Session: 12-08-01: Data-Enabled Predictive Modeling, Scientific Machine Learning, and Uncertainty Quantification in Computational Mechanics

Paper Number: 144618

144618 - Chance Constrained Pde-Constrained Optimal Design Strategies Under High-Dimensional Uncertainty 

This study focuses on developing a computational framework for model-based design of the thermal insulation elements of net-zero buildings, based on silica aerogel porous materials, ensuring they provide superinsulation while upholding structural integrity. This approach employs a multiphase continuum model, capturing the thermomechanical properties of the insulation component through a set of partial differential equations (PDE). The framework considers the uncertainty associated with both the physical parameters like elasticity and thermal conductivity for the solid and fluid phases, as well as the design parameter, which is the spatial distribution of the aerogel porosity over the domain of the component. The combination of spatially varying design and uncertainty parameters, along with their finite element discretization, results in a high dimensional PDE-constrained optimal design problem. A risk-averse cost functional is implemented to achieve both target insulation performance and uncertainty reduction during the design process. To avoid stress concentration in the component, chance constraints are included in the optimization formulation, which ensures that the probability of a function that measures the difference between evaluated stress from the multiphase model and a critical threshold value, lies within a tolerance. To induce sparsity in the porosity field a phase field-type regularization is applied consisting of a weighted sum of Tikhonov and double-well functionals. A continuation numerical scheme is then implemented where we iteratively move from single well to double well with a uniform step size of a scaling hyperparameter related to the double well function to achieve global optima in the design solution. A scalable method is introduced for solving PDE-constrained optimization under uncertainty that is both efficient and dimension-independent. For efficiency, this method exploits a second-order Taylor approximation of the design objective, which solves a generalized eigenvalue problem. This method relies solely on the Hessian’s action on a limited set of random directions, which utilizes a randomized algorithm for approximation that can otherwise become computationally prohibitive for large dimensions. A gradient-based optimization method is used built on Lagrangian formulation, which makes the problem scalable as the construction of the design gradient requires only a few vectors and their gradients, and is irrespective of the dimension of the design parameters. The numerical experiments on the thermal breaks of the buildings demonstrate that the proposed framework leads to a significant reduction in computational cost, up to several orders of magnitude in the optimization solution compared to monte carlo estimation of the moments of objective function.  

Presenting Author: Pratyush Kumar Singh University at Buffalo

Presenting Author Biography: Pratyush Kumar Singh is a dedicated researcher currently pursuing his Ph.D. in Mechanical Engineering at University at Buffalo. He obtained his Master of Science degree in Mechanical Engineering with highest honors(summa cum laude) from University at Buffalo. Pratyush's research interests span a wide range of topics within mechanical engineering, including uncertainty quantification, self assembly, surrogate modeling, bayesian neural networks, etc. He has been actively involved in cutting-edge research, focusing on a nonlocal theory of heat transfer and micro-phase separation of nano-structured copolymers, as evidenced by his publication in the International Journal of Heat and Mass Transfer. As an emerging scholar in the field of mechanical engineering, Pratyush Kumar Singh continues to push the boundaries of knowledge, bringing innovative solutions to the forefront of research and contributing significantly to the scientific community.

Authors:

Pratyush Kumar Singh University at Buffalo
Danial Faghihi University at Buffalo