时空潜变量去噪扩散概率模型用于参数化动力系统的降阶建模
Spatio-temporal Latent Denoising Diffusion Probabilistic Models for Reduced-order Modeling of Parametrized Dynamical Systems
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中文总结 AI 辅助
提出一种基于潜空间去噪扩散概率模型的非侵入式降阶建模方法，生成参数化动力系统的时空解，在二维绕流问题上验证了准确性、泛化性和时间外推能力。
中文摘要 AI 辅助
许多科学问题需要对复杂物理现象进行精确建模，例如流体动力学或气候建模。这些现象通常导致高维且计算成本高昂的计算模型，这可能限制其在实时和多查询问题中的应用。模型降阶（MOR）是一种旨在使用降阶模型（ROMs）近似全阶模型（FOMs）的方法，以精度的小幅降低换取计算成本的大幅减少。在本工作中，我们提出了一种使用生成式机器学习的非侵入式MOR方法，通过去噪扩散概率模型（DDPMs）生成动力系统在不同参数实例下的解。与通常在纯空间域中操作的传统DDPMs不同，我们旨在生成时空解以提高质量和时间连贯性。此外，我们将DDPM嵌入到通过依次应用本征正交分解和自编码器获得的潜空间中，以降低数据维度和DDPM的计算成本。我们在参数化的二维障碍物绕流问题上测试了我们的方法。数值实验表明，我们的潜变量DDPM能够（i）生成准确且时间连贯的解，（ii）实现对未见参数值场景的强泛化能力，以及（iii）在训练时间范围之外进行时间外推。
英文摘要
Many scientific problems require accurate modeling of complex physical phenomena, such as fluid dynamics or climate modeling. These phenomena often result in high-dimensional and thus computationally expensive computational models that can limit their application to real-time and multi-query problems. Model-order reduction (MOR) is an approach that seeks to approximate full-order models (FOMs) using reduced-order models (ROMs), trading a minor reduction in accuracy for a major reduction in computational cost. In this work, we propose a non-intrusive MOR method using generative machine learning by means of denoising diffusion probabilistic models (DDPMs) for generating solutions of the dynamical systems under different instances of their parameters. Unlike conventional DDPMs, which often operate purely in the spatial domain, we aim to generate spatio-temporal solutions to improve quality and temporal coherence. In addition, we embed the DDPM in a latent space obtained by sequentially applying proper orthogonal decomposition and an autoencoder to reduce the data dimensionality and the computational cost of the DDPM. We test our approach on a parametrized 2D fluid flow around an obstacle. The numerical experiments demonstrate that our latent DDPM can (i) produce accurate and temporally coherent solutions, (ii) achieve strong generalization capabilities to scenarios involving unseen parameter values, and (iii) extrapolate in time beyond the training horizon.
发表机构
- University of Twente（特温特大学）
- Politecnico di Milano（米兰理工大学）
机构由 AI 辅助整理，请以论文原文为准。
