MEP-Net: Generating Solutions to Scientific Problems with Limited Knowledge by Maximum Entropy Principle
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913595374174208 |
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| author | Yang, Wuyue Peng, Liangrong Li, Guojie Hong, Liu |
| author_facet | Yang, Wuyue Peng, Liangrong Li, Guojie Hong, Liu |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_02090 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | MEP-Net: Generating Solutions to Scientific Problems with Limited Knowledge by Maximum Entropy Principle Yang, Wuyue Peng, Liangrong Li, Guojie Hong, Liu Machine Learning Data Analysis, Statistics and Probability 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. |
| title | MEP-Net: Generating Solutions to Scientific Problems with Limited Knowledge by Maximum Entropy Principle |
| topic | Machine Learning Data Analysis, Statistics and Probability |
| url | https://arxiv.org/abs/2412.02090 |