arXiv:2605.23966v1 Announce Type: cross Abstract: Optimization modeling serves as the pivotal bridge between natural-language problem descriptions and optimization solvers, and remains a cornerstone for bringing operations research (OR) into real-world decision making. Recent advances in large language models (LLMs) have driven significant progress in automatic optimization modeling. However, existing methods still lack explicit validation during the modeling process, allowing errors introduced in earlier stages to carry through the pipeline and ultimately reduce final modeling accuracy. To address this challenge, we introduce TriVAL, a tri-validation framework that performs explicit validation at three stages of automatic optimization modeling: semantic specification, mathematical formulation, and code generation. At each stage, TriVAL follows a construct-validate-revise loop that assesses the current result against stage-specific criteria and revises it when needed. This design helps identify and correct errors before they accumulate across stages, helping preserve faithfulness throughout the modeling process. To evaluate automatic optimization modeling on more challenging combinatorial problems, we further introduce NL4COP, a benchmark of 150 instances across 50 diverse problem types with more complex decision logic, more tightly coupled constraints, and more demanding modeling requirements than existing benchmarks. Experiments on NL4COP and established benchmarks show that TriVAL consistently outperforms state-ofthe-art methods, with the largest gains on the most challenging problems.

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:2510.16701v2 Announce Type: replace Abstract: Complex vehicle routing problems (VRPs) remain a fundamental challenge, demanding substantial expert effort for intent interpretation and algorithm design. While large language models (LLMs) offer a promising path toward automation, current approaches still rely on external intervention, which restrict autonomy and often lead to execution errors and low solution feasibility. To address these challenges, we propose an Agentic Framework with LLMs (AFL) for solving complex vehicle routing problems, achieving full automation from problem instance to solution. AFL directly extracts knowledge from raw inputs and enables self-contained code generation without handcrafted modules or external solvers. To improve trustworthiness, AFL decomposes the overall pipeline into three manageable subtasks and employs four specialized agents whose coordinated interactions enforce cross-functional consistency and logical soundness. Extensive experiments on 60 complex VRPs, ranging from standard benchmarks to practical variants, validate the effectiveness and generality of our framework, showing comparable performance against meticulously designed algorithms. Notably, it substantially outperforms existing LLM-based baselines in both code reliability and solution feasibility, achieving rates close to 100% on the evaluated benchmarks.