How to integrate a pytorch model into a dynamic optimization, for example in Pyomo or gekko

Question

Let's say I have a pytorch-model describing the evolution of some multidimensional system based on its own state x and an external actuator u. So x_(t+1) = f(x_t, u_t) with f being the artificial neural network from pytorch.

Now i want to solve a dynamic optimization problem to find an optimal sequence of u-values to minimize an objective that depends on x. Something like this:

min sum over all timesteps phi(x_t)

s.t.: x_(t+1) = f(x_t, u_t)

Additionally I also have some upper and lower bounds on some of the variables in x.

Is there an easy way to do this using a dynamic optimization toolbox like pyomo or gekko?

I already wrote some code that transforms a feedforward neural network to a numpy-function which can then be passed as a constraint to pyomo. The problem with this approach is, that it requires significant reprogramming-effort every time the structure of the neural network changes, so quick testing becomes difficult. Also integration of recurrent neural networks gets difficult because hidden cell states would have to be added as additional variables to the optimization problem.

I think a good solution could be to do the function evaluations and gradient calculations in torch and somehow pass the results to the dynamic optimizer. I'm just not sure how to do this.

Thanks a lot for your help!

Answer 1

Tensorflow or Pytorch models can't be directly integrated into the GEKKO at this moment. But, I believe you can retrieve the derivatives from Tensorflow and Pytorch, which allows you to pass them to the GEKKO.

There is a GEKKO Brain module and examples in the link below. You can also find an example that uses GEKKO Feedforward neural network for dynamic optimization.

GEKKO Brain Feedforward neural network examples

MIMO MPC example with GEKKO neural network model

Recurrent Neural Network library in the GEKKO Brain module is currently being developed, which allows using all the GEKKO's dynamic optimization functions easily.

In the meantime, you can use a sequential method by wrapping the TensorFlow or PyTorch models in the available optimization solver such as scipy optimization module.

Check out the below link for a dynamic optimization example with Keras LSTM model and scipy optimize.

Keras LSTM MPC