基于穿透曲线的地下异常输运非局部核函数的机器学习
Machine-learning of nonlocal kernels for anomalous subsurface transport from breakthrough curves
摘要：
由于介质在不同尺度上的高度非均匀性，地下溶质运移中普遍存在异常行为。尽管分数阶模型已被广泛用于描述各种地下应用中的异常输运，但其应用受到计算挑战的阻碍。更简单的非局部模型的特点是可积的内核和有限的相互作用长度代表了一个计算上可行的替代分数模型，然而，知情选择其核函数仍然是一个悬而未决的问题。我们提出了一个通用的数据驱动的框架，发现最佳内核的基础上非常小和稀疏的数据集的背景下，异常地下运输。使用空间稀疏的突破曲线恢复细尺度粒子密度模拟，我们学习最好的粗尺度非局部模型使用非局部算子回归技术。使用最优非局部模型获得的突破曲线的预测显示出良好的协议，即使在不同的位置和时间间隔从用于训练的内核，证实了所提出的算法的优良的泛化性能的精细规模的仿真结果。与训练的经典模型和黑箱深度神经网络的比较证实了所提出的模型的预测能力的优越性。
英文摘要：
Anomalous behavior is ubiquitous in subsurface solute transport due to the presence of high degrees of heterogeneity at different scales in the media. Although fractional models have been extensively used to describe the anomalous transport in various subsurface applications, their application is hindered by computational challenges. Simpler nonlocal models characterized by integrable kernels and finite interaction length represent a computationally feasible alternative to fractional models; yet, the informed choice of their kernel functions still remains an open problem. We propose a general data-driven framework for the discovery of optimal kernels on the basis of very small and sparse data sets in the context of anomalous subsurface transport. Using spatially sparse breakthrough curves recovered from fine-scale particle-density simulations, we learn the best coarse-scale nonlocal model using a nonlocal operator regression technique. Predictions of the breakthrough curves obtained using the optimal nonlocal model show good agreement with fine-scale simulation results even at locations and time intervals different from the ones used to train the kernel, confirming the excellent generalization properties of the proposed algorithm. A comparison with trained classical models and with black-box deep neural networks confirms the superiority of the predictive capability of the proposed model.
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