维数灾难是机器学习和复杂物理系统共同面临的一大挑战，它导致高维空间中的计算问题变得极其困难，复杂度随着维度的增加呈指数级增长。生成模型作为当前生成式人工智能背后的核心技术之一，有效地克服了维数灾难带来的挑战，在人工智能生成内容等领域取得了重大突破，并引起了许多科学研究领域尤其是物理学的广泛关注。生成模型能够在传统方法无法处理或效率低下的情况下提供高效可行的解决方案，在模拟物理系统、构建变分拟设和辅助蒙特卡洛采样等场景中有着重要应用。以生成模型为代表的人工智能技术正逐渐成为探索复杂系统的一般性方法，并为系统科学的发展提供有力的基础和工具。基于此背景，本文针对当前该领域存在的不足之处，从模型、问题和算法三个层面进行了深入研究，以生成模型为主要工具，求解了平衡态、非平衡态和零温下三类典型复杂物理系统中的计算难题。主要内容和创新点包括：（1）针对基于张量网络的生成模型在生成式建模任务上存在的不足，提出了自回归矩阵乘积态模型。该模型将量子多体物理中的矩阵乘积态与机器学习中的自回归建模技术相结合，有效克服了单个矩阵乘积态建模联合概率分布的局限性，具有更强的表达能力和泛化性能。在自旋玻璃和伊辛模型等平衡态复杂物理系统的配分函数计算问题上，该模型达到了与当前最先进的神经网络方法相当的水平。（2）针对非平衡态复杂物理系统中一类称为运动约束模型的动力配分函数计算问题，提出了基于生成模型的有限时间演化算法。该算法将基于生成模型的变分方法从平衡态推广到非平衡态，在经典统计物理领域开辟了新的应用范围。该算法能够有效地处理动力配分函数的计算问题，揭示了运动约束模型所特有的非平衡相变现象，并首次得到了二维和三维系统的临界指数。（3）针对基于生成模型的变分神经退火算法在求解零温基态问题时存在速度慢和扩展性差等不足，提出了基于 Gumbel-softmax 技巧的松弛优化算法。该算法具有较好的扩展性和效率，在求解大规模图上的基态问题时具有明显优势，同时相比受物理启发的图神经网络算法，能够得到更高质量的解。

The curse of dimensionality is a challenge shared by machine learning and complex physical systems, which leads to extremely difficult computational problems in high-dimensional spaces, with complexity increasing exponentially with dimensionality. As one of the core technologies behind current generative artificial intelligence, generative models have effectively overcome the challenges brought by the curse of dimensionality and have made significant breakthroughs in the field of artificial intelligence generated content, also attracting widespread attention from many scientific research communities, especially physical science. Generative models can provide efficient and feasible solutions when traditional methods are unable to handle or have low efficiency, and they have important applications in simulating physical systems, constructing variational ansatz and enhancing Monte Carlo sampling methods. Artificial intelligence techniques represented by generative models are gradually becoming a general method for exploring complex systems, and provide a powerful foundation and tool for the development of systems science. Based on this background, this article has carried out in-depth research from the perspectives of models, problems, and algorithms, with generative models as the main tool, to solve the computational challenges in three typical complex physical systems under equilibrium, non-equilibrium, and zero temperature. The main contents and innovative points include: (1) To address the limitations of tensor-network-based generative models in generative modeling tasks, we propose Autoregressive Matrix Product State model. This model combines matrix product states in quantum many-body physics with autoregressive modeling techniques in machine learning, effectively overcoming the limitations of a single matrix product state in modeling the joint probability distributions. The model has stronger expressive power and generalization performance. It achieves a level of performance similar to state-of-the-art neural network methods in computing the partition function of equilibrium complex physical systems such as Ising and spin glasses models. (2) To address the problem of calculating the dynamic partition function of kinetic constraint models in non-equilibrium complex physical systems, we propose a finite-time evolution algorithm based on generative models. This algorithm extends the variational method based on generative models from equilibrium to non-equilibrium, opening up new applications in the field of classical statistical physics. For kinetic constraint models, the algorithm can accurately calculate the dynamic partition function, reveal unique non-equilibrium phase transition phenomena in kinetic constraint models, and obtain critical exponents of phase transition points in two and three-dimensional systems for the first time. (3) To address the shortcomings of the variational neural annealing method based on generative models in solving ground-state problems at zero temperature, such as slow speed and poor scalability, we proposed a relaxed optimization algorithm based on the Gumbel-softmax technique. This algorithm has better scalability and efficiency, and has advantages in solving ground-state problems on larger graphs. Compared to the physics-inspired graph neural networks algorithm, it can obtain higher quality solutions.