用最大熵原理构建神经网络，从有限信息生成概率分布。
MEP-Net: Generating Solutions to Scientific Problems with Limited Knowledge by Maximum Entropy Principle
- 结合最大熵原则与神经网络，从矩约束生成概率分布
- 在生化反应网络中成功模拟概率分布演化过程
- 适合需要不确定性建模的科研场景，如生物系统分析
最大熵原理（MEP）在信息不全时提供一种有效且无偏的概率分布推断方法，而神经网络则具备从数据中学习复杂分布的灵活性。本文提出一种新型神经网络架构——MEP-Net，将最大熵原理与神经网络结合，实现从矩约束生成概率分布。我们还系统梳理了最大熵原理的基本理论、数学表达，并基于大偏差原理严格论证其对非平衡系统的适用性。通过大量数值实验，验证了MEP-Net在生化反应网络中建模概率分布演化及从数据生成复杂分布方面的有效性。
原文摘要 · Abstract (English)
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.
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