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DGFormer: a physics-guided station level weather forecasting model with dynamic spatial-temporal graph neural network

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Abstract

In recent years, there has been an increased interest in understanding and predicting the weather using weather station data with Spatial-Temporal Graph Neural Networks (STGNN). However, it has large prediction errors as a result of the inherent non-linearities and the influence of dynamic spatio-temporal auto-correlation. Using a continuously-varying graph topology chronologically, while embedding domain knowledge to enforce validity, can effectively resolve the issue, but the implementation of such concept constitutes an interdisciplinary challenge for researchers. A Dynamic Graph Former (DGFormer) model is proposed to address this challenge. It combines a topology learner through a deep generative layer with domain knowledge enhancement inserted into the STGNN structure, where the derived physics-guided method allows for an efficient integration with the earth system. For capture of the optimal topology, we merge a node-embedding-based similarity metric learning and the superposition principle as physical assistants into the dynamic graph module. We evaluate our model with a real-world weather dataset on short-term (12 hours) and medium-range (360 hours) prediction tasks. DGFormer achieves outstanding performance with obvious improvements by up to 34.84% at short-term prediction and by up to 23.25% at medium-range prediction compared with the state-of-the-art methods. We also conducted detailed analyses for cities in three regions and visualized the dynamic graph, revealing the characteristics, advantages, and graph visualization of our model.

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Data Availability

We shared our code and data. Readers can find our model at https://github.com/xzwbsz/DGFormer. The dataset was partly sampled from WeatherBench [60] and partly provided by National Meteorological Center of China.

References

  1. Bauer P, Thorpe A, Brunet G (2015) The quiet revolution of numerical weather prediction. Nature 525(7567):47–55

    Article  CAS  PubMed  ADS  Google Scholar 

  2. Lin H, Gao Z, Xu Y, Wu L, Li L, Li SZ (2022) Conditional local convolution for spatio-temporal meteorological forecasting. Proceedings of the AAAI conference on artificial intelligence 36:7470–7478

    Article  Google Scholar 

  3. Pathak J, Subramanian S, Harrington P, Raja S, Chattopadhyay A, Mardani M, Kurth T, Hall D, Li Z, Azizzadenesheli K, et al (2022) Fourcastnet: A global data-driven high-resolution weather model using adaptive fourier neural operators. arXiv:2202.11214

  4. Worley PH, Mirin AA, Craig AP, Taylor MA, Dennis JM, Vertenstein M (2011) Performance of the community earth system model. In: Proceedings of 2011 international conference for high performance computing, networking, storage and analysis, pp 1–11

  5. Weyn JA, Durran DR, Caruana R (2019) Can machines learn to predict weather? using deep learning to predict gridded 500-hpa geopotential height from historical weather data. Journal of Advances in Modeling Earth Systems 11

  6. Hersbach H, Bell B, Berrisford P, Hirahara S, Horányi A, Muñoz-Sabater J, Nicolas J, Peubey C, Radu R, Schepers D et al (2020) The era5 global reanalysis. Q J R Meteorol Soc 146(730):1999–2049

    Article  ADS  Google Scholar 

  7. Lam R, Sanchez-Gonzalez A, Willson M, Wirnsberger P, Fortunato M, Pritzel A, Ravuri S, Ewalds T, Alet F, Eaton-Rosen Z et al (2022) Graphcast: Learning skillful medium-range global weather forecasting. arXiv:2212.12794

  8. Kashinath K, Mustafa M, Albert A, Wu J, Jiang C, Esmaeilzadeh S, Azizzadenesheli K, Wang R, Chattopadhyay A, Singh A et al (2021) Physics-informed machine learning: case studies for weather and climate modelling. Phil Trans R Soc A 379(2194):20200093

    Article  MathSciNet  CAS  PubMed  ADS  Google Scholar 

  9. Zhou Z, Lin G, Yang K, BAI L, Wang Y et al (2022) Greto: Remedying dynamic graph topology-task discordance via target homophily. In: The eleventh international conference on learning representations

  10. Keisler R (2022) Forecasting global weather with graph neural networks. arXiv:2202.07575

  11. Wang R, Kashinath K, Mustafa M, Albert A, Yu R (2020) Towards physics-informed deep learning for turbulent flow prediction. In: Proceedings of the 26th ACM SIGKDD international conference on knowledge discovery & data mining, pp 1457–1466

  12. Cai W, Ng B, Geng T, Wu L, Santoso A, McPhaden MJ (2020) Butterfly effect and a self-modulating el niño response to global warming. Nature 585(7823):68–73

