论文标题
基于知识的非线性动态和混乱的学习
Knowledge-Based Learning of Nonlinear Dynamics and Chaos
论文作者
论文摘要
从非线性系统中提取预测模型是科学机器学习的核心任务。一个关键问题是现代数据驱动方法与第一原则之间的对帐。尽管机器学习技术取得了迅速的进步，但将域知识嵌入到数据驱动的模型中仍然是一个挑战。在这项工作中，我们提出了一个通用学习框架，用于根据观察结果从非线性系统中提取预测模型。我们的框架可以很容易地纳入第一原理知识，因为它自然地将非线性系统建模为连续时间系统。这既可以提高提取的模型的外推能力，又减少了训练所需的数据量。此外，我们的框架具有鲁棒性，可观察到噪声和对不规则采样数据的适用性。我们通过学习各种系统的预测模型，包括硬范围的振荡器，洛伦兹系统和库拉莫托 - sivashinsky方程来证明我们计划的有效性。对于Lorenz系统，合并了不同类型的领域知识，以证明在数据驱动的系统识别中嵌入知识的强度。
Extracting predictive models from nonlinear systems is a central task in scientific machine learning. One key problem is the reconciliation between modern data-driven approaches and first principles. Despite rapid advances in machine learning techniques, embedding domain knowledge into data-driven models remains a challenge. In this work, we present a universal learning framework for extracting predictive models from nonlinear systems based on observations. Our framework can readily incorporate first principle knowledge because it naturally models nonlinear systems as continuous-time systems. This both improves the extracted models' extrapolation power and reduces the amount of data needed for training. In addition, our framework has the advantages of robustness to observational noise and applicability to irregularly sampled data. We demonstrate the effectiveness of our scheme by learning predictive models for a wide variety of systems including a stiff Van der Pol oscillator, the Lorenz system, and the Kuramoto-Sivashinsky equation. For the Lorenz system, different types of domain knowledge are incorporated to demonstrate the strength of knowledge embedding in data-driven system identification.
