加速替代动力学用于动态、随机系统演化

中文摘要 AI 辅助

动态模拟是深入了解系统动力学演化的一种成熟方法。然而，其计算成本往往高得令人望而却步，尤其是在随机框架的情况下。机器学习算法特别适合作为模拟替代模型。尽管如此，它们面临着一些非常明显的局限性。首先，这些系统的纯维度排除了传统时间序列模型的使用，这些模型难以处理高维特征空间。此外，传统时间序列仅关注长期或短期效应，导致在足够时间后出现局部或全局漂移。在本文中，我们提出了一个解决这些局限性的框架。我们的框架将变分自编码器与卷积或图基结合，以降低系统的维度。这个潜在向量使用时间融合变换器模型在时间上传播，该模型包括长期和短期效应编码以及静态协变量支持。我们在三个不同的案例上测试了我们的框架，以证明其鲁棒性，并且在所有三个案例中，我们以极短的时间获得了与实际模拟几乎相同的结果。此外，我们的框架足够灵活，可以适应任何新系统，并为目标实验设计提供内置的不确定性量化。

英文摘要

Dynamic simulations are an entrenched way of gaining insight into the evolution of system dynamics. Their computational cost however is often prohibitively high, especially in cases of stochastic frameworks. Machine learning algorithms are especially suited as simulation surrogates. Nevertheless, they face some very distinct limitations. Firstly, the sheer dimensionality of these systems, however, precludes the use of traditional time series models who struggle with high dimensional feature spaces. Additionally, traditional time series focus exclusively on either long or short range effects, causing local or global drift given enough time. In this paper, we propose a framework that addresses those limitations. Our framework combines a Variational Autoencoder, with a convolutional or graph basis that reduces the dimensionality of the system. This latent vector is propagated in time using a Temporal Fusion Transformer model, which includes both long range and short range effect encoding, as well as static covariate support. We test our framework on three distinct cases, to prove its robustness and in all three we have achieved practically identical to the simulation results at a fraction of the time. Further, our framework is flexible enough to be adapted to any new system and provides an inbuilt uncertainty quantification for targeted experiment design.

发表机构

• Technical University of Munich（慕尼黑工业大学）

机构由 AI 辅助整理，请以论文原文为准。