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运筹学学报 >

2025 , Vol. 29 >Issue 3: 1 - 33

DOI: https://doi.org/10.15960/j.cnki.issn.1007-6093.2025.03.001

第九届中国运筹学会科学技术奖获奖者专辑

人工智能中的生成式方法: 数学模型、优化算法及其应用

  • 郭田德 ,
  • 幸天驰 ,
  • 韩丛英 ,
  • 孟帅
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  • 1. 中国科学院大学数学科学学院, 北京 100049
韩丛英  E-mail: hancy@ucas.ac.cn

收稿日期: 2025-04-21

  网络出版日期: 2025-09-09

基金资助

国家自然科学基金重点项目(12431012);国家自然科学基金重点项目(U23B2012)

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运筹学学报编辑部, 2025, 版权所有，未经授权，不得转载。
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Generative methods in artificial intelligence: Mathematical models, optimization algorithms and applications

  • Tiande GUO ,
  • Tianchi XING ,
  • Congying HAN ,
  • Shuai MENG
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  • 1. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China

Received date: 2025-04-21

  Online published: 2025-09-09

Copyright

, 2025, All rights reserved. Unauthorized reproduction is prohibited.
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摘要

随着深度学习和神经网络技术的持续发展, 生成式方法在机器学习领域取得了重要突破, 并在多个应用场景中展现出巨大的潜力。本文构建了人工智能生成式方法的统一数学框架, 并系统介绍了其核心技术, 包括变分自编码器(VAE)、生成对抗网络(GAN)、扩散模型和流模型, 同时深入分析了不同方法在各类任务中的优势与局限。进一步地, 本文探讨了人工智能中的生成式方法在数学、物理、生命科学、医学、计算机科学与工程等领域的应用前景。最后, 本文总结了当前人工智能中的生成式方法所面临的关键挑战, 并重点探讨了其在数学与智能优化研究中的未来发展方向。本文期望为相关领域的研究人员和从业者提供有价值的参考与启示。

关键词： 生成式方法; 数学建模; 优化方法; 跨模态生成; 智能优化

本文引用格式

郭田德 , 幸天驰 , 韩丛英 , 孟帅 . 人工智能中的生成式方法: 数学模型、优化算法及其应用[J]. 运筹学学报, 2025 , 29(3) : 1 -33 . DOI: 10.15960/j.cnki.issn.1007-6093.2025.03.001

Abstract

With the continuous development of deep learning and neural network technologies, generative methods have made significant breakthroughs in the field of machine learning and have demonstrated immense potential across various application scenarios. This paper constructs a unified mathematical framework for artificial intelligence generative methods and systematically introduces its core technologies, including variational autoencoder (VAE), generative adversarial network (GAN), diffusion model, and flow-based model. Additionally, it provides an in-depth analysis of the advantages and limitations of different methods in various tasks. Furthermore, this paper explores the application prospects of generative methods in artificial intelligence across fields such as mathematics, physics, life sciences, medicine, computer science, and engineering. Finally, the paper summarizes the key challenges faced by generative methods in artificial intelligence and discusses their future development directions in the fields of mathematics and intelligent optimization. This paper aims to provide valuable insights and references for researchers and practitioners in related fields.

Key words： generative models; mathematical modeling; optimization methods; cross-modal generation; intelligent optimization

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