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

时间序列的分析从机器学习领域得到了显著的推动，例如，专用硬件使神经网络的训练能够适应数据。通常，这些神经网络可以被用作昂贵的数值或实验室实验的替代品。然而，网络拓扑和深度有许多可能性，因此一种选择的糟糕性能几乎不能说明哪种选择可能会更好，而且即使NN拟合良好，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，有很好的证据表明，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，可能会导致更易于理解和健壮的模型。该项目将首先使用利兹和牛津开发的新型优化和数据同化软件来识别和验证依赖时间的流体动力系统的热传输模型，该模型包括托卡马克等离子体的理想化模型。软件中的相关缺陷将通过与其他系统识别代码的比较来确定，例如Sindy(Brunton等人)或储层计算(Pathak等人，2018年)。所获得的数值技能和数据分析经验总体上应该是有用的，特别是对英国的核聚变计划。

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.