I am an academic neuroscientist working on the following project: I am attempting to determine the evoked response of a sensory nerve (time series in voltage) to applied stimuli (time series in pressure). The neural response is a complex function of the stimulus (transient effects, history dependence, etc). In general, the stimulus is not in my control, and varies between trials and experiments.

The problem:
I have developed a system of nonlinear differential equations that predict the time series neural response from the stimulus. I am looking for a goodness of fit measure between the actual observed time series of the nerve and my model’s prediction to quantify how well the model is working in some sense.

I would be grateful if anyone could point me in the right direction, thank you.