Discovery of conservation laws via matrix search

Abstract

One of the main goals of Discovery Science is the development and analysis of methods for automatic knowledge discovery in the natural sciences. A central area of natural science research concerns reactions: how entities in a scientific domain interact to generate new entities. Classic AI research due to Valdés-Pérez, Żytkow, Langley and Simon has shown that many scientific discovery tasks that concern reaction models can be formalized as a matrix search. In this paper we present a method for finding conservation laws, based on two criteria for selecting a conservation law matrix: (1) maximal strictness: rule out as many unobserved reactions as possible, and (2) parsimony: minimize the L1-norm of the matrix. We provide an efficient and scalable minimization method for the joint optimization of criteria (1) and (2). For empirical evaluation, we applied the algorithm to known particle accelerator data of the type that are produced by the Large Hadron Collider in Geneva. It matches the important Standard Model of particles that physicists have constructed through decades of research: the program rediscovers Standard Model conservation laws and the corresponding particle families of baryon, muon, electron and tau number. The algorithm also discovers the correct molecular structure of a set of chemical substances. © 2010 Springer-Verlag.