Physics-informed neural networks (PINNs) have emerged as a promising mesh-free paradigm for solving partial differential equations, yet adoption in science and engineering is limited by slow training and modest accuracy relative to modern numerical solvers. We introduce the Sequential Correction Algorithm for Learning Efficient PINN (Scale-PINN), a learning strategy that bridges modern physics-informed learning with numerical algorithms. Scale-PINN incorporates the iterative residual-correction principle, a cornerstone of numerical solvers, directly into the loss formulation, marking a paradigm shift in how PINN losses can be conceived and constructed. This integration enables Scale-PINN to achieve unprecedented convergence speed across PDE problems from different physics domain, including reducing training time on a challenging fluid-dynamics problem for state-of-the-art PINN from hours to sub-2 minutes while maintaining superior accuracy, and enabling application to representative problems in aerodynamics and urban science. By uniting the rigor of numerical methods with the flexibility of deep learning, Scale-PINN marks a significant leap toward the practical adoption of PINNs in science and engineering through scalable, physics-informed learning. Codes are available at https://github.com/chiuph/SCALE-PINN.

翻译：物理信息神经网络（PINNs）已成为求解偏微分方程的一种有前景的无网格范式，但由于训练速度慢且与现代数值求解器相比精度有限，其在科学与工程领域的应用受到制约。本文提出用于学习高效PINN的序列校正算法（Scale-PINN），该学习策略将现代物理信息学习与数值算法相融合。Scale-PINN将迭代残差校正原理——数值求解器的基石——直接纳入损失函数构建中，标志着PINN损失函数设计与构建范式的转变。这种融合使Scale-PINN在不同物理领域的PDE问题上实现了前所未有的收敛速度：在具有挑战性的流体动力学问题上，将当前最优PINN的训练时间从数小时缩短至2分钟以内，同时保持更高的精度，并成功应用于空气动力学和城市科学中的典型问题。通过融合数值方法的严谨性与深度学习的灵活性，Scale-PINN通过可扩展的物理信息学习，推动了PINN在科学与工程领域实际应用的重要跨越。代码发布于 https://github.com/chiuph/SCALE-PINN。