基于贝叶斯物理信息神经网络的流动场断层成像与不确定性量化
Flow field tomography with uncertainty quantification using a Bayesian physics-informed neural network
AI总结：
本文提出利用贝叶斯物理信息神经网络进行流动场断层成像，通过纳维-斯托克斯和对流-扩散方程正则化重建，实现从稀疏线-of-sight测量中获得高质量流动场估计，同时通过不确定性量化提升重建鲁棒性。
摘要：
我们报告了一种新的流动场断层成像方法，利用纳维-斯托克斯和对流-扩散方程进行正则化重建。断层成像日益被用于从一系列线-of-sight（LoS）积分测量中推断2D或3D流体流动和燃烧结构，利用多种成像模态。通过逆向投影模型将高维流动场从低维测量中重建出来，该模型包含沿每个LoS通过感兴趣区域的路径积分。正则化技术需要获得真实估计，但当前方法依赖于截断迭代解或添加不兼容流物理的惩罚项。物理信息神经网络（PINNs）是新的逆向分析工具，能够利用支配物理正则化流动场估计。我们展示如何利用PINN从稀疏LoS积分测量中重建2D流动场，无需了解边界条件，通过将测量模型纳入用于训练网络的损失函数中。结果重建显著优于由最先进算法生成的重建，即使使用PINN进行后处理。然而，与传统迭代算法一样，我们的方法在高噪声水平时容易半收敛。我们通过使用贝叶斯PINN解决此问题，该方法有助于全面的重建不确定性量化，使损失函数更直观，并揭示半收敛的来源。
英文摘要：
We report a new approach to flow field tomography that uses the Navier-Stokes and advection-diffusion equations to regularize reconstructions. Tomography is increasingly employed to infer 2D or 3D fluid flow and combustion structures from a series of line-of-sight (LoS) integrated measurements using a wide array of imaging modalities. The high-dimensional flow field is reconstructed from low-dimensional measurements by inverting a projection model that comprises path integrals along each LoS through the region of interest. Regularization techniques are needed to obtain realistic estimates, but current methods rely on truncating an iterative solution or adding a penalty term that is incompatible with the flow physics to varying degrees. Physics-informed neural networks (PINNs) are new tools for inverse analysis that enable regularization of the flow field estimates using the governing physics. We demonstrate how a PINN can be leveraged to reconstruct a 2D flow field from sparse LoS-integrated measurements with no knowledge of the boundary conditions by incorporating the measurement model into the loss function used to train the network. The resulting reconstructions are remarkably superior to reconstructions produced by state-of-the-art algorithms, even when a PINN is used for post-processing. However, as with conventional iterative algorithms, our approach is susceptible to semi-convergence when there is a high level of noise. We address this issue through the use of a Bayesian PINN, which facilitates comprehensive uncertainty quantification of the reconstructions, enables the use of a more intuitive loss function, and reveals the source of semi-convergence.
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