Welcome to PyTorch-BSF!
Fit smooth, high-dimensional manifolds to your data — from a single GPU to a multi-node cluster.
PyTorch-BSF brings Bézier Simploid Fitting (BSF) to PyTorch. A Bézier simplex is a high-dimensional generalization of the Bézier curve: it can model an arbitrarily complex point cloud as a smooth parametric hyper-surface in any number of dimensions (see Bézier simplex fitting). Bézier simploids go further: they are tensor products of Bézier simplices defined on products of simplices such as prisms and cubes, and simploidal sets glue such cells along common faces. This makes them a natural tool for representing Pareto fronts in multi-objective optimization, interpolating scattered observations, and fitting geometric structures in high-dimensional spaces.
The project is on GitHub.
Note
BSF formerly stood for Bézier Simplex Fitting, which remains the special case where the parameter domain is a single simplex.
User guide
- What is Bézier simplex fitting?
- Installation
- Quickstart
- Advanced Topics
- Data Normalization
- Scikit-learn Integration
- Initial Control Points
- Bézier Simplex and Simploid Visualization
- Bézier Simplex Splitting
- Automatic Degree Selection
- Smoothness Regularization
- Elastic Net Grid Sampling
- Partial Training
- Advanced Sampling
- Hardware Acceleration
- Active Learning
- Simploidal Sets
- The Category of Simploidal Sets
- Pareto Set Learning by Stochastic Gradient Descent
- Applications
- Elastic Net Model Selection
- Robust Portfolio Management
- Distributed Smart Grids and Energy Operations
- Multi-Task and Federated Learning
- Multi-Objective Model Predictive Control
- Communication Systems and Routing
- Supply Chain and Logistics Optimization
- Medical Imaging and Radiation Therapy
- Facility Location and Continuous Approximations
- Frequently Asked Questions
- References
API reference