PolyFormer: learning efficient reformulations for scalable optimization under complex physical constraints

2026-03-09

AI Summary

This work addresses the poor computational scalability of large-scale physics-constrained optimization by proposing a novel framework that integrates physics-informed machine learning with polyhedral reformulation. Unlike conventional approaches that treat physical and geometric priors merely as regularization terms, this method uniquely embeds such priors directly into the reconstruction of the optimization problem itself, thereby decoupling problem complexity from solution difficulty. The framework reformulates intricate constraints into an efficient polyhedral representation, enabling off-the-shelf solvers to achieve rapid convergence while preserving high solution quality. Evaluated on three canonical problem classes, the approach demonstrates up to a 6400× speedup and a 99.87% reduction in memory usage, with solution accuracy matching or surpassing state-of-the-art methods.

Technology Category

• Constraint Satisfaction and Optimization: Constraint Optimization
• Machine Learning: Optimization
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

Real-world optimization problems are often constrained by complex physical laws that limit computational scalability. These constraints are inherently tied to complex regions, and thus learning models that incorporate physical and geometric knowledge, i.e., physics-informed machine learning (PIML), offer a promising pathway for efficient solution. Here, we introduce PolyFormer, which opens a new direction for PIML in prescriptive optimization tasks, where physical and geometric knowledge is not merely used to regularize learning models, but to simplify the problems themselves. PolyFormer captures geometric structures behind constraints and transforms them into efficient polytopic reformulations, thereby decoupling problem complexity from solution difficulty and enabling off-the-shelf optimization solvers to efficiently produce feasible solutions with acceptable optimality loss. Through evaluations across three important problems (large-scale resource aggregation, network-constrained optimization, and optimization under uncertainty), PolyFormer achieves computational speedups up to 6,400-fold and memory reductions up to 99.87%, while maintaining solution quality competitive with or superior to state-of-the-art methods. These results demonstrate that PolyFormer provides an efficient and reliable solution for scalable constrained optimization, expanding the scope of PIML to prescriptive tasks in scientific discovery and engineering applications.

Problem

• constrained optimization
• physical constraints
• computational scalability
• physics-informed machine learning
• prescriptive optimization

Innovation

• Polytopic reformulation
• Physics-informed machine learning
• Scalable optimization
• Geometric structure learning
• Prescriptive optimization