Contribution
Modelling band structure properties using physics-informed machine learning
* Presenting author
Abstract:
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. However, having access to a numerical model is a good starting point for data-driven discovery. Our approach employed the Webster equation for unit cell and Floquet-Bloch theory for periodic structures with waveguide parametrized by cubic splines. Analytical formulae relating the waveguide geometry to the corresponding dispersion relation were extracted using methods of physics-informed machine learning, such as coordinate transformation and symbolical regression. These results provide a deeper understanding of the underlying principles and offer an efficient alternative to computationally demanding numerical optimization. Moving towards a Schrödinger-like equation and parametrization by Gaussian curvature allows for a more multiphysical approach but also faces some challenges in terms of geometry feasibility limits.