectral hardness. We present a new suite of cosmological, radiation-hydrodynamics simulations, each centred on a massive Lyman-break galaxy that resolves such properties in an inhomogeneous ISM. Many of the simulated systems exhibit transient but well defined gaseous disks that appear as velocity gradients in [CII] 157.6µm emission. Spatial and spectral offsets between [CII] 157.6µm and [OIII] 88.33µm are common, but not ubiquitous, as each line probes a different phase of the ISM. These systems fall on the local [CII]-SFR relation, consistent with newer observations that question previously observed [CII] 157.6µm deficits. Our galaxies are consistent with the nebular line properties of observed z ∼ 2 − 3 galaxies and reproduce offsets on the BPT and mass-excitation diagrams compared to local galaxies due to higher star formation rate (SFR), excitation, and specific-SFR, as well as harder spectra from young, metal-poor binaries. We predict that local calibrations between Hα and [OII] 3727Å luminosity and galaxy SFR apply up to z > 10, as do the local relations between certain strong line diagnostics (R23 and [OIII] 5007Å/Hβ) and galaxy metallicity. Our new simulations are well suited to interpret the observations of line emission from current (ALMA and HST) and upcoming facilities (JWST and ngVLA).

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.