About Our Research
Our group focuses on the intersection of physics-informed machine learning and physical acoustics. We leverage data-driven methods to bridge the gap between complex numerical simulations and interpretable physical models. By employing advanced symbolic regression and optimization algorithms, we discover the underlying governing equations of nonlinear wave phenomena and optimize the band structure properties of periodic sonic crystals.
Topic 1: Data-Driven Discovery of Weakly Nonlinear Wave Equations
In this article, data-driven methods for discovering governing equations are brought to the field of finite-amplitude acoustics, and the associated challenges are examined. One significant difficulty is the numerical evaluation of derivatives in the vicinity of shocks, which is solved by employing a weak formulation of the partial differential equations. For benchmarking, the classical model equations in the weakly nonlinear regime are recovered from data: the Westervelt equation for purely progressive waves and the Kuznetsov equation for interfering waves. The results further demonstrate that the approach is applicable to partial differential equations involving a second time derivative, as well as to problems in more than one spatial dimension.
- We establish a procedure to discover weakly nonlinear acoustic wave equations.
- Weak formulation avoids unreliable numerical derivatives near shocks.
- We benchmark the method in 1D and 2D on Westervelt and Kuznetsov equations.
Topic 2: Modelling Band Structure Properties using Symbolic Regression
Although the variety of analytical approaches and numerical methods to solve sonic crystal problems is wide, the known analytical expressions used to model the band structure properties are limited to a few special cases. Having an access to a numerical model is a good starting point for data-driven discovery. In this case, a symbolic regression based on genetic optimization is employed. Our previous results provide a deeper understanding of the underlying principles and offer an efficient alternative to computationally demanding numerical optimization. Moving towards a Schr ̈odinger-like equation and parametrization by Gaussian curvature allows for a more multiphysical approach but also faces some challenges in terms of geometry feasibility limits.
- Symbolic regression is employed to obtain transmission properties of 1D sonic crystals.
- Discovered formulas directly relate unit cell geometry and bandgap characteristics
- Efficient alternative to computationally demanding numerical optimization and provides a deeper understanding of the underlying principles
Selected Publications
V. Hruška, A. Furmanová, T. Filipská, J. Valášek. "Data-driven discovery of weakly nonlinear wave equations." Journal of Sound and Vibration (2026). DOI: 10.1016/j.jsv.2025.119625
V. Hruška, A. Furmanová, M. Bednařík "Analytical formulae for design of one-dimensional sonic crystals with smooth geometry based on symbolic regression." Journal of Sound and Vibration (2025). DOI: 10.1016/j.jsv.2024.118821
A. Furmanová, V. Hruška, A. Bajićová. "Machine learning for modelling band structure properties" Proceedings of the 11th Convention of the European Acoustics Association Forum Acusticum / EuroNoise 2025. DOI: 10.61782/fa.2025.0539