AI-Hilbert

This repository contains the code and the data used for the experiments in the paper Evolving Scientific Discovery by Unifying Data and Background Knowledge with AI Hilbert.

AI Hilbert is an algebraic geometric based discovery system (based on Putinar's Positivstellensatz), that enables the discovery of fundamental laws of nature (or non-physical systems) based on knowledge (articulated in formal logic terms) and experimental data.

Visit our website for a general overview, references, and some introductory videos: → AI-Hilbert website ←

Code

The code is organized in 3 folders. One containing the problems studied in the main paper, one containing the problems studied in the paper appendix and one for data generation.

The folder main_problems contains:

• A notebook for the Hagen-Poissuille Equation, Einstein’s Relativistic Time Dilation Law and Kepler’s Third Law of Planetary Motion: hagen_einstein_kepler[3.3][3.5][3.6].ipynb
• A folder for the revisited problem of deriving Kepler’s third law of planetary motion from an incomplete background theory kepler_with_missing_axioms[3.7] containing:
  • the corresponding notebook kepler_with_missing_axioms[3.7].ipynb
  • the data used data_kepler.dat, data_kepler_d.dat, and data_kepler_n_points.dat.
• A notebook for the Radiated Gravitational Wave Power Equation: grav_waves[3.4].ipynb
• A notebook for the Bell Inequalities: bell_inequalities[3.8].ipynb

The folder suppl_material_problems contains a notebook for each of the following problems:

• 6 problems from FSRD (Feynman Symbolic Regression Database based on "The Feynman Lectures on Physics"):
  • I.15.10 FSRD: I_15_10.ipynb
  • I.27.6 FSRD: I_27_6.ipynb
  • I.34.8 FSRD: I_34_8.ipynb
  • I.43.16 FSRD: I_43_16.ipynb
  • II.10.9 FSRD: II_10_9.ipynb
  • II.34.2 FSRD: II_34_2.ipynb
• 6 additional problems:
  • Inelastic Relativistic Collision: inelastic.ipynb
  • Decay of Pion into Muon and Neutrino: decay.ipynb
  • Radiation Damping and Light Scattering: light.ipynb
  • Escape Velocity: escape.ipynb
  • Hall Effect: hall.ipynb
  • Compton Scattering: compton.ipynb

The folder data_generation contains:

• A python file for generating the data for the Kepler problem data_gen_kepler.py
• A python file data_gen_mix.py for generating the data for the following problems:
  • Inelastic Relativistic Collision
  • Decay of Pion into Muon and Neutrino
  • Radiation Damping and Light Scattering
  • Escape Velocity
  • Hall Effect
  • Compton Scattering
  • Radiation Gravitational Wave Power
  • Hagen Poiseuille equation

How to cite

@misc{AI_Hilbert_2024,
      title={Evolving Scientific Discovery by Unifying Data and Background Knowledge with AI Hilbert}, 
      author={Ryan Cory-Wright and Cristina Cornelio and Sanjeeb Dash and Bachir El Khadir and Lior Horesh},
      year={2024},
      eprint={2308.09474},
      archivePrefix={arXiv},
      primaryClass={cs.AI}
}