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Description
The investigation of strong acoustic fields in closed, piston-driven resonators is a classical problem in nonlinear acoustics. One of the possible approaches consists in deriving a modified Burgers’ equation for this case and solving it by projecting onto a set of (coupled) harmonics. This procedure even provides certain asymptotic closed-form solutions. In this paper, a similar problem is addressed using data-driven methods. Specifically, symbolic regression is used to provide interpretable analytical expressions that relate the system’s inputs (material parameters, geometry, and excitation amplitude) to its outputs (the magnitude and phase of individual harmonics). The advantage of incorporating prior expert knowledge lies in its ability to constrain the search space and subsequently obtain extensions beyond the asymptotic regime, while seamlessly incorporating boundary layer losses, otherwise formulated through a cumbersome integro-differential expression. The resulting relations very well reflect the energy distribution along the harmonic cascade, and interesting information can also be drawn from the phase shifts when boundary layer losses are taken into account. The results presented correspond to the asymptotic solution by design, and their comparison with numerical validation is satisfactory.