Journal
NEW JOURNAL OF PHYSICS
Volume 23, Issue 4, Pages -Publisher
IOP Publishing Ltd
DOI: 10.1088/1367-2630/abeb90
Keywords
complex systems; nonlinear dynamics; prediction; machine learning; hybrid model; partial differential equations
Categories
Funding
- DFG/FAPESP [IRTG 1740/TRP 2015/50122-0]
- Volkswagen foundation
- European Union's Horizon 2020 research and innovation programme [820970]
- Russian Ministry of Science and Education [13.1902.21.0026]
- German Federal Ministry of Education and Research
- Land Brandenburg
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By augmenting differential equations with artificial neural networks, it is possible to predict complex systems even with short and incomplete datasets. This approach is effective for high-dimensional chaotic systems and can forecast a horizon significantly longer than the training data length.
Video Abstract Video Abstract: Neural partial differential equations for chaotic systems When predicting complex systems one typically relies on differential equation which can often be incomplete, missing unknown influences or higher order effects. By augmenting the equations with artificial neural networks we can compensate these deficiencies. We show that this can be used to predict paradigmatic, high-dimensional chaotic partial differential equations even when only short and incomplete datasets are available. The forecast horizon for these high dimensional systems is about an order of magnitude larger than the length of the training data.
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