The Surrogate Spread

Tau protein spreads through the brain along structural connectivity — white matter tracts that connect regions. The Network Transport Model simulates this spread using the brain’s connectome as a directed graph, with kinetic parameters governing production, clearance, and transmission rates. Running the model takes hours. Fitting it to patient data — estimating the kinetic parameters from PET scans — requires thousands of runs. The simulation is too slow for the inference it enables.

Tau-BNO replaces the simulator with a learned operator. A function operator encodes the kinetic parameters; a query operator preserves the initial tau distribution; spectral kernels capture anisotropic transport along the connectome’s directional structure. The surrogate achieves R² ≈ 0.98 across diverse biophysical scenarios while reducing simulation time from hours to seconds — fast enough for parameter inference and mechanistic discovery.

The key design choice: the spectral kernel. Tau doesn’t spread isotropically. It follows the connectome’s directed edges, moving preferentially along certain pathways. Standard neural operators treat the domain as a continuous field. Tau-BNO respects the graph structure, decomposing transport into spectral components of the connectivity matrix. The operator learns in the brain’s natural basis, not in an imposed grid.

The through-claim: the surrogate doesn’t just accelerate the model. It changes what the model is for. A simulator that takes hours is an analysis tool — you run it, look at the output, adjust. A surrogate that takes seconds is an inference tool — you embed it in an optimization loop and ask it questions the original model was too slow to answer. The speedup is not quantitative but categorical: it moves tau transport modeling from simulation into discovery.