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The inverse problem is studied in multi-body systems with nonlinear dynamicsrepresenting, e.g., phase-locked wave systems, standard multimode and randomlasers. Using a general model for four-body interacting complex-valuedvariables we test two methods based on pseudolikelihood, respectively withregularization and with decimation, to determine the coupling constants fromsets of measured configurations. We test statistical inference predictions forincreasing number of sampled configurations and for an externally tunable {\emtemperature}-like parameter mimicing real data noise and helping minimizationprocedures. Analyzed models with phasors and rotors are generalizations ofproblems of real-valued spherical problems (e.g., density fluctuations),discrete spins (Ising and vectorial Potts) or finite number of states (standardPotts): inference methods presented here can, then, be straightforward appliedto a large class of inverse problems.

Inverse problem for multi-body interaction of nonlinear waves