Modelling multi vector time series in PyMC3

I apologize for being vague, I’ll try to explain myself as well as I can.

I try to figure out whether PyMC3 can help me in this problem

We have ~20 vectors of ~100 measurements each. These vectors represent ~20 biological systems. We let each system evolve over time, and take the ~100 measurements at fixed intervals. In the end, each of the ~20 systems has 15 equally spaced measurements.

We can think of the evolution of the system as a 100x100 matrix that defines the value transition from one vector element to another.

Our goal is to find a model that will shed the light on this 100x100 matrix and, possibly, to predict the final state of the vector, from its initial values.

I guess it is some kind of state space model? I think it is possible to write the timeseries realization using a theano.scan