Journal of Geographical Sciences >
Quantum harmonic oscillator model for simulation of intercity population mobility
Hu Xu (1997-), PhD Candidate, specialized in population mobility modeling, urban geography, and quantum models and applications. E-mail: 211301031@njnu.edu.cn |
Received date: 2022-12-10
Accepted date: 2023-10-23
Online published: 2024-04-24
Supported by
National Natural Science Foundation of China(42230406)
National Natural Science Foundation of China(42130103)
National Natural Science Foundation of China(41971404)
National Natural Science Foundation of China(42201504)
The simulation of intercity population mobility helps to deepen the understanding of intercity population mobility and its underlying laws, which has great importance for epidemic prevention and control, social management, and even urban planning. There are many factors that affect intercity population mobility, such as socioeconomic attributes, geographical distance, and industrial structure. The complexity of the coupling among these factors makes it difficult to simulate intercity population mobility. To address this issue, we propose a novel method named the quantum harmonic oscillator model for simulation of intercity population mobility (QHO-IPM). QHO-IPM describes the intercity population mobility as being affected by coupled driving factors that work as a multioscillator-coupled quantum harmonic oscillator system, which is further transformed by the oscillation process of an oscillator, namely, the breaking point of intercity population mobility. The intercity population mobility among seven cities in the Beijing-Tianjin-Hebei region and its surrounding region is taken as an example for verifying the QHO-IPM. The experimental results show that (1) compared with the reference methods (the autoregressive integrated moving average (ARIMA) and long and short-term memory (LSTM) models), the QHO-IPM achieves better simulation performance regarding intercity population mobility in terms of both overall trend and mutation. (2) The simulation error in the QHO-IPM for different-level intercity population mobility is small and stable, which illustrates the weak sensitivity of the QHO-IPM to intercity population mobility under different structures. (3) The discussion regarding the influence degree of different driving factors reveals the significant “one dominant and multiple auxiliary” factor pattern of driving factors on intercity population mobility in the study area. The proposed method has the potential to provide valuable support for understanding intercity population mobility laws and related decision-making on intercity population mobility control.
HU Xu , QIAN Lingxin , NIU Xiaoyu , GAO Ming , LUO Wen , YUAN Linwang , YU Zhaoyuan . Quantum harmonic oscillator model for simulation of intercity population mobility[J]. Journal of Geographical Sciences, 2024 , 34(3) : 459 -482 . DOI: 10.1007/s11442-024-2213-3
Figure 1 The overall framework of QHO-IPM |
Figure 2 Study area and average intercity population mobility |
Table 1 Definition of evaluation criteria |
Evaluation criteria | Definition |
---|---|
Mean absolute error (MAE) | $M A E=\frac{1}{m} \sum_{i=1}^{m}\left|M_{i}-\hat{M}_{i}\right|$ |
Root mean square error (RMSE) | $R M S E=\sqrt{\frac{1}{m} \sum_{i=1}^{m}\left(M_{i}-\hat{M}_{i}\right)^{2}}$ |
Coefficient of determination (R2) | $R^{2}=1-\sum_{i=1}^{m}\left|M_{i}-\hat{M}_{i}\right|^{2} / \sum_{i=1}^{m}\left|M_{i}-\bar{M}_{i}\right|^{2}$ |
Figure 3 The simulated intercity population mobility using different methods |
Figure 4 The 1:1 diagram between the simulated intercity population mobility and the observed intercity population mobility |
Table 2 The evaluation indicators of different methods |
Origin-Destination | QHO-IPM | ARIMA | LSTM | ||||||
---|---|---|---|---|---|---|---|---|---|
MAE | RMSE | R2 | MAE | RMSE | R2 | MAE | RMSE | R2 | |
Tianjin-Langfang | 2150.11 | 3078.72 | 0.8385 (↑) | 3277.05 | 4682.17 | 0.6265 | 2116.94 | 3380.70 | 0.7943 |
Langfang-Tianjin | 1958.65 | 2633.53 | 0.8804 (↑) | 2204.80 | 3588.58 | 0.7780 | 1958.15 | 3182.78 | 0.8124 |
Langfang-Baoding | 1423.74 | 1996.32 | 0.8046 (↑) | 2140.35 | 3164.85 | 0.5089 | 1442.95 | 2358.47 | 0.7306 |
Baoding-Langfang | 1402.61 | 1869.96 | 0.8159 (↑) | 1901.29 | 2849.91 | 0.5723 | 1506.91 | 2400.10 | 0.6993 |
Langfang-Cangzhou | 919.85 | 1291.55 | 0.8701 (↑) | 1223.93 | 1888.65 | 0.7223 | 1062.79 | 1603.53 | 0.7833 |
Cangzhou-Langfang | 865.24 | 1195.73 | 0.8859 (↑) | 1043.80 | 1706.09 | 0.7676 | 876.13 | 1476.18 | 0.8069 |
Baoding-Cangzhou | 1105.96 | 1624.13 | 0.8978 (↑) | 1485.26 | 2425.42 | 0.7722 | 1230.12 | 2040.40 | 0.8170 |
Cangzhou-Baoding | 1074.19 | 1544.63 | 0.9036 (↑) | 1340.90 | 2197.49 | 0.8048 | 1167.37 | 1910.61 | 0.8303 |
Cangzhou-Hengshui | 810.82 | 1147.95 | 0.9009 (↑) | 1035.55 | 1551.71 | 0.8189 | 972.41 | 1413.72 | 0.8404 |
Hengshui-Cangzhou | 872.09 | 1209.49 | 0.8845 (↑) | 1005.11 | 1525.32 | 0.8163 | 937.35 | 1359.53 | 0.8452 |
Hengshui-Dezhou | 623.81 | 912.34 | 0.8960 (↑) | 663.17 | 1088.31 | 0.8520 | 591.43 | 930.64 | 0.8837 |
Dezhou-Hengshui | 604.51 | 956.79 | 0.8947 (↑) | 612.57 | 1040.43 | 0.8755 | 620.31 | 957.81 | 0.8863 |
Dezhou-Liaocheng | 604.81 | 932.21 | 0.9108 (↑) | 844.78 | 1388.26 | 0.8021 | 707.25 | 1187.19 | 0.8449 |
Liaocheng-Dezhou | 628.42 | 932.13 | 0.9107 (↑) | 787.05 | 1338.48 | 0.8158 | 665.63 | 1137.78 | 0.8565 |
Mean | 1074.63 | 1523.25 | 0.8782 (↑) | 1397.54 | 2173.98 | 0.7524 | 1132.55 | 1809.96 | 0.8165 |
Note: ↑(↓) indicates that the simulation accuracy (R2) of QHO-IPM is superior to (inferior to) that of the reference methods. |
Figure 5 Error distribution of the different methods |
Figure 6 Distribution of the monthly influence degree of different factors |
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