论文标题
物理受限的贝叶斯神经网络用于流体流动重建，稀疏和嘈杂的数据
Physics-Constrained Bayesian Neural Network for Fluid Flow Reconstruction with Sparse and Noisy Data
论文作者
论文摘要
在许多应用中，流量测量通常稀疏，可能嘈杂。从有限和不完美的流量信息中重建高分辨率流场是巨大但具有挑战性的。在这项工作中，我们提出了一种创新的物理受限的贝叶斯深度学习方法，以从稀疏，嘈杂的速度数据中重建流场，其中可以估计通过可能性函数和重建流的不确定性施加基于方程的约束。具体而言，对贝叶斯深神经网络进行了稀疏测量数据的训练，以捕获流场。同时，违反物理法律将在无法进行测量的大量时空点上受到惩罚。采用非参数变异推理方法来实现有效的物理受限的贝叶斯学习。研究了一些具有合成测量数据的理想化血管流的测试用例，以证明该方法的优点。
In many applications, flow measurements are usually sparse and possibly noisy. The reconstruction of a high-resolution flow field from limited and imperfect flow information is significant yet challenging. In this work, we propose an innovative physics-constrained Bayesian deep learning approach to reconstruct flow fields from sparse, noisy velocity data, where equation-based constraints are imposed through the likelihood function and uncertainty of the reconstructed flow can be estimated. Specifically, a Bayesian deep neural network is trained on sparse measurement data to capture the flow field. In the meantime, the violation of physical laws will be penalized on a large number of spatiotemporal points where measurements are not available. A non-parametric variational inference approach is applied to enable efficient physics-constrained Bayesian learning. Several test cases on idealized vascular flows with synthetic measurement data are studied to demonstrate the merit of the proposed method.
