InVAErt网络：用于模型综合与可辨识性分析的数据驱动框架
InVAErt networks: a data-driven framework for model synthesis and identifiability analysis
AI总结：
本文提出inVAErt网络，一个用于参数化物理系统数据驱动分析和综合的框架，结合确定性编解码器、归一化流和变分编码器实现模型反演与可辨识性分析，并通过大量数值实验验证其有效性。
摘要：
目前，生成模型和深度学习在基于物理的系统中的应用主要由模拟任务主导。然而，数据驱动架构所提供的显著灵活性表明，应将这种表示扩展到系统综合的其他方面，包括模型反演和可辨识性。我们引入了inVAErt（发音为“invert”）网络，这是一个用于参数化物理系统数据驱动分析和综合的综合框架。该框架使用确定性编码器和解码器来表示正向和逆向求解映射，使用归一化流来捕获系统输出的概率分布，并使用变分编码器来学习紧凑的潜在表示，以应对输入和输出之间缺乏双射性的问题。我们正式研究了损失函数中惩罚系数的选择和潜在空间采样策略，因为我们发现这些显著影响了训练和测试性能。我们通过广泛的数值示例验证了该框架，包括简单的线性、非线性和周期映射、动力系统以及时空偏微分方程。
英文摘要：
Use of generative models and deep learning for physics-based systems is currently dominated by the task of emulation. However, the remarkable flexibility offered by data-driven architectures would suggest to extend this representation to other aspects of system synthesis including model inversion and identifiability. We introduce inVAErt (pronounced "invert") networks, a comprehensive framework for data-driven analysis and synthesis of parametric physical systems which uses a deterministic encoder and decoder to represent the forward and inverse solution maps, a normalizing flow to capture the probabilistic distribution of system outputs, and a variational encoder designed to learn a compact latent representation for the lack of bijectivity between inputs and outputs. We formally investigate the selection of penalty coefficients in the loss function and strategies for latent space sampling, since we find that these significantly affect both training and testing performance. We validate our framework through extensive numerical examples, including simple linear, nonlinear, and periodic maps, dynamical systems, and spatio-temporal PDEs.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