    Article  CAS  PubMed  ADS  Google Scholar 

  13. Kitaev N, Kaiser Ł, Levskaya A (2020) Reformer: The efficient transformer. arXiv:2001.04451

  14. Molteni F, Buizza R, Palmer TN, Petroliagis T (1996) The ecmwf ensemble prediction system: Methodology and validation. Q J R Meteorol Soc 122(529):73–119

    Article  ADS  Google Scholar 

  15. Lamarque JF, Emmons LK, Hess PG, Kinnison DE, Tilmes S, Vitt F, Heald CL, Holland EA, Lauritzen PH, Neu J (2012) Cam-chem: description and evaluation of interactive atmospheric chemistry in the community earth system model. Geosci Model Dev 5:369–411

    Article  ADS  Google Scholar 

  16. Benjamin SG, Brown JM, Brunet G, Lynch P, Saito K, Schlatter TW (2019) 100 years of progress in forecasting and nwp applications. Meteorol Monogr 59:13–1

    Article  ADS  Google Scholar 

  17. Hewage P, Trovati M, Pereira E, Behera A (2021) Deep learning-based effective fine-grained weather forecasting model. Pattern Anal Applic 24(1):343–366

    Article  Google Scholar 

  18. Ebert-Uphoff I, Hilburn K (2023) The outlook for AI weather prediction. Nature Publishing Group UK London

  19. Shi X, Chen Z, Wang H, Yeung D-Y, Wong W-K, Woo W-C (2015) Convolutional lstm network: A machine learning approach for precipitation nowcasting. Advances in Neural Information Processing Systems 28

  20. Bi K, Xie L, Zhang H, Chen X, Gu X, Tian Q (2022) Pangu-weather: A 3d high-resolution model for fast and accurate global weather forecast. arXiv:2211.02556

  21. Gao Z, Shi X, Wang H, Zhu Y, Wang YB, Li M, Yeung D-Y (2022) Earthformer: Exploring space-time transformers for earth system forecasting. Adv Neural Inf Process Syst 35:25390–25403

    Google Scholar 

  22. Wu H, Zhou H, Long M, Wang J (2023) Interpretable weather forecasting for worldwide stations with a unified deep model. Nature Machine Intelligence, pp 1–10

  23. Kurth T, Subramanian S, Harrington P, Pathak J, Mardani M, Hall D, Miele A, Kashinath K, Anandkumar A (2022) Fourcastnet: Accelerating global high-resolution weather forecasting using adaptive fourier neural operators. arXiv:2208.05419

  24. Qi Y, Li Q, Karimian H, Liu D (2019) A hybrid model for spatiotemporal forecasting of pm2. 5 based on graph convolutional neural network and long short-term memory. Sci Total Environ 664:1–10

    Article  CAS  PubMed  ADS  Google Scholar 

  25. Cachay SR, Erickson E, Bucker AFC, Pokropek E, Potosnak W, Osei S, Lütjens B (2020) Graph neural networks for improved el ni\(\backslash ^{\sim }\) no forecasting. arXiv:2012.01598

  26. Zhou H, Zhang S, Peng J, Zhang S, Li J, Xiong H, Zhang W (2021) Informer: Beyond efficient transformer for long sequence time-series forecasting. In: Proceedings of the AAAI conference on artificial intelligence vol 35, pp 11106–11115

  27. Yu B, Yin H, Zhu Z (2018) Spatio-temporal graph convolutional networks: A deep learning framework for traffic forecasting. In: Proceedings of the 27th international joint conference on artificial intelligence (IJCAI)

  28. Li Y, Yu R, Shahabi C, Liu Y (2018) Diffusion convolutional recurrent neural network: Data-driven traffic forecasting. In: International conference on learning representations (ICLR ’18)

  29. Agarwal A, Caesar L, Marwan N, Maheswaran R, Merz B, Kurths J (2019) Network-based identification and characterization of teleconnections on different scales. Sci Rep 9(1):8808

    Article  PubMed  PubMed Central  ADS  Google Scholar 

  30. Li P, Yu Y, Huang D, Wang Z-H, Sharma A (2023) Regional heatwave prediction using graph neural network and weather station data. Geophys Res Lett 50(7):2023–103405

    Article  Google Scholar 

  31. Wilson T, Tan P-N, Luo L (2018) A low rank weighted graph convolutional approach to weather prediction. In: 2018 IEEE international conference on data mining (ICDM). IEEE

  32. Wang R, Maddix D, Faloutsos C, Wang Y, Yu R (2021) Bridging physics-based and data-driven modeling for learning dynamical systems. In: Learning for dynamics and control, pp 385–398. PMLR

