A modular and fully differentiable Python framework for reconstructing density-based topology optimization results using parametric capsule features.
The system provides analytical gradients and exact Hessians, supports smooth aggregation strategies, and enables staged nonlinear optimization with constraint handling and automatic feature refinement.
Patrick Jung (2026).
Optimizing Initial Feature-Mapping Variables from Given Designs via Tracking.
arXiv:2602.13005
https://arxiv.org/abs/2602.13005
The framework is organized into modular components:
-
pill module
Defines parametric capsule features (line segments with radii) and provides analytical signed distance functions, gradients, and Hessians. -
optimization_definition module
Formulates the nonlinear optimization problem with support for:- Least-squares tracking objectives
- Reward-based initialization objectives
- Exact Hessian or first-order solver interfaces
- IPOPT and SciPy compatibility
-
staged optimization runner
Executes multi-stage optimization pipelines (orientation → convergence), applies geometric constraints, and manages solver settings via JSON configs. -
heuristics & refinement
- Automatic pruning of weak or redundant features
- Feature merging based on geometric criteria
- Greedy additive refinement to extend the design
The system transforms voxel-based density fields into compact, constraint-safe feature representations.
Create a virtual environment and install dependencies:
pip install -r requirements.txt
python scripts/optimize.py
density/files/5bar_80.density.xml
opt_config/example_run.json
--output_dir ./example_run
-
Generate a target density field using CFS:
- Create mesh
- Define physical configuration
- Run CFS solver
- Obtain .density.xml file
-
Run the feature-based reconstruction:
- Load density field
- Initialize features
- Execute staged optimization
- Apply pruning / merging / refinement
- Analytical signed distance functions
- Exact first and second derivatives
- Smooth aggregation (p-norm / softmax)
- Constraint-safe nonlinear optimization
- Exact Hessian support (IPOPT)
- Multi-stage reconstruction strategy
- Automated feature pruning and merging
Patrick Jung
paju_99@web.de
Note: The generation of density XML files requires an external CFS solver. The reconstruction framework itself operates on existing density files. IPOPT must be installed separately on your system before installing cyipopt.
