# BackPropagation Through Time and arbitrary dynamic system

BackPropagation Through Time (BPTT) is well established tool for training Recursive Neural Networks (RNN). The RNN (from my point of view) is a non-linear dynamic system, as it includes internal states and the activation functions are non-linear.

Therefore, BPTT should be viable option of training/adjusting parameters of any non-linear dynamic system. The motivation to change RNN for dynamic system, is that dynamic system may have desired physical representation (e.g. Equivalent Circuit in electronics) while RNN has hyper-parameters (usually not physically representable).

I have searched my university library and internet, but havent found any literature addressing the use of BPTT for other purpose than RNN training.

QUESTIONs:

1) Is there any problem, why BPTT is not used for fitting dynamic systems to measured data ?

2) If it is suitable, can you share any literature/examples/experience regarding the use of BPTT for training arbitrary (non-linear) dynamic system $\frac{dx}{dt}=f_{(x,y,t)}$ with time-series data?

• Why do you think a dynamic system is backprobagatable----like a neural network? – Jiapeng Zhang Jul 3 at 14:48