发表机构
University of California San Diego; Washington University in St. Louis（加州大学圣地亚哥分校; 华盛顿大学圣路易斯分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对实验数据建模复杂物理现象的挑战，采用随机算子推断方法结合Tikhonov正则化，从超高速数字全息显微镜测量的毛细波湍流数据中学习低维随机微分方程，实现了降阶建模。
AI 中文摘要
直接从实验数据建模复杂物理现象存在根本挑战：测量设备会向数据中引入噪声和偏差，控制方程通常未知或难以处理，实验观测到的动力学可能表现出随机行为。本文研究通过超高速数字全息显微镜测量的毛细波湍流——微流体界面处非线性波相互作用的实例。为直接从这些数据学习高效模型，我们对算子推断进行随机扩展，以从实验测量中学习微尺度波动力学的低维随机微分方程表示。每个实验重复16次，通过激励装置改变无量纲声毛细数创建10种不同条件。此外，我们提出一种同时基于均值和协方差误差的降阶模型维度选择新策略。我们还在随机算子推断框架中加入Tikhonov正则化，证明其除了在确定性场景中作为数值稳定技术的常规作用外，还具有控制所学随机动力学频谱内容的物理解释。我们证明所得随机降阶模型能在一系列实验条件下忠实地捕捉毛细波湍流的显著物理特征。
英文摘要
Modeling complex physical phenomena directly from experimental data poses fundamental challenges: measurement devices introduce noise and biases into the data, the governing equations are often unknown or intractable, and the dynamics observed experimentally may exhibit stochastic behavior. In this paper, we consider capillary wave turbulence---an example of nonlinear wave interactions at a microfluidic interface---measured by ultra-high-speed digital holographic microscopy. With the goal to learn an efficient model directly from these data, we adapt a stochastic extension of Operator Inference to learn low-dimensional stochastic differential equation representations of the microscale wave dynamics from experimental measurements. Each experiment is repeated 16 times, and 10 different conditions are created by changing the nondimensional acoustic capillary number through an excitation device. In addition, we propose a new strategy to select the reduced-order model dimension, based on both mean and covariance errors. We further add Tikhonov regularization to the stochastic Operator Inference framework and show that, beyond its conventional role as a numerical stabilization technique in deterministic settings, it has a physically meaningful interpretation as controlling the spectral content of the learned stochastic dynamics. We demonstrate that the resulting stochastic reduced-order models faithfully capture salient physical features of capillary wave turbulence across a range of experimental conditions.
Comments32 pages, 12 figures
