FisMat2017 - Submission - View

Abstract's title: Statistical Inference in Non-linearly Interacting Wave Systems
Submitting author: Luca Leuzzi
Affiliation: CNR-NANOTEC, Istituto di Nanotecnologia, SLiM Lab. Roma
Affiliation Address: CNR-NANOTEC, Sede Secondaria di Roma, c/o Dipartimento di Fisica, Università Sapienza, Piazzale Aldo Moro 5, 00185, Roma
Country: Italy
Oral presentation/Poster (Author's request): Oral presentation
Other authors and affiliations: Alessia Marruzzo [CINECA, Bologna], Payal Tyagi [CNR-NANOTEC, Roma], Fabrizio Antenucci [CEA, Saclay, Francia]

The graphical inverse problem is approached 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 of Bayesian statistical inference based on pseudolikelihood, respectively with regularization and with decimation, to determine the coupling constants from sets of measured configurations. We test predictions for increasing number of sampled configurations and for an externally tunable temperature-like parameter mimicing real data noise and improving 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. The high versatility of the exposed techniques also concerns the number of expected interactions: results are presented for different graph topologies, ranging from sparse to dense graphs.