# Limitations of Physics-Informed Neural Networks: a Study on Smart Grid Surrogation

arXiv: https://arxiv.org/abs/2508.21559 · HTML: https://mlsanity.com/paper/2508.21559/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 26 references that are in the map.
- First posted on arXiv 29 Aug 2025.

## Builds on (most cited first, 15 of 15)

- [Theory-guided Data Science: A New Paradigm for Scientific Discovery from Data](https://mlsanity.com/paper/1612.08544/) (2016)
- [Physics-Informed Neural Networks for Power Systems](https://mlsanity.com/paper/1911.03737/) (2019)
- [Reliable extrapolation of deep neural operators informed by physics or sparse observations](https://mlsanity.com/paper/2212.06347/) (2022)
- [Physics-Informed Neural Networks for Multiphysics Data Assimilation with Application to Subsurface Transport](https://mlsanity.com/paper/1912.02968/) (2019)
- [The Old and the New: Can Physics-Informed Deep-Learning Replace Traditional Linear Solvers?](https://mlsanity.com/paper/2103.09655/) (2021)
- [When Do Extended Physics-Informed Neural Networks (XPINNs) Improve Generalization?](https://mlsanity.com/paper/2109.09444/) (2021)
- [DPM: A Novel Training Method for Physics-Informed Neural Networks in Extrapolation](https://mlsanity.com/paper/2012.02681/) (2020)
- [Physics-Guided Deep Neural Networks for Power Flow Analysis](https://mlsanity.com/paper/2002.00097/) (2020)
- [Physics-Informed Neural Networks for Minimising Worst-Case Violations in DC Optimal Power Flow](https://mlsanity.com/paper/2107.00465/) (2021)
- [Gym-ANM: Reinforcement Learning Environments for Active Network Management Tasks in Electricity Distribution Systems](https://mlsanity.com/paper/2103.07932/) (2021)
- [On the Generalization of PINNs outside the training domain and the Hyperparameters influencing it](https://mlsanity.com/paper/2302.07557/) (2023)
- [Physics-Informed Machine Learning for Data Anomaly Detection, Classification, Localization, and Mitigation: A Review, Challenges, and Path Forward](https://mlsanity.com/paper/2309.10788/) (2023)
- [Transient Stability Analysis with Physics-Informed Neural Networks](https://mlsanity.com/paper/2106.13638/) (2021)
- [Advancing Generalization in PINNs through Latent-Space Representations](https://mlsanity.com/paper/2411.19125/) (2024)
- [KKT-Informed Neural Network](https://mlsanity.com/paper/2409.09087/) (2024)

## Abstract (arXiv)

Physics-Informed Neural Networks (PINNs) present a transformative approach for smart grid modeling by integrating physical laws directly into learning frameworks, addressing critical challenges of data scarcity and physical consistency in conventional data-driven methods. This paper evaluates PINNs' capabilities as surrogate models for smart grid dynamics, comparing their performance against XGBoost, Random Forest, and Linear Regression across three key experiments: interpolation, cross-validation, and episodic trajectory prediction. By training PINNs exclusively through physics-based loss functions (enforcing power balance, operational constraints, and grid stability) we demonstrate their superior generalization, outperforming data-driven models in error reduction. Notably, PINNs maintain comparatively lower MAE in dynamic grid operations, reliably capturing state transitions in both random and expert-driven control scenarios, while traditional models exhibit erratic performance. Despite slight degradation in extreme operational regimes, PINNs consistently enforce physical feasibility, proving vital for safety-critical applications. Our results contribute to establishing PINNs as a paradigm-shifting tool for smart grid surrogation, bridging data-driven flexibility with first-principles rigor. This work advances real-time grid control and scalable digital twins, emphasizing the necessity of physics-aware architectures in mission-critical energy systems.