Physics-based and Machine learning predictions of maneuvering forces in unsteady inflow conditions

Multi-vessel coordination and controlled maneuvering through upstream wakes is important to a wide range of marine applications; from surface ships to autonomous underwater vehicles. In this work we study the predictive performance of physics-based and machine-learning (ML) models for unsteady inflow maneuvering forces using tandem flapping foils as a model system. Two physics-based approaches, one following simple quasi-steady assumptions and another that modifies classical Theodorsen, are found to perform fairly well when there are only mild interactions with the upstream wake, with minimum error levels of around 6%. However, this error increases to 40% when there is strong wake interaction. Three ML models were trained and tested; a Long Short-Term Memory (LSTM) model, a Neural Ordinary Differential Equations (NODE) model, and a Sparse Identification of Nonlinear Dynamics (SINDy) approach. We find that all three models can match the low error of the physics-based for mild inflow unsteadiness and are capable of improving the predictions in the case of strong interactions, reducing the error levels below 20%. While these ML models require substantial training data and care in choosing their meta-parameters, their predictions do prove to be more reliable for a wider range of unsteadiness conditions as well as potentially still producing human-interpretable models (in the case of SINDy), making them an interesting research direction for further study.