LSDO Lab
Methods

Fast, differentiable geometry parameterization

Context
Multidisciplinary shape optimization varies component dimensions and positions subject to prescribed geometric relationships.
Gap
Explicit geometry queries can require iterative searches, which becomes costly as component count and geometric complexity grow.
Research goal
Develop differentiable geometry maps that remain efficient as component count and geometric complexity increase.

Selected studies

References
Implicit geometry parameterization

Preserving component relationships as geometry changes

An implicit optimization problem maps geometric design variables to internal deformation states while enforcing geometric equality and inequality constraints. The hierarchical parameterization in lsdo_geo combines existing deformation methods; aircraft and robot examples demonstrate how configuration-specific dimensions and component relationships can be imposed.

Primary paper

Andrew H. Fletcher, John T. Hwang. Implicit Nonlinear Geometry Parameterization for Multidisciplinary Design Optimization. ASME IDETC/CIE 2026 · DETC2026-192508, 2026.

Dependency-structure matrix for an implicit geometry parameterization map, with geometric design variables, parameterization states, geometry evaluations, and constraint residuals.
The implicit geometry parameterization map solves coupled parameterization states so geometric design variables, evaluated geometry, and geometric constraints remain consistent. Fig. 1, Fletcher and Hwang, 2026 [1]
A lift-plus-cruise configuration illustrates differentiable geometry updates that preserve the intended component relationships during design changes. Fletcher and Hwang, 2026 [1]
Four panels show parameterized electric aircraft, laser-powered aircraft, a quadruped robot, and a blended-wing-body wing.
Aircraft and robot examples illustrate a shared parameterization framework for prescribing component shapes, positions, and geometric relationships. [1] Fig. 3, Fig. 4, Fig. 5, Fig. 6

References

  1. Andrew H. Fletcher, John T. Hwang. Implicit Nonlinear Geometry Parameterization for Multidisciplinary Design Optimization. ASME IDETC/CIE 2026 · DETC2026-192508, 2026. Manuscript

Research connections

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