论文标题
动态系统建模的张力变压器
Tensorized Transformer for Dynamical Systems Modeling
论文作者
论文摘要
从观察结果鉴定非线性动力学对于理论思想和实验数据的对齐至关重要。反过来，最后一个经常被不同本质的副作用和噪音所损坏，因此概率方法可以更笼统地了解该过程。同时，高维概率建模是一项具有挑战性和数据密集型任务。在本文中，我们建立了动态系统建模和语言建模任务之间的平行。我们提出了一个基于变压器的模型，该模型结合了数据的几何特性，并提供了一种迭代训练算法，从而允许高维动力系统的条件概率进行细网格近似。
The identification of nonlinear dynamics from observations is essential for the alignment of the theoretical ideas and experimental data. The last, in turn, is often corrupted by the side effects and noise of different natures, so probabilistic approaches could give a more general picture of the process. At the same time, high-dimensional probabilities modeling is a challenging and data-intensive task. In this paper, we establish a parallel between the dynamical systems modeling and language modeling tasks. We propose a transformer-based model that incorporates geometrical properties of the data and provide an iterative training algorithm allowing the fine-grid approximation of the conditional probabilities of high-dimensional dynamical systems.
