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Many real-world dynamical systems relevant in acoustics are nonlinear, from the most straightforward vibrating string to the propagation of large-amplitude sound waves. Likewise, most of the sound-emitting interactions between two or more bodies are nonlinear. These phenomena have been traditionally described by partial differential equations, which are often hard to solve and expensive to simulate numerically. In recent years, data-driven methods have proven to be a promising approach in modeling physical systems. We aim at investigating the application of deep learning-based techniques in solving nonlinear differential equations in the acoustic domain. In particular, we focus on modern advancements of the Koopman theory, which allow linearizing strongly nonlinear dynamics by learning a tractable representation of the otherwise infinite-dimensional Koopman operator from data. The motivation is twofold. First, linear system theory is well-understood, and the linearization of nonlinear dynamics enables the application of standard textbook methods for analysis, prediction, and control. Second, advancing a linear system in time amounts to simple matrix multiplication, a highly desired property with a view to the real-time simulation of complex physical systems.