ROMNet：一种结合降阶建模与机器学习的波形反演混合方法
ROMNet: a hybrid reduced order modeling and machine learning approach to waveform inversion
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- Columbia University（哥伦比亚大学）
- University of Houston（休斯顿大学）
- University of Maryland（马里兰大学）
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中文总结 AI 辅助
该研究针对全波形反演的周期跳跃问题，提出ROMNet混合方法，用神经网络优化降阶模型到波速的映射，结合数值模拟在两类数据集上验证其性能。
中文摘要 AI 辅助
波形反演旨在通过用户控制传感器获取的随时间变化的波测量值，估算非均匀、不可达介质的波速。本文针对声波的该逆问题，采用主动源/接收器阵列，该阵列发射探测信号并测量产生的压力波。从波速到测量值的正映射是非线性且振荡的，振荡会引发周期跳跃，这是使用标准非线性最小二乘数据拟合公式（即全波形反演FWI）的主要障碍。近期提出的替代波形反演方法可从测量值计算波算子的代数代理——降阶模型ROM矩阵，再用其估算波速。从测量值到ROM的映射是非线性的，但已被充分理解，且以非迭代方式高效计算；而从ROM到波速的非线性映射理解不足，其近似涉及耗时的优化。本文目标是用神经网络将ROM矩阵映射到另一对波速有更简单显式依赖的ROM矩阵，以简化并降低基于ROM的波形反演的计算成本。我们引入名为ROMNet的方法，并通过数值模拟测试，使用两个训练数据集：第一组是由随机振幅和标准差的高斯叠加建模的波速变化随机介质；第二组是公开可用的GeoFWI数据集，专为用深度学习对FWI进行基准测试而设。我们将ROMNet的性能与直接基于ROM的反演，以及两种代表性的FWI深度学习方法——“Fourier-DeepONet”和“InversionNet”进行对比。
英文摘要
Waveform inversion seeks to estimate the wave speed of a heterogeneous, inaccessible medium, from time-resolved measurements of the waves at user controlled sensors. We consider this inverse problem for acoustic waves and an active array of source/receiver sensors that emit probing signals and measure the generated pressure waves. The forward map, from the wave speed to the measurements, is nonlinear and oscillatory. The oscillations cause cycle skipping, the main impediment to using the standard, nonlinear least-squares data fitting formulation, known as full waveform inversion (FWI). A recently introduced alternative waveform inversion approach computes from the measurements an algebraic surrogate of the wave operator, a reduced order model (ROM) matrix, which is then used to estimate the wave speed. The mapping from the measurements to the ROM is nonlinear, but well understood. It is computed efficiently, in a non-iterative manner. The nonlinear mapping from the ROM to the wave speed is less understood, and its approximation involves time-consuming optimization. Our goal in this paper is to use a neural network to map the ROM matrix to a nearby one, that has a simpler and explicit dependence on the wave speed. This simplifies and reduces the computational cost of the ROM-based waveform inversion. We introduce the methodology, called ROMNet, and test it with numerical simulations, using two training data sets: The first set consists of random media with variations of the wave speed modeled by a superposition of Gaussians with random amplitudes and standard deviations. The second is the publicly available GeoFWI dataset introduced for benchmarking FWI using deep learning. We compare the performance of ROMNet with the direct ROM-based inversion and with two representative deep learning approaches to FWI: ``Fourier-DeepONet" and ``InversionNet".
