Gradient Diffusion: Enhancing Existing Neural Models with Homeostatic Control and Tuning

Abstract: Realistic brain modeling requires precise estimation of numerous unobserved parameters, a task hindered by complex nonlinearities and the inaccessibility of the brain's full dynamical state. Current multicompartmental-model simulations predominantly rely on gradient-free optimization methods, which suffer from the ``curse of dimensionality'' and are incompatible with online tuning crucial for emulating biological homeostasis. Gradient-based methods offer superior scalability and facilitate online adaptation but are currently inaccessible within existing brain simulators due to the significant resource investment and incompatibility with established simulators. This work introduces a novel methodology for computing parameter gradients for any existing model-and-simulator combination, enabling both offline and online tuning, including the implementation of homeostatic-control mechanisms. Our approach seamlessly integrates traditional simulations with gradient-based optimization, facilitating scalable, robust and adaptive brain simulation without the need for developing new simulators.