Section: Research Program

Full waveform inversion for the optimal design of wind musical instruments

Makers have improved wind musical instruments (as flutes, trumpets, clarinets, bassoons, ...) in the past by a “trial and error” procedure, where the final sound and ease of the instrument in playing conditions are the main criteria. Although the playing context should still be the final reference, we can consider intermediate measurements of the pipe entry impedance  [75], [69], which quantifies the Dirichlet-to-Neumann map of the wave propagation in the pipe, and relies on mathematical simulations based on accurate and concise models of the pipe  [84], [59] and the embouchure  [77], [59], [55], [56], [86] in order to foresee the behavior of a given instrument, and therefore optimize it. A strong interaction with makers and players is necessary for defining both operable criteria quantified as a cost function and a design parameters space. We aim at building efficient musical instrument via handcrafted techniques but also modern tools as additive synthesis (3D printers). We plan to implement state-of-the-art numerical methods (finite elements, full waveform inversion, neuronal networks fed by numerical simulations, diverse optimization techniques...) that are versatile (in terms of models, formulations, couplings...) in order to solve the optimization problem, after a proper modeling of the linear and nonlinear coupled phenomena. We wish to take advantage of the fact that sound waves in musical instruments satisfy the laws of acoustics in pipes (PDEs), which leads to use FWI technique, in harmonic or temporal regime. We propose to implement an iterative process between instrument making and optimal design in order to build instruments that optimize tone quality and playability. We are currently collaborating with musical acoustics teams who have a strong experimental background on this question  [66], [67] [DCY12, DF07, GPP98], we wish to strenghten the links we have with other teams  [78], [72], [80], [81], [85], we will participate to professional clusters [ITE], and we are currently collaborating with makers and museums directly : Augustin Humeau (Dordogne) for the bassoon, Luc Gallois (Oise) and the Museum of Cité de la Musique - Philharmonie de Paris for the brass instruments. This research axis is surely the most exploratory of our research program and follows the successful ”Exploratory Research Program” Inria grant obtained in 2017. It could pave the way for significant progresses in inverse problem solving. Indeed, the problem depends on a few number of parameters unlike geophysical or astrophysical problems. We can thus use it to test different methods like neuronal networks, statistical methods, coupling with nonlinear phenomena, and decide if it could be applied to large scale applications.