GeoID-PINN: Identifiability-Aware Regional Epidemic Inference with Geographic Coupling

GeoID-PINN：具有地理耦合的识别感知型区域流行病推断

Abstract: 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.

摘要： 区域监测数据反映了当地的传播、报告、播种以及外部感染压力，这些因素很难被单独识别。我们引入了 GeoID-PINN，这是一种用于易感-感染-康复-死亡（SIRD）动力学的物理信息神经网络（PINN）。

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.

该模型使用行随机源组成矩阵来表示空间依赖性，其行分配非负的源权重，且权重之和为一。我们将该矩阵正则化，使其趋向于由距离、邻接性、通勤或超前-滞后信息构建的空间先验。

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.

在已知真值的四区域模拟中，兼容的距离先验产生的源组成误差为 0.099。在没有正则化的情况下，误差上升至 0.159；在严重错误的先验下，误差上升至 0.577，而轨迹拟合和传播规模估计保持相似。因此，准确的轨迹并不能保证能够恢复区域依赖结构。

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.

我们还使用路易斯安那州 64 个县的 COVID-19 数据对 GeoID-PINN 进行了回顾性评估。相对于自回归负二项式基准模型，经过预测训练的 Geo-PINN 将均方误差 (MSE) 从 32,957 降低至 11,468，平均绝对误差 (MAE) 从 70.60 降低至 57.73。基准模型的负对数似然 (NLL) 更低（5.158 对比 5.346），这表明其分布拟合更好，但点预测准确性较差。

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.

在 15 个县的对照比较中，县邻接性使 MSE 降低了 6.85%，MAE 降低了 3.1%。在合理的先验条件下表现相似，支持结构化正则化，但不支持唯一的边缘恢复。这些结果在解释之前需要进行先验敏感性和观测模型检查。