A Network Reconstruction Method Based on a Local-Deviation-based Iterative Sparse Regression

Reconstructing the connectivity of neuronal networks remains a fundamental challenge in neuroscience. However, directly measuring the structure of large-scale neural networks remains technically challenging with current methodologies, underscoring the importance of inference methods based on time series data. Accurately recovering connectivity is particularly difficult in the presence of strong network synchronization, observational noise, and large-scale systems. To overcome these challenges, we introduce a novel reconstruction framework grounded in iterative local linearization, based on the principle that nonlinear systems can be locally linearized in phase space. We systematically validate our method using both Hodgkin-Huxley and Izhikevich neuron models, demonstrating superior accuracy over existing techniques, especially under conditions of pronounced synchronization or noise. Notably, the approach maintains robust performance as network size increases. Further application to a network of coupled Lorenz oscillators confirms its versatility and precision. Our framework thus provides a practical and effective approach for structural reconstruction of neuronal networks or networks in other fields.