This paper proposes a novel algorithm using an artificial neural network for modeling simultaneously both a 3-D flow velocity vector and a concentration field. The neural network is trained so that four outputted values of the network, three components of a 3-D velocity vector and a concentration of substances such as air pollutants or bacilli, agree with measured ones and additionally the continuity and diffusion equations are satisfied in the flow field. An approximate model for the velocity and concentration field can be constructed in the neural network from sparsely measured data. When any 3-D position, (x, y, z), is inputted to the neural network model, it outputs a 3-D velocity vector and a concentration at the position. The entire 3-D velocity vector and concentration field, therefore, can be easily estimated using the model. To validate the algorithm, the smoke concentration distribution estimated from a very limited set of measured data is compared with the measured one in which most of the data is unused for the modeling. Even from sparsely measured velocity vectors and smoke concentrations, the novel algorithm gives the entire concentration distribution whose flow characteristics are almost similar to the experimental result.

中文翻译：

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基于神经网络的速度场和浓度场建模

本文提出了一种使用人工神经网络同时建模 3-D 流速矢量和浓度场的新算法。对神经网络进行训练，使得网络的四个输出值、3D 速度矢量的三个分量和空气污染物或细菌等物质的浓度与测量值一致，此外，连续性和扩散方程在流场。速度场和浓度场的近似模型可以在神经网络中根据稀疏测量数据构建。当任何 3-D 位置 (x, y, z) 输入到神经网络模型时，它会输出一个 3-D 速度向量和该位置的浓度。因此，可以使用该模型轻松估计整个 3-D 速度矢量和浓度场。为了验证算法，将从一组非常有限的测量数据中估计的烟雾浓度分布与大部分数据未用于建模的测量数据进行比较。即使从稀疏测量的速度矢量和烟雾浓度，新算法也给出了整个浓度分布，其流动特性几乎与实验结果相似。