Deep learning for predicting frequency lock-in of a freely vibrating sphere
Bibliographic record
Abstract
In this paper, we present a deep learning-based reduced-order model (DL-ROM) for the stability prediction of unsteady three-dimensional fluid–structure interaction systems. The proposed DL-ROM has the format of a nonlinear state-space model and employs a recurrent neural network with long short-term memory (LSTM) cells. We consider a canonical fluid–structure system of an elastically mounted sphere coupled with the incompressible fluid flow in a state-space format. Specifically, we develop a nonlinear data-driven coupling for predicting the unsteady forces and the vortex-induced vibration (VIV) lock-in of the freely vibrating sphere in a transverse direction. We design an input–output relationship as a temporal sequence of force and displacement datasets for a low-dimensional approximation of the fluid–structure system. Based on the prior knowledge of the VIV lock-in process, the input function contains a range of frequencies and amplitudes, which significantly affects the system realization ability and enables an efficient DL-ROM without the need for a massive training dataset for the low-dimensional modeling. Once trained, the network provides a nonlinear mapping of input–output dynamics that can predict the coupled fluid–structure dynamics for a longer horizon via the feedback process. By integrating the LSTM network with the eigensystem realization algorithm (ERA), we construct a data-driven state-space model for the reduced-order stability analysis. We investigate the underlying mechanism and stability characteristics of VIV of a freely vibrating sphere via an eigenvalue selection process. Using the reduced-order eigenvalue analysis, we characterize the vibrating sphere-wake lock-in phenomenon and demonstrate that the lock-in responds at preferred vibration frequencies. To understand the frequency lock-in mechanism, we study the eigenvalue trajectories for a range of the reduced oscillation frequencies and the mass ratios. Consistent with the full-order simulations, the frequency lock-in branches are accurately captured by the combined LSTM-ERA procedure. The proposed DL-ROM aligns with the development of physics-based digital twin of engineering systems involving moving boundaries and fluid–structure interactions.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".