# Scale-PINN: Learning Efficient Physics-Informed Neural Networks Through Sequential Correction

arXiv: https://arxiv.org/abs/2602.19475 · HTML: https://mlsanity.com/paper/2602.19475/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 64 references that are in the map.
- First posted on arXiv 23 Feb 2026.

## Builds on (most cited first, 14 of 14)

- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [An Expert's Guide to Training Physics-informed Neural Networks](https://mlsanity.com/paper/2308.08468/) (2023)
- [CAN-PINN: A Fast Physics-Informed Neural Network Based on Coupled-Automatic-Numerical Differentiation Method](https://mlsanity.com/paper/2110.15832/) (2021)
- [Weak baselines and reporting biases lead to overoptimism in machine learning for fluid-related partial differential equations](https://mlsanity.com/paper/2407.07218/) (2024)
- [PirateNets: Physics-informed Deep Learning with Residual Adaptive Networks](https://mlsanity.com/paper/2402.00326/) (2024)
- [Learning in Sinusoidal Spaces with Physics-Informed Neural Networks](https://mlsanity.com/paper/2109.09338/) (2021)
- [Gradient Alignment in Physics-informed Neural Networks: A Second-Order Optimization Perspective](https://mlsanity.com/paper/2502.00604/) (2025)
- [EvoJAX: Hardware-Accelerated Neuroevolution](https://mlsanity.com/paper/2202.05008/) (2022)
- [A finite element-based physics-informed operator learning framework for spatiotemporal partial differential equations on arbitrary domains](https://mlsanity.com/paper/2405.12465/) (2024)
- [Evolutionary Optimization of Physics-Informed Neural Networks: Evo-PINN Frontiers and Opportunities](https://mlsanity.com/paper/2501.06572/) (2025)
- [LSA-PINN: Linear Boundary Connectivity Loss for Solving PDEs on Complex Geometry](https://mlsanity.com/paper/2302.01518/) (2023)
- [TSONN: Time-stepping-oriented neural network for solving partial differential equations](https://mlsanity.com/paper/2310.16491/) (2023)
- [Automated machine learning for physics-informed convolutional neural networks](https://mlsanity.com/paper/2407.06151/) (2024)
- [Finite-difference-informed graph network for solving steady-state incompressible flows on block-structured grids](https://mlsanity.com/paper/2406.10534/) (2024)

## Built on by (most cited first, 5 of 5)

- [When PINNs Go Wrong: Pseudo-Time Stepping Against Spurious Solutions](https://mlsanity.com/paper/2604.23528/) (2026)
- [On the training of physics-informed neural operators for solving parametric partial differential equations](https://mlsanity.com/paper/2606.06164/) (2026)
- [An Optimisation Framework for the Well-Conditioned Training of Physics-Informed Neural Networks](https://mlsanity.com/paper/2607.02194/) (2026)
- [RINS: Residual-Image Neural Subspace Solvers for Large Sparse Linear Systems](https://mlsanity.com/paper/2610.02217/) (2026)
- [Physics-Informed Neural Plasticity: PDE Solvers That Reshape Themselves](https://mlsanity.com/paper/2610.09510/) (2026)

## Abstract (arXiv)

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.