MURI: Probabilistic Multiscale Inference of Interface Models under Extreme Conditions

Abstract The transfer of mass, momentum, and energy at the solid-gas interface under extreme conditions and non-equilibrium gas flows is dictated by several complex physical phenomena occurring across multiple scales. These include chemical reactions of the gas constituents (recombination) at the interface, finite rate chemical reactions between the solid and gas constituents leading to sublimation, oxidation, catalysis, and complex variations in the effective properties (viscosity, thermal conductivity, etc.) of various constituents while accounting for non-equilibrium states, and the time-dependent evolution of surface morphology and accompanying aerothermodynamic loads. Efforts aimed at inferring or validating continuum-level models from experimental data for these processes are challenged by multiple interacting complex physical processes that often contribute to the same observable effect. For example, the chemical composition of the gas phase at the interface is determined by surface chemical reactions between the constituents at the interface, as well as the chemical reactions between the solid and gas constituents. Further, due to the extreme conditions, measuring quantities that directly inform interface models is challenging even in controlled environments. For instance, measuring the interface temperature using IR is complicated by the distortions to the IR wave path introduced by shocks, boundary layers and rapidly varying physical properties of the gas. These challenges are somewhat alleviated by the fact that the physical phenomena at the interface can be modeled at smaller scales, and these finer-scale simulations provide data that can be used to confine the range of possible models by developing suitable priors. In particular, molecular dynamics (MD) simulations can provide information regarding transport properties which can be used directly in continuum models. MD simulations can also provide information regarding reaction rates which can be used in mesoscale models, like those based on Direct Simulation Monte Carlo (DSMC) models. These mesoscale models can then provide information about the interface transfer models to be used in continuum-scale models. Methods based on Bayesian inference meet the desiderata described above, however most fall short when applied to the experimental-scale problems at hand because of several reasons. First, they tend to be computationally prohibitive for cases where the dimension of the inferred vector is large (say greater than 50). This is clearly a limitation for problems of interest, where we may wish to infer a large dimensional vector of parameters, or sometimes even entire fields defined on the interface. Second, they require and explicit and simple (Gaussian, for example) expressions for the prior probability density for the inferred quantity. In the problems of interest, prior information regarding the interface quantities will be obtained from results of fine-scale simulations (MD or DSMC) and will therefore be in the form of samples. Thus, methods that can work with sample- based priors are needed. Finally, most current methods assume simple (Gaussian) additive models for model and observation errors. On the other hand, the scenarios we wish to consider involve complex experimental conditions and measurements where the appropriate models for model and measurement error are expected to be neither additive nor Gaussian.