Realising reduced order models for heat transfer problems via Data Assimilation and machine learning

时间序列的分析已经从机器学习领域得到了显著的推动，例如专用硬件可以训练神经网络来拟合数据。通常这些神经网络可以用作昂贵的数值或实验室实验的替代品。然而，网络拓扑和深度有很多可能性，因此一个选择的糟糕表现几乎不能说明哪个可能做得更好，即使NN拟合很好，也经常不清楚它是否可以用于原始训练集以外的参数。然而，有充分的证据表明，在拟合过程中包括（磁）流体动力学作为时间序列现象基础的信息可能导致更易于理解和更健壮的模型。该项目将首先使用利兹大学和牛津大学开发的新型优化和数据同化软件来识别和验证时间相关流体动力系统的热传输模型，包括托卡马克等离子体的理想模型。通过与其他系统识别码（例如SINDy （Brunton et al）或油藏计算（Pathak et al 2018））进行比较，可以识别软件中的相关缺陷。获得的数值技能和数据分析经验在一般情况下应该是有用的，特别是对英国的核聚变项目。

The analysis of time series has received a significant boost from the field of machine learning, where for example dedicated hardware enables training of neural nets to fit the data. Often these NNs can be used as surrogates for expensive numerical or laboratory experiments. However, there are many possibilities for net topology and depth, so that the poor performance of one choice gives little indication as to what might do better, and even if the NN fit is good, it will frequently be unclear whether it can be used for parameters outside the original training set. There is however good evidence that including in the fitting process the information that (magneto-) fluid dynamics underlies the time series phenomena may lead to more comprehensible and robust models. The project will begin by using novel optimization and data assimilation software developed by Leeds and Oxford to identify and validate models of heat transport by time dependent fluid dynamical systems, taken to include idealized models of tokamak plasma. Relevant deficiencies in the software will be identified by comparison with other system identification codes, for example SINDy (Brunton et al) or reservoir computing (Pathak et al 2018). The numerical skills and data analysis experience gained should be useful in general, and in particular for the UK fusion programme.