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The hydrodynamic forces on an oscillating circular cylinder are predicted using neural networks under flow conditions where Vortex-Induced Vibrations (VIV) are known to occur. The derived neural network approximators are then incorporated in a dynamical model that allows prediction of the cylinder motion given flow conditions and initial conditions. Using experimental data, a minimum-least-squares compensator is tuned that includes linear stiffness and damping su-perimposed with a constant force offset. The compensator is decoupled, i.e., with equations in-dependent for each degree of freedom. By applying the neural network approximators and the derived compensator simulated experiments can be performed. These simulated experiments show that the compensator which cancels the linear components and any bias in the hydrody-namic forces effectively stabilizes the VIV motion. To support this time-domain analysis is per-formed along with phase-plane investigations. Maximum Lyapunov exponent analysis is also shown.
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Simulating Partial Differential Equations with Neural Networks
In this paper, we present a novel approach for simulating solutions of partial differential equations using neural networks. We consider a time-stepping method similar to the finite-volume method, where the flux terms are computed using neural networks. To train the neural network, we collect 'sensor' data on small subsets of the computational domain. Thus, our neural network learns the local behavior of the solution rather than the global one. This leads to a much more versatile method that can simulate the solution to equations whose initial conditions are not in the same form as the initial conditions we train with. Also, using sensor data from a small portion of the domain is much more realistic than methods where a neural network is trained using data over a large domain.
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- PAR ID:
- 10535725
- Editor(s):
- Pares, C; Castro, M; Morales_de_Luna, T; Munoz_Ruiz, M
- Publisher / Repository:
- Springer Nature Switzerland
- Date Published:
- Volume:
- 35
- ISSN:
- 978-3-031-55264-9
- ISBN:
- 978-3-031-55264-9
- Page Range / eLocation ID:
- 39-49
- Subject(s) / Keyword(s):
- Neural networks · Partial differential equations · Finite-volume methods
- Format(s):
- Medium: X
- Location:
- Hyperbolic Problems: Theory, Numerics, Applications. Volume II
- Sponsoring Org:
- National Science Foundation
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