Mechanistic modeling provides a biophysically grounded framework for studying the spread of pathological tau protein in tauopathies like Alzheimer's disease. Existing approaches typically model tau propagation as a diffusive process on the brain's structural connectome, reproducing macroscopic patterns but neglecting microscale cellular transport and reaction mechanisms. The Network Transport Model (NTM) was introduced to fill this gap, explaining how region-level progression of tau emerges from microscale biophysical processes. However, the NTM faces a common challenge for complex models defined by large systems of partial differential equations: the inability to perform parameter inference and mechanistic discovery due to high computational burden and slow model simulations. To overcome this barrier, we propose Tau-BNO, a Brain Neural Operator surrogate framework for rapidly approximating NTM dynamics that captures both intra-regional reaction kinetics and inter-regional network transport. Tau-BNO combines a function operator that encodes kinetic parameters with a query operator that preserves initial state information, while approximating anisotropic transport through a spectral kernel that retains directionality. Empirical evaluations demonstrate high predictive accuracy ($R^2\approx$ 0.98) across diverse biophysical regimes and an 89\% performance improvement over state-of-the-art sequence models like Transformers and Mamba, which lack inherent structural priors. By reducing simulation time from hours to seconds, we show that the surrogate model is capable of producing new insights and generating new hypotheses. This framework is readily extensible to a broader class of connectome-based biophysical models, showcasing the transformative value of deep learning surrogates to accelerate analysis of large-scale, computationally intensive dynamical systems.

翻译：机理建模为研究阿尔茨海默病等tau蛋白病中病理性tau蛋白的扩散提供了一个生物物理基础框架。现有方法通常将tau传播建模为大脑结构连接组上的扩散过程，能够再现宏观模式但忽略了微观尺度的细胞运输与反应机制。网络传输模型（NTM）的提出填补了这一空白，解释了区域水平的tau蛋白进展如何从微观生物物理过程中产生。然而，NTM面临着由大型偏微分方程组定义的复杂模型的共同挑战：由于计算负担重和模型仿真速度慢，无法进行参数推断和机理发现。为克服这一障碍，我们提出Tau-BNO——一种用于快速近似NTM动力学的脑神经算子代理框架，该框架同时捕捉区域内反应动力学和区域间网络传输。Tau-BNO结合了编码动力学参数的函数算子与保留初始状态信息的查询算子，同时通过保留方向性的谱核来近似各向异性传输。实证评估表明，该方法在多种生物物理状态下均具有较高的预测精度（$R^2\approx$ 0.98），且性能较缺乏固有结构先验的先进序列模型（如Transformer和Mamba）提升了89%。通过将仿真时间从数小时缩短至数秒，我们证明该代理模型能够产生新的见解并生成新的假设。该框架可轻松扩展至更广泛的基于连接组的生物物理模型，展示了深度学习代理在加速分析大规模计算密集型动力系统中的变革性价值。