Numerical Solver

Numerical solvers are algorithms designed to approximate solutions to mathematical equations, particularly partial differential equations (PDEs), which model numerous physical phenomena. Current research focuses on improving solver efficiency and accuracy, particularly for complex geometries and high-dimensional problems, using machine learning techniques such as physics-informed neural networks (PINNs), graph neural networks (GNNs), and Fourier neural operators (FNOs), often combined with traditional methods. These advancements aim to overcome limitations of classical solvers, such as computational cost and scalability issues, enabling faster and more accurate simulations across diverse scientific and engineering disciplines. The resulting improvements have significant implications for fields like fluid dynamics, climate modeling, and high-energy physics.