论文标题
使用自动编码器学习减少动力系统的基础
Learning a Reduced Basis of Dynamical Systems using an Autoencoder
论文作者
论文摘要
机器学习模型已成为物理和工程学的强大工具。尽管灵活，但仍在将新机器学习模型与已知物理学联系起来的基本挑战。在这项工作中，我们提出了一个具有潜在空间惩罚的自动编码器，该自动编码器发现了物理学部分微分方程的有限维歧管。我们在Kuramoto-Sivashinsky（K-S），Korteweg-De Vries（KDV）和抑制KDV方程式上测试了此方法。我们表明，K-S方程的最佳潜在空间与惯性歧管的维度一致。 KDV方程的结果表明，没有减少的潜在空间，这与KDV方程的真正无限尺寸动力学一致。在阻尼KDV方程的情况下，我们发现活动尺寸的数量随着阻尼系数的增加而减小。然后，我们发现代表K-S方程潜在空间的多种歧管的非线性基础。
Machine learning models have emerged as powerful tools in physics and engineering. Although flexible, a fundamental challenge remains on how to connect new machine learning models with known physics. In this work, we present an autoencoder with latent space penalization, which discovers finite dimensional manifolds underlying the partial differential equations of physics. We test this method on the Kuramoto-Sivashinsky (K-S), Korteweg-de Vries (KdV), and damped KdV equations. We show that the resulting optimal latent space of the K-S equation is consistent with the dimension of the inertial manifold. The results for the KdV equation imply that there is no reduced latent space, which is consistent with the truly infinite dimensional dynamics of the KdV equation. In the case of the damped KdV equation, we find that the number of active dimensions decreases with increasing damping coefficient. We then uncover a nonlinear basis representing the manifold of the latent space for the K-S equation.
