Manifold Geometry and Scalable Computation for Brain Dynamics

Understanding brain dynamics increasingly requires geometric methods to describe high dimensional activity. This is especially important for models and datasets that span multiple scales, from local circuits to whole-brain networks. These geometric approaches must also support comparisons across individual subjects, population-scale simulations, parameter ensembles, and perturbation studies. These approaches face three connected challenges: (1) brain activity is high dimensional and requires interpretable geometric descriptions, (2) manifold structure must be compared across subjects, models, parameters, and perturbations, and (3) multiarea simulations are computationally expensive and must be interpreted in biologically meaningful ways. Manifold approaches can help organize high-dimensional neural activity into interpretable structures. However, dimensionality reduction alone does not make large-scale models understandable: manifold representations can still contain many degrees of freedom and can be difficult to interpret, especially across subjects, parameters, and perturbations. This creates a need to devise methods to relate geometric structure to biological mechanisms.

Recent advances in High Performance Computing make it increasingly feasible to apply manifold-based analyses across ensembles of whole-brain simulations, subject-specific virtual brains, multiple parameter settings, and perturbation studies. The bottleneck has shifted from running any one model to comparing across many, and to validating simulated activity against recorded activity. A geometric framework can provide a shared metric in which ensembles can be compared, perturbations can be characterized, and models can be tested against data. It is critical, however, that the scaling of those computations is paired with reproducible workflows, validation, and interpretable analysis.

This Research Topic seeks all article types, with a keen eye on methods papers, modelling studies, reviews, benchmarks, and open resources that connect manifold geometry, neural dynamics, and scalable computation. We invite contributions on manifold-based metrics, comparison of simulated individuals, validation of simulations against recorded activity, geometric analyses that guide where expensive simulations are most informative, and computational tools for making large-scale brain models interpretable. Our aim is to bring geometry and scale into a single methodological program for understanding brain dynamics.