Pablo Norczyk Simon

PhD Thesis

Surrogate-Based Aerodynamic Shape Optimization under Noisy Functions.

Supervisors

Rauno Cavallaro (BSC-CNS) & Joaquim R. R. A. Martins (MDOLab – University of Michigan).

Tutor: Rodrigo Castellanos García de Blas (UC3M).

Abstract

The increasing computational power of HPC systems and advances in aerodynamic solvers enable larger, higher-fidelity aerodynamic optimization studies. However, integration with geometry modification workflows and black-box analysis functions (common in distributed industrial systems) introduces numerical noise and instabilities. These effects cause objective and constraint functions to become noisy or discontinuous, significantly reducing the efficiency and reliability of gradient-based algorithms.
This thesis develops machine learning-aided hybrid optimization methods that retain gradient-based efficiency while accommodating non-differentiable functions. The methodology is designed for seamless HPC integration, incorporating parallelized surrogate-assisted approximations within gradient-based frameworks while optimizing resource utilization and adapting to queuing system constraints.
Key objectives include designing hybrid optimization strategies that combine gradient-based methods with surrogate models and adaptive sampling to efficiently navigate noisy design spaces; implementing scalable parallelization schemes for surrogate-assisted gradient evaluation to fully utilize HPC resources; and demonstrating the methodology on aerodynamic shape optimization problems, including high-fidelity CFD with and without gradient sensitivity information, extending to multidisciplinary optimization workflows.
The work explores robust gradient reconstruction strategies in the presence of noise, using machine learning models to both approximate function values and estimate derivatives in non-smooth regions. This dual-purpose application addresses approximation challenges and gradient estimation problems inherent in noisy optimization landscapes.
The methodology will be benchmarked on canonical aerodynamic problems and validated on industrially relevant configurations where solver instability poses significant challenges. This research bridges the gap between traditional gradient-based optimization efficiency and the robustness required for real-world engineering applications, providing a practical framework for complex aerodynamic optimization in noisy computational environments.