  33. Skarding J, Gabrys B, Musial K (2021) Foundations and modeling of dynamic networks using dynamic graph neural networks: A survey. IEEE Access 9:79143–79168

    Article  Google Scholar 

  34. Sankar A, Wu Y, Gou L, Zhang W, Yang H (2020) Dysat: Deep neural representation learning on dynamic graphs via self-attention networks. In: Proceedings of the 13th international conference on web search and data mining, pp 519–527

  35. Kazemi SM, Goel R, Jain K, Kobyzev I, Sethi A, Forsyth P, Poupart P (2020) Representation learning for dynamic graphs: A survey. J Mach Learn Res 21(1):2648–2720

    MathSciNet  Google Scholar 

  36. BELYTSCHKO T (1989) The finite element method: linear static and dynamic finite element analysis: Thomas jr hughes. Comput Aided Civ Infrastruct Eng 4(3):245–246

  37. Wang R, Yu R (2021) Physics-guided deep learning for dynamical systems: A survey. arXiv:2107.01272

  38. Khandelwal A, Xu S, Li X, Jia X, Kumar V (2020) Physics guided machine learning methods for hydrology

  39. Yuan K, Zhu Q, Li F, Riley WJ, Torn M, Chu H, McNicol G, Chen M, Knox S, Delwiche K et al (2022) Causality guided machine learning model on wetland ch4 emissions across global wetlands. Agric For Meteorol 324:109115

    Article  Google Scholar 

  40. Reichstein M, Camps-Valls G, Stevens B, Jung M, Denzler J, Carvalhais N (2019) Deep learning and process understanding for data-driven earth system science. Nature 566(7743):195–204

    Article  CAS  PubMed  ADS  Google Scholar 

  41. Willard J, Jia X, Xu S, Steinbach M, Kumar V (2020) Integrating physics-based modeling with machine learning: A survey. 1(1):1–34. arXiv:2003.04919

  42. Greenleaf A, Kurylev Y, Lassas M, et al. Cloaked electromagnetic, acoustic, and quantum interference, based on the description in 'Gudder SP (1970) A superposition principle in physics. J Math Phys 11(3):1037–1040

  43. Oroian M, Amariei S, Escriche I, Gutt G (2013) A viscoelastic model for honeys using the time-temperature superposition principle (ttsp). Food Bioproc Tech 6:2251–2260

    Article  Google Scholar 

  44. Helias M, Dahmen D (2020) Statistical field theory for neural networks. Lecture Notes in Physics

  45. Halmos PR, Savage LJ (1949) Application of the radon-nikodym theorem to the theory of sufficient statistics. Ann Math Stat 20(2):225–241

    Article  MathSciNet  Google Scholar 

  46. Sutskever I, Vinyals O, Le QV (2014) Sequence to sequence learning with neural networks. Advances in Neural Information Processing Systems 27

  47. Chen Y, Wu L, Zaki MJ (2020) Iterative deep graph learning for graph neural networks: Better and robust node embeddings

  48. Tian FR (1994) The whitham-type equations and linear overdetermined systems of euler-poisson-darboux type. Duke Math J 74(1):203–221

    Article  MathSciNet  Google Scholar 

  49. Cattaneo C, Fontana L (2003) D’alembert formula on finite one-dimensional networks. J Math Anal Appl 284(2):403–424

    Article  MathSciNet  Google Scholar 

  50. Wazwaz, A-M (2010) Partial Differential Equations and Solitary Waves Theory

  51. Distribution, M (2005) Maxwell-boltzmann distribution. Curve

  52. Cubasch U, Voss R, Hegerl GC, Waszkewitz J, Crowley TJ (1997) Simula935 tion of the influence of solar radiation variations on the global climate with an 936 ocean-atmosphere circulation model. Climate Dynamics 13(11):757–767

    Article  ADS  Google Scholar 

  53. Black CA, Macdonald TH (1965) Long-wave radiation

  54. Carpenter I, Archibald R, Evans KJ, Larkin J, Micikevicius P, Norman M, Rosinski J, Schwarzmeier J, Taylor MA (2013) Progress towards accelerating homme on hybrid multi-core systems. Int J High Perform Comput Appl 27(3):335–347

    Article  Google Scholar 

  55. Kopera MA, Giraldo FX (2014) Analysis of adaptive mesh refinement for imex discontinuous galerkin solutions of the compressible euler equations with application to atmospheric simulations. J Comput Phys 275:92–117

    Article  MathSciNet  ADS  Google Scholar 

  56. Qin R, Duan C (2017) The principle and applications of bernoulli equation. In: Journal of physics: conference series, vol 916, pp 012038. IOP Publishing

