Wave Equation

The wave equation, a fundamental partial differential equation describing wave propagation, is a subject of intense research focusing on efficient and accurate solution methods, particularly for complex nonlinear systems. Current efforts leverage machine learning, employing architectures like physics-informed neural networks (PINNs), Fourier neural operators (FNOs), and deep operator networks, often incorporating physical constraints and conservation laws into the model design to improve accuracy and generalization. These advancements have significant implications for diverse fields, including seismic imaging, acoustic modeling, and the simulation of nonlinear phenomena, offering faster and potentially more accurate solutions than traditional numerical techniques.