Project 39 NeuroSim As A Physics Constrained Model for Finite Horizon Network Control Theory

The application of Network Control Theory to medical neuroimaging consistently faces the approximation crisis. Current tools rely on infinite-horizon continuous models, binary structural masking and statistically inaccurate harmonization. They fail to capture the discrete, finite time and stochastic truth of brain dynamics grounded in biology. This limits their use in computational psychiatry and biomarker discovery. NeuroSim is intended as a Python model built from scratch to resolve these problems. It aims to simulate in-silico brain stimulation with rigorous physics-based constraints. Over the 350 hour period, the three prime modules will be made available to the community:- 1. Discrete Finite Horizon Physics: A transition from standard iterative summations to discrete time Van Loan Doubling algorithm, significantly reducing computational load for large scale neural networks. 2. GraphNet based Laplacian Regularization: Implementation of a proximal gradient descent module to generate soft-prior connectivity matrices. This resolves the problem of structural blindness in binary DTI-based masking. 3. Bias-less Harmonization and Ground-truthing: Deployment of a NeuroCombat protocol to ensure data security in multi-site studies. Validation to be done against non-linear Wilson-Cowan neural mass simulations. Using the above modules, NeuroSim positions itself as a highly scalable, diagnostic-adjacent toolset capable of modelling complex neural mass transitions. It establishes a standard for next generation non invasive neuromodulation and macro-scale brain stimulation.