Learning PDE Solvers with Physics and Data: A Unifying View of Physics-Informed Neural Networks and Neural Operators

Partial differential equations (PDEs) are central to scientific modeling. Modern workflows increasingly rely on learning-based components to support model reuse, inference, and integration across large computational processes. Despite the emergence of various physics-aware data-driven approaches, the field still lacks a unified perspective to uncover their relationships, limitations, and appropriate roles in scientific workflows. To this end, we propose a unifying perspective to place two dominant paradigms: Physics-Informed Neural Networks (PINNs) and Neural Operators (NOs), within a shared design space. We organize existing methods from three fundamental dimensions: what is learned, how physical structures are integrated into the learning process, and how the computational load is amortized across problem instances. In this way, many challenges can be best understood as consequences of these structural properties of learning PDEs. By analyzing advances through this unifying view, our survey aims to facilitate the development of reliable learning-based PDE solvers and catalyze a synthesis of physics and data.

Persona-aware and Explainable Bikeability Assessment: A Vision-Language Model Approach

Bikeability assessment is essential for advancing sustainable urban transportation and creating cyclist-friendly cities, and it requires incorporating users' perceptions of safety and comfort. Yet existing perception-based bikeability assessment approaches face key limitations in capturing the complexity of road environments and adequately accounting for heterogeneity in subjective user perceptions. This paper proposes a persona-aware Vision-Language Model framework for bikeability assessment with three novel contributions: (i) theory-grounded persona conditioning based on established cyclist typology that generates persona-specific explanations via chain-of-thought reasoning; (ii) multi-granularity supervised fine-tuning that combines scarce expert-annotated reasoning with abundant user ratings for joint prediction and explainable assessment; and (iii) AI-enabled data augmentation that creates controlled paired data to isolate infrastructure variable impacts. To test and validate this framework, we developed a panoramic image-based crowdsourcing system and collected 12,400 persona-conditioned assessments from 427 cyclists. Experiment results show that the proposed framework offers competitive bikeability rating prediction while uniquely enabling explainable factor attribution.