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Questions on AI Platform..

I am working on inverse problems, essentially data assimilation using partial differential equations in fluids and heat transfer. I am using a deep neural net formulation. The loss function in my formulation has derivatives of the output variables (velocities, temperatures) w.r.t. the input (position x,y,z and time t).  It appears that computation of these derivatives is the most expensive part of this formulation. We are using TensorFlow right now. It appears that the gradients of the output w.r.t. input are done using the same framework as the one used for net variables (i.e. the back propagation). It appears that it does a lot of redundant computations. 

 

Any help would be much appreciated.