Inverse problem for multi-body interaction of nonlinear waves

TL;DR

This paper investigates inverse problems in multi-body nonlinear wave systems, proposing and testing inference methods to determine coupling constants from data, applicable to various physical models like lasers and spin systems.

Contribution

It introduces and evaluates pseudolikelihood-based inference methods with regularization and decimation for multi-body nonlinear wave systems, extending applicability to diverse models.

Findings

Inference methods accurately recover coupling constants from simulated data.

Regularization and decimation improve inference robustness under noise.

Methods are applicable to a broad class of inverse problems in physics.

Abstract

The inverse problem is studied in multi-body systems with nonlinear dynamics representing, e.g., phase-locked wave systems, standard multimode and random lasers. Using a general model for four-body interacting complex-valued variables we test two methods based on pseudolikelihood, respectively with regularization and with decimation, to determine the coupling constants from sets of measured configurations. We test statistical inference predictions for increasing number of sampled configurations and for an externally tunable {\em temperature}-like parameter mimicing real data noise and helping minimization procedures. Analyzed models with phasors and rotors are generalizations of problems of real-valued spherical problems (e.g., density fluctuations), discrete spins (Ising and vectorial Potts) or finite number of states (standard Potts): inference methods presented here can, then, be straightforward applied to a large class of inverse problems.