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Alessia Marruzzo1, Payal Tyagi2, Fabrizio Antenucci2

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This study introduces pseudolikelihood methods to solve inverse problems in complex multi-body systems. These techniques accurately determine coupling constants from measured data, even with noise, for diverse nonlinear dynamics.

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Area of Science:

  • Complex Systems
  • Statistical Physics
  • Nonlinear Dynamics

Background:

  • Inverse problems are crucial for understanding complex systems with nonlinear dynamics, such as lasers and wave systems.
  • Existing methods often struggle with complex-valued variables and noise in multi-body interactions.

Purpose of the Study:

  • To develop and test robust statistical inference methods for solving inverse problems in nonlinear multi-body systems.
  • To determine coupling constants from measured configurations using pseudolikelihood-based approaches.

Main Methods:

  • A general four-body interacting complex-valued variable model was employed.
  • Two pseudolikelihood methods, regularization and decimation, were tested for parameter estimation.
  • Statistical inference was evaluated across varying sampled configurations and a noise-mimicking parameter.

Main Results:

  • The pseudolikelihood methods successfully determined coupling constants in complex systems.
  • Performance was validated with increasing data and adjustable noise levels.
  • The methods demonstrated versatility across different graph topologies and interaction types.

Conclusions:

  • Pseudolikelihood methods with regularization and decimation are effective for inverse problems in nonlinear multi-body systems.
  • These techniques offer a versatile framework applicable to a wide range of physical and statistical problems.
  • The study provides a robust approach for analyzing complex systems with potential applications in physics and engineering.