Chance-constrained optimal design of porous thermal insulation systems under spatially correlated uncertainty

This paper introduces a computationally efficient framework for the optimal design of engineering systems governed by multiphysics, nonlinear partial differential equations (PDEs) and subject to high-dimensional spatial uncertainty. The focus is on 3D printed silica aerogel-based thermal break components in building envelopes, where the objective is to maximize thermal insulation performance while ensuring mechanical reliability by mitigating stress concentrations. Material porosity is modeled as a spatially correlated Gaussian random field, yielding a high-dimensional stochastic design space whose dimensionality corresponds to the mesh resolution after finite element discretization. A robust design objective is employed, incorporating statistical moments of the thermal performance metric and in conjunction with a probabilistic (chance) constraint that restricts the p-norm of the von Mises stress field below a critical threshold, effectively controlling stress concentrations across the domain. To alleviate the substantial computational burden associated with Monte Carlo estimation of statistical moments, a second-order Taylor series approximation is introduced as a control variate, significantly accelerating convergence. Furthermore, a continuation-based strategy is developed to regularize the non-differentiable chance constraints, enabling the use of an efficient gradient-based Newton–Conjugate Gradient optimization algorithm. The proposed framework achieves computational scalability that is effectively independent of the stochastic design space dimensionality. Numerical experiments on two- and three-dimensional thermal breaks in building insulation demonstrate the method’s efficacy in solving large-scale, PDE-constrained, chance-constrained optimization problems with uncertain parameter spaces reaching dimensions in the hundreds of thousands.