LSDO Lab
Methods

Projection-based model reduction for accelerated high-fidelity simulation

Context
Proper orthogonal decomposition approximates simulation states in a small basis assembled from previously computed solutions.
Gap
A fixed basis can lose accuracy as the design changes, while sampling an entire high-dimensional design space is impractical.
Research goal
Adapt reduced bases to the designs visited during optimization while limiting the cost of basis updates and full-order simulations.

Selected studies

References
Weighted POD for aerodynamic designDesign-adaptive POD for shell optimization

Accelerating transonic aerodynamic design with weighted POD

Global and weighted POD approximate compressible-Euler solutions during lift-constrained drag minimization of the Simple Transonic Wing. The weighted basis improves state accuracy, and both reduced models evaluate at least an order of magnitude faster than the full model on the tested coarse mesh with zeroth-order elements.

Primary paper

Sebastiaan P. van Schie, John T. Hwang. Computational Framework for High-Fidelity Aerodynamic Shape Optimization Using Weighted POD. AIAA AVIATION 2026 Forum, 2026.

DOIPDF
Simple Transonic Wing geometry with its surface mesh superimposed.
The Simple Transonic Wing surface mesh defines the geometry for the compressible-Euler shape-optimization benchmark. Fig. 2, van Schie and Hwang, 2026 [1]
Box plots compare relative total-state errors for global and weighted POD models with 10 and 20 retained modes.
Weighted POD lowers the relative total-state error of the reduced Euler model compared with a global basis at the tested 10- and 20-mode dimensions. Fig. 5, van Schie and Hwang, 2026 [1]
Box plots compare total wall times for global and weighted POD models and their full-order-model counterparts with 10 and 20 retained modes.
Global and weighted POD evaluations are at least an order of magnitude faster than full-order evaluations for this coarse, zeroth-order discretization. Fig. 7, van Schie and Hwang, 2026 [1]

Updating reduced bases through structural design changes

Weighted POD assigns greater importance to snapshots near the current design and updates the basis during optimization. Efficient basis updates and an extension using basis derivatives reduce shell-solution errors relative to global POD and Grassmann interpolation, without requiring an offline training set spanning the design space.

Primary paper

Sebastiaan P. C. van Schie, Boris Kramer, John T. Hwang. Weighted Proper Orthogonal Decomposition for High-Dimensional Optimization. arXiv:2508.09084v1, 2025.

PDFarXiv
Deformed cantilevered shell colored by displacement magnitude under a uniform pressure load.
A cantilevered shell under constant pressure supplies the dynamic thickness-optimization benchmark; displacement is magnified threefold. Fig. 2, van Schie et al., 2025 [2]
Median relative error is plotted against median wall time for global, Grassmann, weighted, and derivative-enriched weighted POD approaches at several reduced-basis sizes.
Weighted POD lowers shell-solution error at comparable evaluation times; basis derivatives further improve accuracy in this comparison. Fig. 5, van Schie et al., 2025 [2]

References

  1. Sebastiaan P. van Schie, John T. Hwang. Computational Framework for High-Fidelity Aerodynamic Shape Optimization Using Weighted POD. AIAA AVIATION 2026 Forum, 2026.
    DOIPDF
  2. Sebastiaan P. C. van Schie, Boris Kramer, John T. Hwang. Weighted Proper Orthogonal Decomposition for High-Dimensional Optimization. arXiv:2508.09084v1, 2025. Preprint
    PDFarXiv
  3. Sebastiaan P. van Schie, John T. Hwang. Model Reduction of Isogeometric Shell Structures For Large-Scale Design Optimization. AIAA AVIATION 2023 Forum, 2023.
    DOIPDF
  4. Sebastiaan P. van Schie, John T. Hwang. Towards Hyper-Reduced Weighted POD for Large-Scale Aerodynamic Design Optimization. AIAA SCITECH 2026 Forum, 2026.
    DOIPDF

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