MEP-Net: Generating solutions to scientific problems with limited knowledge by maximum entropy principle.

Area of Science:

• Computational Biology
• Statistical Physics
• Machine Learning

Background:

• The Maximum Entropy Principle (MEP) is a powerful tool for inferring probability distributions with incomplete information.
• Neural networks excel at learning complex data distributions.
• Integrating these approaches can enhance probabilistic modeling.

Purpose of the Study:

• To propose a novel neural network architecture, MEP-Net, that integrates the Maximum Entropy Principle (MEP) with neural networks.
• To generate probability distributions from moment constraints using this new architecture.
• To provide a theoretical foundation for MEP in non-equilibrium systems.

Main Methods:

• Development of the MEP-Net architecture, combining MEP and neural networks.
• Mathematical formulation and theoretical justification of MEP for non-equilibrium systems using large deviations principle.
• Numerical experiments to validate MEP-Net's performance.

Main Results:

• Demonstration of MEP-Net's capability to generate probability distributions from moment constraints.
• Successful application in modeling the evolution of probability distributions in biochemical reaction networks.
• Effectiveness in generating complex distributions from data.

Conclusions:

• MEP-Net offers an effective and unbiased method for probabilistic inference.
• The architecture shows significant promise for applications in computational biology and complex data modeling.
• The theoretical framework supports MEP's use in non-equilibrium statistical physics.