PDE Solver

Partial differential equation (PDE) solvers are crucial for modeling diverse physical phenomena, but traditional numerical methods can be computationally expensive. Current research focuses on developing faster and more accurate deep learning-based solvers, employing architectures like Fourier Neural Operators, graph neural networks, and physics-informed neural networks (PINNs), often incorporating techniques like operator splitting and autoregressive models to improve stability and efficiency. These advancements aim to accelerate simulations across various scientific and engineering disciplines, enabling real-time applications and tackling previously intractable problems. However, challenges remain in addressing issues like generalization, data efficiency, and ensuring the reliability and interpretability of these learned solvers.