CS4ML: A general framework for active learning with arbitrary data based on Christoffel functions

Christoffel Sampling for Machine Learning is a general framework for active learning in regression problems. It approximates a target function arising from general types of data, rather than pointwise samples.

This generalization covers many cases of practical interest, such as data acquired in transform domains (e.g., Fourier data), vector-valued data (e.g., gradient-augmented data), data acquired along continuous curves, and, multimodal data, i.e., combinations of different types of measurements.

This library shows the efficacy of our framework for gradient-augmented learning with polynomials, Magnetic Resonance Imaging (MRI) using generative models and adaptive sampling for solving PDEs using Physics-Informed Neural Networks (PINNs), see spotlight presentation at spotlight. You can use the tools provided in this repository for your own data.

This is a repository associated with the paper:

CS4ML: A general framework for active learning with arbitrary data based on Christoffel functions by Juan M. Cardenas, Ben Adcock and Nick Dexter

published by NeurIPS 2023, available at https://openreview.net/pdf?id=aINqoP32cb .

If you have questions or comments about the code, please contact juan.cardenascardenas@colorado.edu, ben_adcock@sfu.ca, or nick.dexter@fsu.edu.

Parts of this repository are based on the code for the paper "CAS4DL: Christoffel Adaptive Sampling for function approximation via Deep Learning" by Ben Adcock, Juan M. Cardenas and Nick Dexter, which is available in the repository https://github.com/JMcardenas/CAS4DL.

Code organization

Files are organized into three main directories:

Gradient-Augmented-with-polynomials

Contains the main matlab files used to create the data/results/figures in each section related to example number 1 and appendix section B.

Generative-models

Contains the main matlab, python files used to create the data/results/figures in each section related to example number 2 and appendix section C.

Physic-Informed-Neural-Networks with CAS

Contains the main matlab, python files used to create the data/results/figures in each section related to example number 3 and appendix section D.

Installation and Quick Start

You can clone the repository and install locally. It is highly recommended to clone in editable mode so the changes are applied without having to reinstall:

git clone https://github.com/JMcardenas/CS4ML.git

Next, run the main files for each section.

Citing

In case you use CS4ML in academic papers or scientific reports, please go ahead and cite:

@inproceedings{
cardenas2023csml,
title={{CS}4{ML}: A general framework for active learning with arbitrary data based on Christoffel functions},
author={Juan M Cardenas and Ben Adcock and Nick Dexter},
booktitle={Thirty-seventh Conference on Neural Information Processing Systems},
year={2023},
url={https://openreview.net/forum?id=aINqoP32cb}
}

@inproceedings{adcock2024unified,
  title={A Unified Framework for Learning with Nonlinear Model Classes from Arbitrary Linear Samples},
  author={Adcock, Ben and Cardenas, Juan M and Dexter, Nick},
  booktitle={Forty-first International Conference on Machine Learning},
  year={2024},
  url={https://openreview.net/forum?id=wG2SgnH6Zv}
}