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Geoscientific Model Development An interactive open-access journal of the European Geosciences Union
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Discussion papers
https://doi.org/10.5194/gmd-2020-35
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/gmd-2020-35
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.

Submitted as: model description paper 02 Mar 2020

Submitted as: model description paper | 02 Mar 2020

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This preprint is currently under review for the journal GMD.

PDE-NetGen 1.0: from symbolic PDE representations of physical processes to trainable neural network representations

Olivier Pannekoucke1 and Ronan Fablet2 Olivier Pannekoucke and Ronan Fablet
  • 1INPT-ENM, UMR CNRS CNRM, CERFACS, 42, av. G. Coriolis 31057 Toulouse, France
  • 2IMT-Atlantic, UMR CNRS Lab-STICC, Brest, France

Abstract. Bridging physics and deep learning is a topical challenge. While deep learning frameworks open avenues in physical science, the design of physically-consistent deep neural network architectures is an open issue. In the spirit of physics-informed NNs, PDE-NetGen package provides new means to automatically translate physical equations, given as PDEs, into neural network architectures. PDE-NetGen combines symbolic calculus and a neural network generator. The later exploits NN-based implementations of PDE solvers using Keras. With some knowledge of a problem, PDE-NetGen is a plug-and-play tool to generate physics-informed NN architectures. They provide computationally-efficient yet compact representations to address a variety of issues, including among others adjoint derivation, model calibration, forecasting, data assimilation as well as uncertainty quantification. As an illustration, the workflow is first presented for the 2D diffusion equation, then applied to the data-driven and physics-informed identification of uncertainty dynamics for the Burgers equation.

Olivier Pannekoucke and Ronan Fablet

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Status: open (until 27 Apr 2020)
Status: open (until 27 Apr 2020)
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Olivier Pannekoucke and Ronan Fablet

Olivier Pannekoucke and Ronan Fablet

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Latest update: 28 Mar 2020
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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.
Learning physics from data using a deep neural network is a challenge that requires an...
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