A Trust-Region Algorithm for PDE-Constrained Optimization with Bound Constraints Using Reduced-Order Modeling
M.A. Aguilo
Abstract
We present a trust-region algorithm for large-scale PDE-constrained optimization with bound constraints that uses proper orthogonal decomposition (POD) to accelerate the iterative solution. The algorithm samples high-fidelity state and Lagrange-multiplier data along the optimization trajectory and automatically computes and updates the POD basis used to construct reduced-order models, which replace computationally intensive high-fidelity finite element evaluations. A trust-region acceptance criterion detects loss of predictive accuracy in the reduced model and triggers adaptive enrichment of the POD basis, providing a sound mathematical metric to control inexactness during optimization. Bound constraints on the control variables are handled natively through a projected-gradient method. On three benchmark topology optimization problems, namely the symmetric MBB beam, the Michell beam, and the cantilever beam, it is shown that the algorithm delivers substantial speedups over the high-fidelity baseline without degrading the optimal topology.
Find peer-reviewed article here
Stay in the Loop!
Subscribe to get the latest news, product updates, and exclusive event invitations – delivered straight to your inbox. Be the first to know what’s next.
👉 Contact us for early access, demonstrations, and collaboration opportunities.
About Morphorm
Morphorm® is an emerging leader in engineering simulation and modeling technologies. Founded in 2022 and headquartered in Albuquerque, New Mexico, Morphorm is advancing state-of-the-art optimization and simulation technologies to drive product innovation in clean energy, semiconductors, and defense. The company’s pioneering real-time design solutions are setting new industry benchmarks in performance and efficiency.
Morphorm
Redefining Simulation. Empowering Innovation.
