[2603.03211] Shape Derivative-Informed Neural Operators with Application to Risk-Averse Shape Optimization

Mathematics > Optimization and Control arXiv:2603.03211 (math) [Submitted on 3 Mar 2026] Title:Shape Derivative-Informed Neural Operators with Application to Risk-Averse Shape Optimization Authors:Xindi Gong, Dingcheng Luo, Thomas O'Leary-Roseberry, Ruanui Nicholson, Omar Ghattas View a PDF of the paper titled Shape Derivative-Informed Neural Operators with Application to Risk-Averse Shape Optimization, by Xindi Gong and 4 other authors View PDF HTML (experimental) Abstract:Shape optimization under uncertainty (OUU) is computationally intensive for classical PDE-based methods due to the high cost of repeated sampling-based risk evaluation across many uncertainty realizations and varying geometries, while standard neural surrogates often fail to provide accurate and efficient sensitivities for optimization. We introduce Shape-DINO, a derivative-informed neural operator framework for learning PDE solution operators on families of varying geometries, with a particular focus on accelerating PDE-constrained shape OUU. Shape-DINOs encode geometric variability through diffeomorphic mappings to a fixed reference domain and employ a derivative-informed operator learning objective that jointly learns the PDE solution and its Fréchet derivatives with respect to design variables and uncertain parameters, enabling accurate state predictions and reliable gradients for large-scale OUU. We establish a priori error bounds linking surrogate accuracy to optimization error and prove universal...