Articles | Volume 13, issue 7
https://doi.org/10.5194/gmd-13-3373-2020
https://doi.org/10.5194/gmd-13-3373-2020
Model description paper
 | 
30 Jul 2020
Model description paper |  | 30 Jul 2020

PDE-NetGen 1.0: from symbolic partial differential equation (PDE) representations of physical processes to trainable neural network representations

Olivier Pannekoucke and Ronan Fablet

Related authors

HyPhAICC v1.0: a hybrid physics–AI approach for probability fields advection shown through an application to cloud cover nowcasting
Rachid El Montassir, Olivier Pannekoucke, and Corentin Lapeyre
Geosci. Model Dev., 17, 6657–6681, https://doi.org/10.5194/gmd-17-6657-2024,https://doi.org/10.5194/gmd-17-6657-2024, 2024
Short summary
Toward a multivariate formulation of the parametric Kalman filter assimilation: application to a simplified chemical transport model
Antoine Perrot, Olivier Pannekoucke, and Vincent Guidard
Nonlin. Processes Geophys., 30, 139–166, https://doi.org/10.5194/npg-30-139-2023,https://doi.org/10.5194/npg-30-139-2023, 2023
Short summary
SymPKF (v1.0): a symbolic and computational toolbox for the design of parametric Kalman filter dynamics
Olivier Pannekoucke and Philippe Arbogast
Geosci. Model Dev., 14, 5957–5976, https://doi.org/10.5194/gmd-14-5957-2021,https://doi.org/10.5194/gmd-14-5957-2021, 2021
Short summary
A methodology to obtain model-error covariances due to the discretization scheme from the parametric Kalman filter perspective
Olivier Pannekoucke, Richard Ménard, Mohammad El Aabaribaoune, and Matthieu Plu
Nonlin. Processes Geophys., 28, 1–22, https://doi.org/10.5194/npg-28-1-2021,https://doi.org/10.5194/npg-28-1-2021, 2021
Short summary
Parametric covariance dynamics for the nonlinear diffusive Burgers equation
Olivier Pannekoucke, Marc Bocquet, and Richard Ménard
Nonlin. Processes Geophys., 25, 481–495, https://doi.org/10.5194/npg-25-481-2018,https://doi.org/10.5194/npg-25-481-2018, 2018
Short summary

Related subject area

Numerical methods
Hydro-geomorphological modelling of leaky wooden dam efficacy from reach to catchment scale with CAESAR-Lisflood 1.9j
Joshua M. Wolstenholme, Christopher J. Skinner, David Milan, Robert E. Thomas, and Daniel R. Parsons
Geosci. Model Dev., 18, 1395–1411, https://doi.org/10.5194/gmd-18-1395-2025,https://doi.org/10.5194/gmd-18-1395-2025, 2025
Short summary
Enhancing single precision with quasi-double precision: achieving double-precision accuracy in the Model for Prediction Across Scales – Atmosphere (MPAS-A) version 8.2.1
Jiayi Lai, Lanning Wang, Qizhong Wu, Yizhou Yang, and Fang Wang
Geosci. Model Dev., 18, 1089–1102, https://doi.org/10.5194/gmd-18-1089-2025,https://doi.org/10.5194/gmd-18-1089-2025, 2025
Short summary
Advances in land surface forecasting: a comparison of LSTM, gradient boosting, and feed-forward neural networks as prognostic state emulators in a case study with ecLand
Marieke Wesselkamp, Matthew Chantry, Ewan Pinnington, Margarita Choulga, Souhail Boussetta, Maria Kalweit, Joschka Bödecker, Carsten F. Dormann, Florian Pappenberger, and Gianpaolo Balsamo
Geosci. Model Dev., 18, 921–937, https://doi.org/10.5194/gmd-18-921-2025,https://doi.org/10.5194/gmd-18-921-2025, 2025
Short summary
Subgrid corrections for the linear inertial equations of a compound flood model – a case study using SFINCS 2.1.1 Dollerup release
Maarten van Ormondt, Tim Leijnse, Roel de Goede, Kees Nederhoff, and Ap van Dongeren
Geosci. Model Dev., 18, 843–861, https://doi.org/10.5194/gmd-18-843-2025,https://doi.org/10.5194/gmd-18-843-2025, 2025
Short summary
Introducing Iterative Model Calibration (IMC) v1.0: a generalizable framework for numerical model calibration with a CAESAR-Lisflood case study
Chayan Banerjee, Kien Nguyen, Clinton Fookes, Gregory Hancock, and Thomas Coulthard
Geosci. Model Dev., 18, 803–818, https://doi.org/10.5194/gmd-18-803-2025,https://doi.org/10.5194/gmd-18-803-2025, 2025
Short summary

Cited articles

Auer, M., Tschurtschenthaler, T., and Biffl, S.: A Flyweight UML Modelling Tool for Software Development in Heterogeneous Environments, in: Proceedings of the 29th Conference on EUROMICRO, EUROMICRO '03, 267 pp., IEEE Computer Society, Washington, DC, USA, https://doi.org/10.5555/942796.943259, 2003. a
Bolton, T. and Zanna, L.: Applications of Deep Learning to Ocean Data Inference and Subgrid Parameterization, J. Adv. Model. Earth Syst., 11, 376–399, https://doi.org/10.1029/2018ms001472, 2019. a
Cai, J.-F., Dong, B., Osher, S., and Shen, Z.: Image restoration: Total variation, wavelet frames, and beyond, J. Am. Math. Soc., 25, 1033–1089, https://doi.org/10.1090/s0894-0347-2012-00740-1, 2012. a
Chollet, F.: Deep Learning with Python, Manning Publications, 2018. a
Dong, B., Jiang, Q., and Shen, Z.: Image Restoration: Wavelet Frame Shrinkage, Nonlinear Evolution PDEs, and Beyond, Multiscale Model. Sim., 15, 606–660, https://doi.org/10.1137/15m1037457, 2017. a
Download
Short summary
Learning physics from data using a deep neural network is a challenge that requires an appropriate but unknown network architecture. The package introduced here helps to design an architecture by translating known physical equations into a network, which the experimenter completes to capture unknown physical processes. A test bed is introduced to illustrate how this learning allows us to focus on truly unknown physical processes in the hope of making better use of data and digital resources.
Share