Numerical simulations provide key insights into many physical, real-world problems. However, while these simulations are solved on a full 3D domain, most analysis only require a reduced set of metrics (e.g. plane-level concentrations). This work presents a hybrid physics-neural model that predicts scalar transport in a complex domain orders of magnitude faster than the 3D simulation (from hours to less than 1 min). This end-to-end differentiable framework jointly learns the physical model parameterization (i.e. orthotropic diffusivity) and a non-Markovian neural closure model to capture unresolved, 'coarse-grained' effects, thereby enabling stable, long time horizon rollouts. This proposed model is data-efficient (learning with 26 training data), and can be flexibly extended to an out-of-distribution scenario (with a moving source), achieving a Spearman correlation coefficient of 0.96 at the final simulation time. Overall results show that this differentiable physics-neural framework enables fast, accurate, and generalizable coarse-grained surrogates for physical phenomena.

翻译：数值模拟为许多物理及现实问题提供了关键洞见。然而，尽管这些模拟在完整三维域上求解，大多数分析仅需简化后的度量集（例如平面层级浓度）。本研究提出一种混合物理-神经模型，可在复杂域中预测标量输运，其速度比三维模拟快数个数量级（从数小时缩短至不足1分钟）。该端到端可微分框架联合学习物理模型参数化（即正交各向异性扩散率）与非马尔可夫神经闭合模型，以捕捉未解析的'粗粒度'效应，从而实现稳定、长时域的推演。所提模型具有数据高效性（仅需26个训练数据即可学习），并可灵活扩展至分布外场景（如移动源），在最终模拟时刻达到0.96的斯皮尔曼相关系数。总体结果表明，这种可微分物理-神经框架能够为物理现象构建快速、精确且可泛化的粗粒度代理模型。