Experimental data are often affected by uncontrolled variables that make analysis and interpretation difficult. For spatiotemporal systems, this problem is further exacerbated by their intricate dynamics. Modern machine learning methods are particularly well suited for analyzing and modeling complex datasets, but to be effective in science, the result needs to be interpretable. We demonstrate an unsupervised learning technique for extracting interpretable physical parameters from noisy spatiotemporal data and for building a transferable model of the system. In particular, we implement a physics-informed architecture based on variational autoencoders that is designed for analyzing systems governed by partial differential equations. The architecture is trained end to end and extracts latent parameters that parametrize the dynamics of a learned predictive model for the system. To test our method, we train our model on simulated data from a variety of partial differential equations with varying dynamical parameters that act as uncontrolled variables. Numerical experiments show that our method can accurately identify relevant parameters and extract them from raw and even noisy spatiotemporal data (tested with roughly 10% added noise). These extracted parameters correlate well (linearly with $R^2>0.95$) with the ground truth physical parameters used to generate the datasets. We then apply this method to nonlinear fiber propagation data, generated by an ab initio simulation, to demonstrate its capabilities on a more realistic dataset. Our method for discovering interpretable latent parameters in spatiotemporal systems will allow us to better analyze and understand real-world phenomena and datasets, which often have unknown and uncontrolled variables that alter the system dynamics and cause varying behaviors that are difficult to disentangle.

中文翻译：

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使用无监督学习从时空系统中提取可解释的物理参数

实验数据通常受到不受控制的变量的影响，这些变量使分析和解释变得困难。对于时空系统，其复杂的动力学进一步加剧了这个问题。现代机器学习方法特别适合于对复杂数据集进行分析和建模，但是要在科学上有效，结果必须是可解释的。我们演示了一种无监督的学习技术，用于从嘈杂的时空数据中提取可解释的物理参数，并用于构建系统的可转移模型。特别是，我们实现了一种基于变分自动编码器的物理信息架构，该架构旨在分析由偏微分方程控制的系统。对该体系结构进行端到端训练，并提取潜在参数，这些潜在参数对系统学到的预测模型的动力学参数化。为了测试我们的方法，我们在来自各种偏微分方程的模拟数据上训练我们的模型，这些偏微分方程具有变化的动力学参数，这些动力学参数充当不受控制的变量。数值实验表明，我们的方法可以准确地识别相关参数，并从原始甚至嘈杂的时空数据中提取相关参数（经过大约10％的添加噪声测试）。这些提取的参数相关性很好（与 数值实验表明，我们的方法可以准确地识别相关参数，并从原始甚至嘈杂的时空数据中提取相关参数（经过大约10％的添加噪声测试）。这些提取的参数相关性很好（与 数值实验表明，我们的方法可以准确地识别相关参数，并从原始甚至嘈杂的时空数据中提取相关参数（经过大约10％的添加噪声测试）。这些提取的参数相关性很好（与${\mathrm{[R}}^2>0.95$）和用于生成数据集的地面真实物理参数。然后，我们将该方法应用于从头算生成的非线性光纤传播数据，以在更现实的数据集上展示其功能。我们在时空系统中发现可解释的潜在参数的方法将使我们能够更好地分析和理解现实世界的现象和数据集，这些现象和数据集通常具有未知且不受控制的变量，这些变量会改变系统动力学并导致难以解开的各种行为。