DeepMultiConnectome: Deep Multi-Task Prediction of Structural Connectomes Directly from Diffusion MRI Tractography

Diffusion MRI (dMRI) tractography enables in vivo mapping of brain structural connections, but traditional connectome generation is time-consuming and requires gray matter parcellation, posing challenges for large-scale studies. We introduce DeepMultiConnectome, a deep-learning model that predicts structural connectomes directly from tractography, bypassing the need for gray matter parcellation while supporting multiple parcellation schemes. Using a point-cloud-based neural network with multi-task learning, the model classifies streamlines according to their connected regions across two parcellation schemes, sharing a learned representation. We train and validate DeepMultiConnectome on tractography from the Human Connectome Project Young Adult dataset ($n = 1000$), labeled with an 84 and 164 region gray matter parcellation scheme. DeepMultiConnectome predicts multiple structural connectomes from a whole-brain tractogram containing 3 million streamlines in approximately 40 seconds. DeepMultiConnectome is evaluated by comparing predicted connectomes with traditional connectomes generated using the conventional method of labeling streamlines using a gray matter parcellation. The predicted connectomes are highly correlated with traditionally generated connectomes ($r = 0.992$ for an 84-region scheme; $r = 0.986$ for a 164-region scheme) and largely preserve network properties. A test-retest analysis of DeepMultiConnectome demonstrates reproducibility comparable to traditionally generated connectomes. The predicted connectomes perform similarly to traditionally generated connectomes in predicting age and cognitive function. Overall, DeepMultiConnectome provides a scalable, fast model for generating subject-specific connectomes across multiple parcellation schemes.

Variational operator learning: A unified paradigm for training neural operators and solving partial differential equations

Based on the variational method, we propose a novel paradigm that provides a unified framework of training neural operators and solving partial differential equations (PDEs) with the variational form, which we refer to as the variational operator learning (VOL). We first derive the functional approximation of the system from the node solution prediction given by neural operators, and then conduct the variational operation by automatic differentiation, constructing a forward-backward propagation loop to derive the residual of the linear system. One or several update steps of the steepest decent method (SD) and the conjugate gradient method (CG) are provided in every iteration as a cheap yet effective update for training the neural operators. Experimental results show the proposed VOL can learn a variety of solution operators in PDEs of the steady heat transfer and the variable stiffness elasticity with satisfactory results and small error. The proposed VOL achieves nearly label-free training. Only five to ten labels are used for the output distribution-shift session in all experiments. Generalization benefits of the VOL are investigated and discussed.