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arXiv 2309.13645physics.geo-ph
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地震波动方程的鲁棒数据驱动发现

Robust data driven discovery of a seismic wave equation

Shijun Cheng, Tariq Alkhalifah

AI总结:

本文提出 D-WE 方法,通过预训练神经网络、遗传算法和物理信息准则,从时空波场数据中自动发现波动方程结构及系数,并在含噪稀疏数据上验证了其鲁棒性。

摘要:

尽管我们的物理观测通常可以用推导出的物理定律(如波动方程)来描述,但在许多情况下,我们观测到的数据与这些定律不匹配,或者尚未得到物理上的描述。因此,近年来机器学习的一个分支致力于从数据中发现物理定律。我们测试了这类发现算法,并采用我们自己的实现方式 D-WE,从观测到的时空波场中发现波动方程。D-WE 首先以监督方式预训练一个神经网络(NN),以建立时空位置 (x,y,z,t) 与观测位移波场函数 u(x,y,z,t) 之间的映射。训练好的神经网络用于生成元数据,并通过自动微分提供波场的时间和空间导数(例如 u_tt 和 u_xx)。然后,利用遗传算法从一个过完备库中优化出波动方程潜在项的初步库。接着,我们使用物理信息准则评估初步库中潜在方程的精度和简洁性,并确定波动方程的最佳结构。最后,我们训练“物理信息”神经网络来识别每个函数项对应的系数。发现二维声波方程的实例验证了 D-WE 的可行性和有效性。我们还通过在含噪和稀疏采集的波场数据上进行测试,验证了该方法的鲁棒性。

英文摘要:

Despite the fact that our physical observations can often be described by derived physical laws, such as the wave equation, in many cases, we observe data that do not match the laws or have not been described physically yet. Therefore recently, a branch of machine learning has been devoted to the discovery of physical laws from data. We test such discovery algorithms, with our own flavor of implementation D-WE, in discovering the wave equation from the observed spatial-temporal wavefields. D-WE first pretrains a neural network (NN) in a supervised fashion to establish the mapping between the spatial-temporal locations (x,y,z,t) and the observation displacement wavefield function u(x,y,z,t). The trained NN serves to generate meta-data and provide the time and spatial derivatives of the wavefield (e.g., u_tt and u_xx) by automatic differentiation. Then, a preliminary library of potential terms for the wave equation is optimized from an overcomplete library by using a genetic algorithm. We, then, use a physics-informed information criterion to evaluate the precision and parsimony of potential equations in the preliminary library and determine the best structure of the wave equation. Finally, we train the "physics-informed" neural network to identify the corresponding coefficients of each functional term. Examples in discovering the 2D acoustic wave equation validate the feasibility and effectiveness of D-WE. We also verify the robustness of this method by testing it on noisy and sparsely acquired wavefield data.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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