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The widespread integration of deep neural networks in developing data-driven surrogate models for high-fidelity simulations of complex physical systems highlights the critical necessity for robust uncertainty quantification techniques and credibility assessment methodologies, ensuring the reliable deployment of surrogate models in consequential decision-making. This study presents the Occam Plausibility Algorithm for surrogate models (OPAL-surrogate), providing a systematic framework to uncover predictive neural network-based surrogate models within the large space of potential models, including various neural network classes and choices of architecture and hyperparameters. The framework is grounded in hierarchical Bayesian inferences and employs model validation tests to evaluate the credibility and prediction reliability of the surrogate models under uncertainty. Leveraging these principles, OPAL- surrogate introduces a systematic and efficient strategy for balancing the trade-off between model complexity, accuracy, and prediction uncertainty. The effectiveness of OPAL-surrogate is demonstrated through two modeling problems, including the deformation of porous materials for building insulation and turbulent combustion flow for ablation of solid fuels within hybrid rocket motors. 

This paper introduces a scalable computational framework for optimal design under high-dimensional uncertainty, with application to thermal insulation components. The thermal and mechanical behaviors are described by continuum multi-phase models of porous materials governed by partial differential equations (PDEs), and the design parameter, material porosity, is an uncertain and spatially correlated field. After finite element discretization, these factors lead to a high-dimensional PDE-constrained optimization problem. The framework employs a risk-averse formulation that accounts for both the mean and variance of the design objectives. It incorporates two regularization techniques, the L0-norm and phase field functionals, implemented using continuation numerical schemes to promote spatial sparsity in the design parameters. To ensure efficiency, the framework utilizes a second-order Taylor approximation for the mean and variance and exploits the low-rank structure of the preconditioned Hessian of the design objective. This results in computational costs that are determined by the rank of preconditioned Hessian, remaining independent of the number of uncertain parameters. The accuracy, scalability with respect to the parameter dimension, and sparsity-promoting abilities of the framework are assessed through numerical examples involving various building insulation components. 

Flexible thermal insulating membranes are ubiquitous in thermal management. Nevertheless, difficulties arise for composite membranes to combine a resilient, robust structural framework with uniform percolation networks purposefully conceived for thermal insulation. Herein, by controlling the microstructure homogeneity, we report flexible, hydrophobic thermal insulating membranes consisting of ceramic fiber and porous silica materials. The resulting nanofibrous membrane composites exhibit a low thermal insulation of 11.4 mW m−1 K−1, a low density of 0.245 g cm−3, mechanical flexibility with a bending rigidity of 1.25 cN mm−1, and hydrophobicity with a water contact angle of 144°. These nanofibrous-reinforced, silica-aerogel-based nanocomposite membranes are potential candidates for advanced thermal management applications.