Biologically Plausible Neural Networks for Simulating Brain Dynamics and Inferring Connectivity

We present Cerebrum, a novel framework that bridges biologically plausible neural networks with rigorous mathematical modeling. By grounding neural network simulations in a range of empirically-founded neuronal models (Hodgkin-Huxley, Izhikevich, and Adaptive Exponential Integrate-and-Fire), Cerebrum captures dynamics from intricate ion channel kinetics to general, large-scale network behavior. Our methodology integrates these mathematical models within a unified simulation pipeline, featuring mechanisms for short-term synaptic plasticity, precise state integration via the Runge-Kutta and Euler methods, and refractory spike regulation. We use a Graph Attention Network (GAT), to infer synaptic connectivity directly from dynamic activity patterns. This approach not only ensures biological realism but also facilitates robust connectivity reconstruction across diverse network topologies, including Erd[o]s-Renyi, Small-World, and Scale-Free architectures. Results demonstrate that our framework reliably reproduces key neuronal firing patterns and synchronization phenomena, while its modular design paves the way for scalable investigations into the interplay between network structure and neural dynamics. Cerebrum thus offers a powerful tool for advancing both theoretical and applied aspects of computational neuroscience.