lsdo_geo

lsdo_geo is a Python library for geometry representation, implicit deformational parameterization, and analytic adjoint sensitivity analysis tailored for gradient-based Multidisciplinary Design Optimization (MDO).

Developed by the Large-Scale Design Optimization (LSDO) Lab at the University of California, San Diego.

Key Features

• Geometry-Centric MDO: Serves as a single, consistent geometric "source of truth", generating and updating discipline-specific meshes (CFD, FEA, acoustics) without manual re-meshing or geometric inconsistency.
• Implicit Parameterization Framework: Formulates geometry parameterization as an inner constrained optimization problem, solving the first-order Karush-Kuhn-Tucker (KKT) system with an exact Newton solver.
• Hierarchical Free-Form Deformation (FFD): Supports trivariate spline volume lattices with sectional deformation modes—twist, sweep, dihedral, spanwise stretching, and chord taper.
• Analytic Adjoint Sensitivities: Provides exact implicit derivatives $\frac{d\mathbf{x}}{d\mathbf{x}_g}$ through the converged KKT state, seamlessly propagating gradients across the CSDL computational graph.
• CAD & Mesh Interoperability: Direct import, fitting, and export across OpenVSP (.vsp3), IGES (.iges), STEP (.stp), and surface/volume meshes (.msh, .stl).

Architecture Overview

Quickstart

import numpy as np
import csdl_alpha as csdl
import lsdo_geo as lg

# 1. Initialize CSDL graph recorder
recorder = csdl.Recorder(inline=True)
recorder.start()

# 2. Define or import geometry
geometry = lg.import_geometry("path/to/wing.stp")

# 3. Create a Free-Form Deformation (FFD) block around the geometry
ffd_block = lg.construct_ffd_block_around_entities(
    geometry,
    num_control_points=(4, 4, 2),
)

# 4. Apply geometric transformations (rotation, translation)
rotation_origin = np.array([0.0, 0.0, 0.0])
rotation_axis = np.array([0.0, 0.0, 1.0])
rotated_points = lg.rotate(
    geometry.coefficients,
    rotation_origin=rotation_origin,
    axis_vector=rotation_axis,
    angles=15.0,
    units="degrees",
)

Installation

Prerequisites & Installation

lsdo_geo relies on CSDL_alpha and lsdo_function_spaces:

# 1. Install dependencies
pip install jax
pip install git+https://github.com/LSDOlab/CSDL_alpha.git@dev_andrew
pip install git+https://github.com/LSDOlab/lsdo_function_spaces.git

# 2. Install lsdo_geo (User)
pip install lsdo_geo
# Or install development version directly from GitHub:
pip install git+https://github.com/LSDOlab/lsdo_geo.git

For Developers

Clone the repository and install in editable mode with testing and documentation extras:

git clone https://github.com/LSDOlab/lsdo_geo.git
cd lsdo_geo
pip install jax
pip install git+https://github.com/LSDOlab/CSDL_alpha.git@dev_andrew
pip install git+https://github.com/LSDOlab/lsdo_function_spaces.git
pip install -e ".[test,docs]"

Testing

Run the test suite using pytest:

pytest

To run fast unit tests only:

pytest -m "not slow"

Documentation

Full documentation, theoretical background, tutorials, and API reference are hosted on Read the Docs: 👉 lsdo-geo.readthedocs.io

To build the documentation locally:

sphinx-build -b html docs docs/_build/html

Citation

If you use lsdo_geo in your work or research, please cite:

@inproceedings{fletcher2026implicit,
  title     = {Implicit Nonlinear Geometry Parameterization for Multidisciplinary Design Optimization},
  author    = {Fletcher, Andrew H. and Hwang, John T.},
  booktitle = {Proceedings of the ASME 2026 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference (IDETC/CIE2026)},
  number    = {DETC2026-192508},
  year      = {2026},
  address   = {Houston, TX}
}

License

lsdo_geo is distributed under the terms of the Apache License, Version 2.0. See LICENSE.txt for details.