DFS-PINN: A Dynamic Feature Separation Physics-Informed Neural Network

Abstract

Physics-Informed Neural Networks (PINNs) have shown great promise for solving partial differential equations (PDEs), but their application to multi-dimensional problems often suffers from the curse of dimensionality, leading to exponential growth in computational and memory requirements. Moreover, accurately capturing complex local features, such as those found in fluid flows, remains a significant challenge for existing approaches. To address these challenges, we propose the Dynamic Feature Separation Physics-Informed Neural Network (DFS-PINN), which introduces an innovative input-decoupling and dynamic interaction mechanism. This approach reduces computational complexity from $O\left(N^d\right)$ to $O(N\times d)$, enabling efficient training and improved accuracy for multi-dimensional problems, especially in real-time rendering and fluid simulations. When applied to the lid-driven cavity flow problem, DFS-PINN achieves a 6$\times$ reduction in runtime and a 62$\times$ reduction in memory usage with $2^{15}$ collocation points, compared to standard PINNs. For large-scale datasets with over $2^{20}$ points, DFS-PINN attains a mean squared error (MSE) of 0.000122, showcasing its superior computational efficiency and predictive accuracy. These results position DFS-PINN as a scalable and robust framework for solving multi-dimensional PDEs, demonstrating substantial improvements in both computational efficiency and modeling accuracy.