Machine-Learning based model order reduction of a biomechanical model of the human tongue

Abstract

Background and Objectives: This paper presents the results of a Machine-Learning based Model Order Reduction (MOR) method applied to a complex 3D Finite Element (FE) biomechanical model of the human tongue, in order to create a Digital Twin Model (DTM) that enables real-time simulations. The DTM is designed for future inclusion in a computer assisted protocol for tongue surgery planning. Methods: The proposed method uses an "a posteriori" MOR that allows, from a limited number of simulations with the FE model, to predict in real time mechanical responses of the human tongue to muscle activations. Results: The MOR method is evaluated for simulations associated with separate single tongue muscle activations. It is shown to be able to account with a sub-millimetric spatial accuracy for the non-linear dynamical behavior of the tongue model observed in these simulations.

Data-driven modeling and prediction of non-linearizable dynamics via spectral submanifolds

“…at leading order in ϵ. All stable and unstable periodic responses on the SSM are fixed points of system (7), with their amplitudes ρ 0 and phases ψ 0 satisfying the equations…”

“…( 8) predicts the behavior of a nonlinearizable dynamical system under forcing based solely on unforced training data. The stability of the predicted periodic response follows from a simple linear analysis at the corresponding fixed point of the ODE (7). The first formula in (8) also contains another frequently used notion of nonlinear vibration analysis, the dissipative backbone curve ω(ρ), which describes the instantaneous amplitude-frequency relation along freely decaying vibrations within the SSM.…”

“…6, steady states of periodically forced sloshing were measured in sweeps over a range of forcing frequencies under three different shaker amplitudes. As in the previous beam example, we identify the corresponding forcing amplitude, f, in (7) at the maximal amplitude response of each frequency sweep. Shown in panels (e, f) of Fig.…”

“…Projecting the full dynamics to the most energetic linear modes, POD requires the knowledge of the governing equations of the system and hence is inapplicable when only data is available. As purely data-based alternatives, machine learning methods are broadly considered and tested in various fields [4][5][6][7] . While the black-box approach of machine learning might often seem preferable to a detailed nonlinear analysis, the resulting neural network models require extensive tuning, lack physical interpretability, generally perform poorly outside their training range and tend to be unnecessarily complex 8 .…”

A Pointwise Evaluation Metric to Visualize Errors in Machine Learning Surrogate Models

“…Despite their benefits, especially in simple quantitative comparison of the ML and numerical models, they might be barely interpretable [22]. Therefore, it is a common practice to visualize the prediction, comparing to the corresponding testing target, typically by mapping the results onto the numerical model [23][24][25]. However, they may not replace the local metrics that can enable pointwise visualization of the errors associated with all the samples.…”