Learning Interacting Theories from Data

arXiv (Cornell University)

Abstract

One challenge of physics is to explain how collective properties arise from microscopic interactions. Indeed, interactions form the building blocks of almost all physical theories and are described by polynomial terms in the action. The traditional approach is to derive these terms from elementary processes and then use the resulting model to make predictions for the entire system. But what if the underlying processes are unknown? Can we reverse the approach and learn the microscopic action by observing the entire system? We use invertible neural networks (INNs) to first learn the observed data distribution. By the choice of a suitable nonlinearity for the neuronal activation function, we are then able to compute the action from the weights of the trained model; a diagrammatic language expresses the change of the action from layer to layer. This process uncovers how the network hierarchically constructs interactions via nonlinear transformations of pairwise relations. We test this approach on simulated data sets of interacting theories. The network consistently reproduces a broad class of unimodal distributions; outside this class, it finds effective theories that approximate the data statistics up to the third cumulant. We explicitly show how network depth and data quantity jointly improve the agreement between the learned and the true model. This work shows how to leverage the power of machine learning to transparently extract microscopic models from data.

Authors 8

1. Claudia Merger Aachen

   Forschungszentrum Jülich · RWTH Aachen University

   Affiliation as printed

   Institute of Neuroscience and Medicine (INM-6) and Institute for Advanced Simulation (IAS-6 ) and

   RWTH Aachen University , Aachen , Germany

2. Alexandre René
3. Kirsten Fischer Aachen

   Forschungszentrum Jülich · RWTH Aachen University

   Affiliation as printed

   Institute of Neuroscience and Medicine (INM-6) and Institute for Advanced Simulation (IAS-6 ) and

   RWTH Aachen University , Aachen , Germany

4. Peter Bouss Aachen

   Forschungszentrum Jülich · RWTH Aachen University

   Affiliation as printed

   Institute of Neuroscience and Medicine (INM-6) and Institute for Advanced Simulation (IAS-6 ) and

   RWTH Aachen University , Aachen , Germany

5. Sandra Nestler Aachen

   Forschungszentrum Jülich · RWTH Aachen University

   Affiliation as printed

   Institute of Neuroscience and Medicine (INM-6) and Institute for Advanced Simulation (IAS-6 ) and

   RWTH Aachen University , Aachen , Germany

6. David Dahmen

   Forschungszentrum Jülich

   Affiliation as printed

   Institute of Neuroscience and Medicine (INM-6) and Institute for Advanced Simulation (IAS-6 ) and

7. Carsten Honerkamp Aachen

   Forschungszentrum Jülich · Jülich Aachen Research Alliance · RWTH Aachen University

   Affiliation as printed

   JARA-Institute Brain Structure-Function Relationships (INM-10) , Jülich Research Centre , Jülich , Germany

   RWTH Aachen University , Aachen , Germany

8. Moritz Helias Aachen

   Forschungszentrum Jülich · RWTH Aachen University

   Affiliation as printed

   Institute of Neuroscience and Medicine (INM-6) and Institute for Advanced Simulation (IAS-6 ) and

   RWTH Aachen University , Aachen , Germany