  Cellular regulatory dynamics is driven by large and intricate networks of
interactions at the molecular scale, whose sheer size obfuscates understanding.
In light of limited experimental data, many parameters of such dynamics are
unknown, and thus models built on the detailed, mechanistic viewpoint overfit
and are not predictive. At the other extreme, simple ad hoc models of complex
processes often miss defining features of the underlying systems. Here we
propose an approach that instead constructs phenomenological, coarse-grained
models of network dynamics that automatically adapt their complexity to the
amount of available data. Such adaptive models lead to accurate predictions
even when microscopic details of the studied systems are unknown due to
insufficient data. The approach is computationally tractable, even for a
relatively large number of dynamical variables, allowing its software
realization, named Sir Isaac, to make successful predictions even when
important dynamic variables are unobserved. For example, it matches the known
phase space structure for simulated planetary motion data, avoids overfitting
in a complex biological signaling system, and produces accurate predictions for
a yeast glycolysis model with only tens of data points and over half of the
interacting species unobserved.
