Abstract
General circulation models are essential tools in weather and hydrodynamic simulation. They solve discretized, complex physical equations in order to compute evolutionary states of dynamical systems, such as the hydrodynamics of a lake. However, high-resolution numerical solutions using such models are extremely computational and time consuming, often requiring a high performance computing architecture to be executed satisfactorily. Machine learning (ML)-based low-dimensional surrogate models are a promising alternative to speed up these simulations without undermining the quality of predictions. In this work, we develop two examples of fast, reliable, low-dimensional surrogate models to produce a 36 h forecast of the depth-averaged hydrodynamics at Lake George NY, USA. Our ML approach uses two widespread artificial neural network (ANN) architectures: fully connected neural networks and long short-term memory. These ANN architectures are first validated in the deterministic and chaotic regimes of the Lorenz system and then combined with proper orthogonal decomposition (to reduce the dimensionality of the incoming input data) to emulate the depth-averaged hydrodynamics of a flow simulator called SUNTANS. Results show the ANN-based reduced order models have promising accuracy levels (within \(6\%\) of the prediction range) and advocate for further investigation into hydrodynamic applications.
Keywords
- Model reduction
- Dynamical systems
- Artificial neural networks
- Water circulation
Supported by The Jefferson Project at Lake George, which is a collaboration of Rensselaer Polytechnic Institute, IBM, and The FUND for Lake George.
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- 1.
Writing the correlation matrix as an integral over the domain \(\varOmega \) means that we are weighting each variable in the vector \(q'\) associated to a lattice point \(\mathbf {x}_{i}\) with the corresponding volume \(V_{i}\) of a fictitious control volume enclosing that lattice point. For fluctuation data \(q'\) collected from unstructured finite element-like grids, the enclosing volume of a point \(\mathbf {x}_{i}\) taken at the centroid of a mesh cell is the cell’s own volume.
- 2.
Relative errors are not suited for the analysis because the time derivative of the reference solution has many values close to zero.
- 3.
The LSTM minimization algorithm finds 264, 690 optimal weights and biases while FCNN requires only 55, 101.
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Costa Nogueira, A., de Sousa Almeida, J.L., Auger, G., Watson, C.D. (2020). Reduced Order Modeling of Dynamical Systems Using Artificial Neural Networks Applied to Water Circulation. In: Jagode, H., Anzt, H., Juckeland, G., Ltaief, H. (eds) High Performance Computing. ISC High Performance 2020. Lecture Notes in Computer Science(), vol 12321. Springer, Cham. https://doi.org/10.1007/978-3-030-59851-8_8
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