arXiv:2602.19475v1 Announce Type: cross Abstract: 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.

arXiv:2601.05525v2 Announce Type: replace Abstract: Artificial intelligence now outperforms humans in several scientific and engineering tasks, yet its internal representations often remain opaque. In this Perspective, we argue that explainable artificial intelligence (XAI), combined with causal reasoning, enables {\it learning from the learners}. Focusing on discovery, optimization and certification, we show how the combination of foundation models and explainability methods allows the extraction of causal mechanisms, guides robust design and control, and supports trust and accountability in high-stakes applications. We discuss challenges in faithfulness, generalization and usability of explanations, and propose XAI as a unifying framework for human-AI collaboration in science and engineering.