A big issue touched upon in this article is that the space of possible dynamical systems represented in the brain is large, and trying to collect data is not a practical way of trimming this search space. It's more useful to look at types of dynamical systems that have certain stability properties that are desirable for computation.
But the issue then becomes that these dynamical systems become mathematically intractable past a few simplified neurons. So it's really hard to make progress either by looking at data, or by studying simplified dynamical systems mathematically.
There is a third option. Evolve smart dynamical systems by large scale brute force computation. Start with guesses about neuron-like subsystems with desirable information processing properties (at the single neuron level, such properties are mathematically tractable). Play with the configurations, the rules of evolution, the reward functions, the environment, everything. This may sound a lot like witchcraft but look at how far witchcraft has taken machine learning in recent years (deep learning is just principled witchcraft). This is IMO the only way we will learn how biological intelligence works.