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 simplex fitting 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. This makes it 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.

User guide

• What is Bézier simplex fitting?
  • Bézier Simplex
  • Bézier Simplex Fitting
  • Approximation Theorem
  • Relation to Multi-Objective Optimization
  • Statistical Test for Simplicial Topology
• Quickstart
  • Run as a Docker Container
  • Run as an MLflow Project
  • Run as a Python Package
  • Run as Python Code
• Advanced Topics
  • Data Normalization
  • Scikit-learn Integration
  • Initial Control Points
  • Bézier Simplex Visualization
  • Bézier Simplex Splitting
  • Automatic Degree Selection
  • Smoothness Regularization
  • Elastic Net Grid Sampling
  • Partial Training
  • Advanced Sampling
  • Hardware Acceleration
  • Active Learning
• 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
  • General Information
  • Mathematical Foundations
  • Practical Usage
  • Troubleshooting
• References

API reference

• torch_bsf
  • torch_bsf package

Indices and tables

• Index

• Module Index

• Search Page