发表机构
University of Michigan（密歇根大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究提出GeoID-PINN，一种结合地理耦合与正则化的物理信息神经网络，用于区域流行病SIRD动力学推断，在模拟数据与路易斯安那州64个县COVID-19数据上均提升了预测准确性。
AI 中文摘要
区域监测数据反映了当地传播、报告、输入病例及外部感染压力，这些因素难以单独识别。本文提出GeoID-PINN，一种用于易感-感染-康复-死亡（SIRD）动力学的物理信息神经网络（PINN）。该模型通过行随机源组成矩阵表征空间依赖性，其行分配非负源权重且和为1。我们对该矩阵进行正则化，使其趋近于由距离、邻接性、通勤或领先滞后信息构建的空间先验。在4个区域的已知真实值模拟中，兼容距离先验的源组成误差为0.099；无正则化时误差升至0.159，先验严重误设时误差达0.577，而轨迹拟合和传播规模估计仍保持相似，因此准确的轨迹并不保证能恢复区域依赖结构。我们还使用路易斯安那州64个县的COVID-19数据对GeoID-PINN进行回顾性评估：相较于自回归负二项基线，经预测训练的Geo-PINN将均方误差（MSE）从32957降至11468，平均绝对误差（MAE）从70.60降至57.73；基线的负对数似然（NLL）更低，为5.158，而GeoID-PINN为5.346，表明基线分布拟合更好但点预测准确性更差。在15个县的对照比较中，县邻接性使MSE降低6.85%，MAE降低3.1%；合理先验间的相似性能支持结构化正则化，但无法支持唯一边的恢复，这些结果在解释前需进行先验敏感性和观测模型检查。
英文摘要
Regional surveillance data reflect local transmission, reporting, seeding, and external infection pressure, which are difficult to identify separately. We introduce GeoID-PINN, a physics-informed neural network (PINN) for susceptible-infectious-recovered-deceased (SIRD) dynamics. The model represents spatial dependence with a row-stochastic source-composition matrix whose rows assign nonnegative source weights that sum to one. We regularize this matrix toward a spatial prior constructed from distance, adjacency, commuting, or lead-lag information. In a four-region simulation with known truth, a compatible distance prior gives source-composition error 0.099. The error rises to 0.159 without regularization and 0.577 under a strongly misspecified prior, while trajectory fit and transmission-scale estimates remain similar. Accurate trajectories therefore do not guarantee recovery of the regional dependence structure. We also evaluate GeoID-PINN retrospectively using COVID-19 data from 64 Louisiana counties. Relative to an autoregressive negative-binomial baseline, Forecast-Trained Geo-PINN reduces mean squared error (MSE) from 32,957 to 11,468 and mean absolute error (MAE) from 70.60 to 57.73. The baseline has lower negative log likelihood (NLL), 5.158 versus 5.346, indicating better distributional fit but worse point accuracy. In a controlled 15-county comparison, county adjacency reduces MSE by 6.85 percent and MAE by 3.1 percent. Similar performance across plausible priors supports structured regularization but not unique edge recovery. These results require prior-sensitivity and observation-model checks before interpretation.
Comments11 pages, 3 figures. Accepted at the 8th epiDAMIK ACM SIGKDD Workshop on Data-driven Decision Making for Public and Population Health (epiDAMIK @ KDD 2026)
