How can I distribute samples optimally to fit a model?

I'm trying to fit a model to a low number (~5-10) of data points. I might be able to suggest the optimal distribution of the data points beforehand, knowing a bit about the data and the model I created. Is there an established method or do you have any ideas on how to choose the best sampling intervals? Maybe based on the gradient of the model or similar? The model consists of several differential equations describing a biological system and sorption processes.

What I've done so far: I took a simple model (exponential decay) distributed the samples randomly, estimated the uncertainty (with Gaussian Process Regression, not sure whether this is the best method) and chose the best (figure 1) and worst distribution (figure 2) for comparison. However, I feel like this brought no more insights than distribute points evenly.