Many processes in science and engineering can be described by partial
differential equations (PDEs). Traditionally, PDEs are derived by considering
first principles of physics to derive the relations between the involved
physical quantities of interest. A different approach is to measure the
quantities of interest and use deep learning to reverse engineer the PDEs which
are describing the physical process.
In this paper we use machine learning, and deep learning in particular, to
discover PDEs hidden in complex data sets from measurement data. We include
examples of data from a known model problem, and real data from weather station
measurements. We show how necessary transformations of the input data amounts
to coordinate transformations in the discovered PDE, and we elaborate on
feature and model selection. It is shown that the dynamics of a non-linear,
second order PDE can be accurately described by an ordinary differential
equation which is automatically discovered by our deep learning algorithm. Even
more interestingly, we show that similar results apply in the context of more
complex simulations of the Swedish temperature distribution.
%0 Generic
%1 berg2018datadriven
%A Berg, Jens
%A Nyström, Kaj
%D 2018
%K deeplearning pde sparseregression
%R 10.1016/j.jcp.2019.01.036
%T Data-driven discovery of PDEs in complex datasets
%U http://arxiv.org/abs/1808.10788
%X Many processes in science and engineering can be described by partial
differential equations (PDEs). Traditionally, PDEs are derived by considering
first principles of physics to derive the relations between the involved
physical quantities of interest. A different approach is to measure the
quantities of interest and use deep learning to reverse engineer the PDEs which
are describing the physical process.
In this paper we use machine learning, and deep learning in particular, to
discover PDEs hidden in complex data sets from measurement data. We include
examples of data from a known model problem, and real data from weather station
measurements. We show how necessary transformations of the input data amounts
to coordinate transformations in the discovered PDE, and we elaborate on
feature and model selection. It is shown that the dynamics of a non-linear,
second order PDE can be accurately described by an ordinary differential
equation which is automatically discovered by our deep learning algorithm. Even
more interestingly, we show that similar results apply in the context of more
complex simulations of the Swedish temperature distribution.
@misc{berg2018datadriven,
abstract = {Many processes in science and engineering can be described by partial
differential equations (PDEs). Traditionally, PDEs are derived by considering
first principles of physics to derive the relations between the involved
physical quantities of interest. A different approach is to measure the
quantities of interest and use deep learning to reverse engineer the PDEs which
are describing the physical process.
In this paper we use machine learning, and deep learning in particular, to
discover PDEs hidden in complex data sets from measurement data. We include
examples of data from a known model problem, and real data from weather station
measurements. We show how necessary transformations of the input data amounts
to coordinate transformations in the discovered PDE, and we elaborate on
feature and model selection. It is shown that the dynamics of a non-linear,
second order PDE can be accurately described by an ordinary differential
equation which is automatically discovered by our deep learning algorithm. Even
more interestingly, we show that similar results apply in the context of more
complex simulations of the Swedish temperature distribution.},
added-at = {2021-09-10T14:14:48.000+0200},
author = {Berg, Jens and Nyström, Kaj},
biburl = {https://www.bibsonomy.org/bibtex/2d61a3ac2e5a8ac82c9603df6c7be5397/annakrause},
description = {1808.10788.pdf},
doi = {10.1016/j.jcp.2019.01.036},
interhash = {9d89a8619337d3894f8f1e93650629c3},
intrahash = {d61a3ac2e5a8ac82c9603df6c7be5397},
keywords = {deeplearning pde sparseregression},
note = {cite arxiv:1808.10788},
timestamp = {2021-09-10T14:14:48.000+0200},
title = {Data-driven discovery of PDEs in complex datasets},
url = {http://arxiv.org/abs/1808.10788},
year = 2018
}