  57. Meniko R, Plohr BJ (1989) The riemann problem for fluid flow of real materials. Rev Mod Phys 61(1):75–130

    Article  MathSciNet  ADS  Google Scholar 

  58. Belkin M, Niyogi P (2001) Laplacian eigenmaps and spectral techniques for embedding and clustering. Adv Neural Inf Process Syst 14(6):585–591

    Google Scholar 

  59. Wang S, Li Y, Zhang J, Meng Q, Meng L, Gao F (2020) Pm2. 5-gnn: A domain knowledge enhanced graph neural network for pm2. 5 forecasting. In: Proceedings of the 28th international conference on advances in geographic information systems, pp 163–166

  60. Rasp S, Dueben PD, Scher S, Weyn JA, Thuerey N (2020) Weatherbench: A benchmark data set for data-driven weather forecasting. Journal of Advances in Modeling Earth Systems 12(11)

  61. Bai L, Yao L, Li C, Wang X, Wang C (2020) Adaptive graph convolutional recurrent network for traffic forecasting. Adv Neural Inf Process Syst 33:17804–17815

    Google Scholar 

  62. Xu D, Ruan C, Korpeoglu E, Kumar S, Achan K (2020) Inductive representation learning on temporal graphs. arXiv:2002.07962

  63. Wu Z, Pan S, Long G, Jiang J, Zhang C (2019) Graph wavenet for deep spatial-temporal graph modeling. CoRR arXiv:1906.00121

  64. Vitart F, Ardilouze C, Bonet A, Brookshaw A, Chen M, Codorean C, Déqué M, Ferranti L, Fucile E, Fuentes M et al (2017) The subseasonal to seasonal (s2s) prediction project database. Bull Am Meteorol Soc 98(1):163–173

    Article  ADS  Google Scholar 

  65. Medium-Range Weather Forecasts EC (2023) S2S, ECMWF, Reforecasts, Instantaneous and Accumulated. https://apps.ecmwf.int/datasets/data/s2s-reforecasts-instantaneous-accum-ecmf/

  66. Liang J, Chen K, Xian Z (2021) Assessment of fy-2g atmospheric motion vector data and assimilating impacts on typhoon forecasts. Earth Space Sci 8(6):2020–001628

    Article  Google Scholar 

  67. Runge J, Petoukhov V, Donges JF, Hlinka J, Jajcay N, Vejmelka M, Hartman D, Marwan N, Paluš M, Kurths J (2015) Identifying causal gateways and mediators in complex spatio-temporal systems. Nat Commun 6(1):8502

    Article  CAS  PubMed  ADS  Google Scholar 

  68. Li F, Zhu Q, Riley WJ, Yuan K, Wu H, Gui Z (2022) Wetter california projected by cmip6 models with observational constraints under a high ghg emission scenario. Earth’s Future 10(4):2022–002694

    Article  Google Scholar 

  69. Silva FN, Vega-Oliveros DA, Yan X, Flammini A, Menczer F, Radicchi F, Kravitz B, Fortunato S (2021) Detecting climate teleconnections with granger causality. Geophys Res Lett 48(18):2021–094707

    Article  Google Scholar 

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Funding

This work was supported by the Natural Science Foundation of Jilin Province (Grant 20230101062JC), the National Key Research and Development Plan of China (Grant 2017YFC1502306), and the National Natural Science Foundation of China (No. 42175052, No. 61902143, No. 62272190, and No. U19A2061).

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Z. Xu. (First Author) : Conceptualization, Methodology, Software, Investigation, Formal Analysis, Writing - Original Draft; X. Wei: Resources, Supervision; J. Hao: Data Curation, Software, Validation; J. Han: Data Curation, Software; H. Li (Corresponding Author): Resources, Supervisio, Visualization, Writing - Review and Editing; C. Liu: Resources, Supervision; Z. Li: Visualization, Investigation; D. Tian: Conceptualization, Investigation; N. Zhang: Software, Validation; All authors have reviewed the manuscript. We confirm that the manuscript has been read and approved by all named authors and that there are no other persons who satisfied the criteria for authorship but are not listed. We further confirm that the order of authors listed in the manuscript has been approved by all of us. We understand that the Corresponding Author is the sole contact for the Editorial process. He/she is responsible for communicating with the other authors about progress, submissions of revisions and final approval of proofs.

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Correspondence to Hongliang Li.

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Xu, Z., Wei, X., Hao, J. et al. DGFormer: a physics-guided station level weather forecasting model with dynamic spatial-temporal graph neural network. Geoinformatica (2024). https://doi.org/10.1007/s10707-024-00511-1

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