  First-principles-based modelings have been extremely successful in providing
crucial insights and predictions for complex biological functions and
phenomena. However, they can be hard to build and expensive to simulate for
complex living systems. On the other hand, modern data-driven methods thrive at
modeling many types of high-dimensional and noisy data. Still, the training and
interpretation of these data-driven models remain challenging. Here, we combine
the two types of methods to model stochastic neuronal network oscillations.
Specifically, we develop a class of first-principles-based artificial neural
networks to provide faithful surrogates to the high-dimensional, nonlinear
oscillatory dynamics produced by neural circuits in the brain. Furthermore,
when the training data set is enlarged within a range of parameter choices, the
artificial neural networks become generalizable to these parameters, covering
cases in distinctly different dynamical regimes. In all, our work opens a new
avenue for modeling complex neuronal network dynamics with artificial neural
networks.
