近似面误差是如何计算的？

ppp546

采用近似面技术可以最大限度地节省计算量。同时用户也可以设定最大可接受的误差范围，在error Type中可以有以下几种形式：

• Average. The differences between the actual (workflow execution) and predicted (approximation model execution) values for all errors samples are averaged and then normalized by the range of the actual values for each response. The value is thus a fraction of the response data range for the error sample points. Normalizing the error value allows the error level of different responses with different magnitudes to be compared with respect to approximation model quality of predictions.
• Maximum. The maximum difference between the actual (workflow execution) and predicted (approximation model execution) values for all error samples is taken for this error type, and normalized by the range of the actual values for each response The value is thus a fraction of the response data range for the error sample points. Normalizing the error value allows the error level of different responses with different magnitudes to be compared with respect to approximation model quality of predictions.
• Root Mean Square. The squared differences between the actual (workflow execution) and predicted (approximation model execution) values for all errors samples are averaged. The square root is then taken and the result is normalized by the range of the actual values for each response. The value is thus a fraction of the response data range for the error sample points. Normalizing the error value allows the error level of different responses with different magnitudes to be compared with respect to approximation model quality of predictions.
• R-Squared. The coefficient of determination is calculated based on the error samples. The coefficient of determination always ranges between 0 and 1, where 1 represents a perfect fit (or no prediction error).
  

ppp546

我有一个问题：
    比如，它的这个Average究竟是如何计算的呢？比如取20个样点，它的误差表达式是怎样的呢？
谢谢指点

lucycui

平均值分析方法，是指的近似值与真实仿真值之差的平均值，然后再与实际值做归一化处理。假设xi为近似值，xa为实际值计算公式为：
∑{（xi1-xa1）/xa1+（xi2-xa2）/xa2+……}/n