# A Survey of Physics-Informed AI for Complex Urban Systems

arXiv: https://arxiv.org/abs/2506.13777 · HTML: https://mlsanity.com/paper/2506.13777/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 80 of its 246 references that are in the map.
- First posted on arXiv 9 Jun 2025.

## Builds on (most cited first, 30 of 80)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next](https://mlsanity.com/paper/2201.05624/) (2022)
- [AI Feynman: a Physics-Inspired Method for Symbolic Regression](https://mlsanity.com/paper/1905.11481/) (2019)
- [Machine learning accelerated computational fluid dynamics](https://mlsanity.com/paper/2102.01010/) (2021)
- [LSTM: A Search Space Odyssey](https://mlsanity.com/paper/1503.04069/) (2015)
- [hp-VPINNs: Variational Physics-Informed Neural Networks With Domain Decomposition](https://mlsanity.com/paper/2003.05385/) (2020)
- [Understanding World or Predicting Future? A Comprehensive Survey of World Models](https://mlsanity.com/paper/2411.14499/) (2024)
- [Dynamic Graph Convolutional Recurrent Network for Traffic Prediction: Benchmark and Solution](https://mlsanity.com/paper/2104.14917/) (2021)
- [Data-Driven Forecasting of High-Dimensional Chaotic Systems with Long Short-Term Memory Networks](https://mlsanity.com/paper/1802.07486/) (2018)
- [A Survey of Graph Neural Networks for Recommender Systems: Challenges, Methods, and Directions](https://mlsanity.com/paper/2109.12843/) (2021)
- [Spatio-Temporal Graph Neural Networks for Predictive Learning in Urban Computing: A Survey](https://mlsanity.com/paper/2303.14483/) (2023)
- [Enhancing Computational Fluid Dynamics with Machine Learning](https://mlsanity.com/paper/2110.02085/) (2021)
- [Physics-guided Neural Networks (PGNN): An Application in Lake Temperature Modeling](https://mlsanity.com/paper/1710.11431/) (2017)
- [DeepInf: Social Influence Prediction with Deep Learning](https://mlsanity.com/paper/1807.05560/) (2018)
- [Predicting AC Optimal Power Flows: Combining Deep Learning and Lagrangian Dual Methods](https://mlsanity.com/paper/1909.10461/) (2019)
- [Physics-Informed Machine Learning: A Survey on Problems, Methods and Applications](https://mlsanity.com/paper/2211.08064/) (2022)
- [UniST: A Prompt-Empowered Universal Model for Urban Spatio-Temporal Prediction](https://mlsanity.com/paper/2402.11838/) (2024)
- [Multiscale Simulations of Complex Systems by Learning their Effective Dynamics](https://mlsanity.com/paper/2006.13431/) (2020)
- [Physics-Guided Machine Learning for Scientific Discovery: An Application in Simulating Lake Temperature Profiles](https://mlsanity.com/paper/2001.11086/) (2020)
- [Deep Gravity: enhancing mobility flows generation with deep neural networks and geographic information](https://mlsanity.com/paper/2012.00489/) (2020)
- [Physics-Informed Neural Networks for AC Optimal Power Flow](https://mlsanity.com/paper/2110.02672/) (2021)
- [A Physics-Informed Machine Learning Approach for Solving Heat Transfer Equation in Advanced Manufacturing and Engineering Applications](https://mlsanity.com/paper/2010.02011/) (2020)
- [Spatio-temporal Diffusion Point Processes](https://mlsanity.com/paper/2305.12403/) (2023)
- [A Dual-Dimer Method for Training Physics-Constrained Neural Networks with Minimax Architecture](https://mlsanity.com/paper/2005.00615/) (2020)
- [STDEN: Towards Physics-Guided Neural Networks for Traffic Flow Prediction](https://mlsanity.com/paper/2209.00225/) (2022)
- [A Physics-Informed Deep Learning Paradigm for Traffic State and Fundamental Diagram Estimation](https://mlsanity.com/paper/2106.03142/) (2021)
- [Urban Generative Intelligence (UGI): A Foundational Platform for Agents in Embodied City Environment](https://mlsanity.com/paper/2312.11813/) (2023)

## Built on by (most cited first, 2 of 2)

- [Aligning Perception, Reasoning, Modeling and Interaction: A Survey on Physical AI](https://mlsanity.com/paper/2510.04978/) (2025)
- [Inferring Network Evolutionary History via Structure-State Coupled Learning](https://mlsanity.com/paper/2601.02121/) (2026)

## Abstract (arXiv)

Urban systems are typical examples of complex systems, where the integration of physics-based modeling with artificial intelligence (AI) presents a promising paradigm for enhancing predictive accuracy, interpretability, and decision-making. In this context, AI excels at capturing complex, nonlinear relationships, while physics-based models ensure consistency with real-world laws and provide interpretable insights. We provide a comprehensive review of physics-informed AI methods in urban applications. The proposed taxonomy categorizes existing approaches into three paradigms - Physics-Integrated AI, Physics-AI Hybrid Ensemble, and AI-Integrated Physics - and further details seven representative methods. This classification clarifies the varying degrees and directions of physics-AI integration, guiding the selection and development of appropriate methods based on application needs and data availability. We systematically examine their applications across eight key urban domains: energy, environment, economy, transportation, information, public services, emergency management, and the urban system as a whole. Our analysis highlights how these methodologies leverage physical laws and data-driven models to address urban challenges, enhancing system reliability, efficiency, and adaptability. By synthesizing existing methodologies and their urban applications, we identify critical gaps and outline future research directions, paving the way toward next-generation intelligent urban system modeling.