Our mathematical models of gas-phase chemical kinetics, thermal and chemical gas-surface interactions, and non- equilibrium response of solid materials encompass a vast array of uncertainties. Even when some model parameters or constitutive relations are developed from ab initio calculations, extrapolation away from idealized conditions, stochas- ticity in materials microstructure, and our broader program of bridging scales require a quantitative assessment of these uncertainties and their impact. Our rigorous and comprehensive UQ program aims to quantify, prioritize, and reduce these uncertainties in a goal-oriented fashion—i.e., with regard to their impact on the final predictive QoIs. Our UQ program will include aspects of forward UQ (e.g., sensitivity analyses, dimension reduction, accelerated with sur- rogate models and multi-fidelity methods); Bayesian inference and model calibration (including adaptive choices of prior and stochastic representations of model error); in-house and external experiments for model validation, augment- ing available benchmark data; and methods of optimal experimental design (aimed at creating a closed-loop interaction between simulations and experiments). In each of these areas, we will not only harness leading UQ methodologies, but advance the methodological state of the art. In this vein, we will focus a portion of our UQ effort on quantify- ing uncertainty in our ML surrogate model predictions (ENNs, MLS) that we will employ throughout our multiscale simulations.
Forward UQ. While many aspects of parametric forward UQ have matured over the past decade, the present coupled- model and multiscale simulation architecture, along with strong nonlinearities and high dimensionality of relevant parameter spaces, present many important challenges. Our work in this regard will focus on the deployment of surro- gates and ROMs in a hierarchical framework; on new methods for global sensitivity analysis that handle dependent inputs while accounting for higher moments and tail behavior; and on gradient-based dimension reduction methods with error guarantees.
Bayesian inference and model calibration. In this project, we have the ability to use existing data sources (including
simulations at finer scales) as well as new experimental data to inform our models and refine their predictions— not only by refining the values of model parameters, but also by calibrating stochastic representations of structural model errors. To this end, we will deploy and advance Bayesian methodologies for inference, posterior prediction, and model checking. Key tools will include measure transport methods for Bayesian computation, which we may apply in an amortized setting, enabling both accurate posterior approximations and rich cost/accuracy trade-offs. We will pay specific attention to understanding the UQ guarantees for these Bayesian methods in the presence of model misspecification, which is inevitably present in the complex physical setting at hand.
UQ for ML models. A special focus of our UQ effort will be to quantify uncertainty in the surrogate ENN models that we will employ throughout our multiscale simulations—to represent, e.g., constitutive models in continuum fluid and solid simulations as well as interatomic potentials. We will develop new methods for predicting the generalization error of these deep neural network models in relevant scaling regimes, elucidating the value of different kinds of data. Specifically for ENNs, we will characterize how group invariances encoded within these models interact with uncertainty resulting from finite network size (i.e., model bias), noisy and finite training data, stochastic optimization methods, and distributional shift. We will also assess the value of approximate Bayesian methods in this setting, which involves tackling open questions regarding both prior specification and approximate sampling.
Optimal experimental design. A final focus of our UQ effort is optimal experimental design (OED), which will help guide the validation experiments discussed below. Our work will focus on the following thrusts: maximizing goal-oriented OED criteria, aimed at maximizing information gain in chosen observables, rather than parameters; tight and computationally tractable lower bounds for these information theoretic objectives; and performing OED in the presence of model error. For the latter, we will consider both embedded stochastic discrepancy models and, more powerfully, adversarial approaches to OED based on distributionally robust optimization.
Expanding experimental capabilities. We will design and construct a custom, lab-scale environmental test chamber combining CO2 laser-based sample heating with pre-heated flows of oxygen, and nitrogen gases. We will install a residual gas analyzer (RGA) to analyze gas-phase species and to enable measurements of ablation rates and desorption energies. These results will be complemented by gas-phase, laser-based emission spectroscopy to further analyze gas species. We will implement multiple-band pyrometry and broadband emission spectroscopy to measure and map sample temperature. In addition, we will look into performing complimentary experiments at the Laser Hardened Materials Evaluation Laboratory (LHMEL) at the Air Force Research Laboratory and the Energy Matter Interaction Tunnel (EMIT) at Lawrence Livermore National Laboratory.
Post-mortem characterization. Using transmission electron microscopy (TEM) on cross-section samples prepared by focused ion beam (FIB) milling, we will resolve changes in structure, composition, and defect density and type, all with atomic-scale resolution. We will fabricate multilayer calibration samples with pre-determined layer thicknesses to enable direct measurement of ablation rates. Our TEM measurements will be performed in plan view, to enable for imaging and analysis over micrometer-scale fields of view, providing orders-of-magnitude more data than available in typical cross-section TEM. This will include the development of methods to rapidly and automatically quantify grain size, defects and grain boundary orientations.