Maximum entropy principle (MEP) offers an effective and unbiased approach to inferring unknown probability distributions when faced with incomplete information, while neural networks provide the flexibility to learn complex distributions from data. This paper proposes a novel neural network architecture, the MEP-Net, which combines the MEP with neural networks to generate probability distributions from moment constraints. We also provide a comprehensive overview of the fundamentals of the maximum entropy principle, its mathematical formulations, and a rigorous justification for its applicability for non-equilibrium systems based on the large deviations principle. Through fruitful numerical experiments, we demonstrate that the MEP-Net can be particularly useful in modeling the evolution of probability distributions in biochemical reaction networks and in generating complex distributions from data.

翻译：最大熵原理（MEP）为在信息不完备情况下推断未知概率分布提供了一种有效且无偏的方法，而神经网络则提供了从数据中学习复杂分布的灵活性。本文提出了一种新颖的神经网络架构——MEP-Net，它将最大熵原理与神经网络相结合，从矩约束生成概率分布。我们还全面综述了最大熵原理的基本原理、其数学表述，并基于大偏差原理为其在非平衡系统中的适用性提供了严格论证。通过丰富的数值实验，我们证明MEP-Net在生化反应网络中的概率分布演化建模以及从数据生成复杂分布方面具有显著的应用价值。