PI-NOMT：面向脑部流体动力学的物理信息神经最优质量传输
PI-NOMT: Physics-Informed Neural Optimal Mass Transport for Brain Fluid Dynamics
- Istanbul Technical University（伊斯坦布尔理工大学）
- Yale University（耶鲁大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
针对脑部示踪剂成像中从稀疏观测恢复隐藏传输机制的逆问题，提出物理信息神经最优质量传输（PI-NOMT）框架，通过连续神经场和物理约束准确重建速度场，在合成基准和九只大鼠DCE-MRI数据上验证了其有效性。
AI中文摘要：
从稀疏的时空观测中恢复隐藏的传输机制是科学机器学习中的一个基本逆问题。在脑部示踪剂成像中，动态对比增强磁共振成像（DCE-MRI）提供了示踪剂浓度的时间分辨测量，而控制示踪剂传播的潜在速度和源机制仍未被观测到。我们将此问题表述为物理信息潜在状态推断，其中传输场本身是推断的主要对象，而非仅用于重建观测密度的辅助变量。我们提出了物理信息神经最优质量传输（PI-NOMT），该框架将密度、速度和源表示为连续的神经场，并结合了连续神经密度教师、递归可微平流-扩散-源展开、非平衡最优传输正则化以及控制方程监督。物理定律作为结构先验，约束了可接受传输机制的空间，而观测到的示踪剂动力学为估计潜在传输状态提供了证据。我们在具有已知真实传输的合成基准以及来自九只对照大鼠的DCE-MRI序列上评估了PI-NOMT。在合成基准上，PI-NOMT准确恢复了指定的速度场，包括其大小、方向和积分轨迹，而不仅仅是重建端点密度。在九个大鼠数据集中，该框架产生了亚百分比的局部端点误差、一致的物理速度尺度以及训练后低PDE和不可压缩性残差。这些结果支持物理信息潜在状态推断作为从观测动态标量场恢复隐藏传输机制的通用框架。
英文摘要：
Recovering hidden transport mechanisms from sparse spatiotemporal observations is a fundamental inverse problem in scientific machine learning. In brain tracer imaging, dynamic contrast-enhanced MRI (DCE-MRI) provides time-resolved measurements of tracer concentration, while the underlying velocity and source mechanisms governing tracer propagation remain unobserved. We formulate this problem as physics-informed latent-state inference, in which the transport field itself is the primary object of inference rather than an auxiliary variable used only to reconstruct observed densities. We propose Physics-Informed Neural Optimal Mass Transport (PI-NOMT), a framework that represents density, velocity, and source as continuous neural fields and combines a continuous neural density teacher, recursive differentiable advection--diffusion--source rollout, unbalanced optimal-transport regularization, and governing-equation supervision. Physical laws act as structural priors that constrain the space of admissible transport mechanisms, while observed tracer dynamics provide evidence for estimating the latent transport state. We evaluate PI-NOMT on a synthetic benchmark with known ground-truth transport and on DCE-MRI sequences from nine control rats. On the synthetic benchmark, PI-NOMT accurately recovers the prescribed velocity field, including its magnitude, direction, and integrated trajectories, rather than merely reconstructing endpoint densities. Across the nine rat datasets, the framework yields sub-percent local endpoint error, consistent physical speed scales, and low post-training PDE and incompressibility residuals. These results support physics-informed latent-state inference as a general framework for recovering hidden transport mechanisms from observed dynamic scalar fields.
