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

## TL;DR

This paper evaluates the effectiveness of Physics-Informed Neural Networks (PINNs) as surrogate models for smart grid dynamics, demonstrating their superior generalization and physical consistency over traditional data-driven models in various operational scenarios.

## Contribution

It provides a comprehensive assessment of PINNs for smart grid modeling, highlighting their advantages in physical consistency and generalization compared to conventional machine learning methods.

## Key findings

- PINNs outperform traditional models in error reduction.
- PINNs maintain physical feasibility in dynamic operations.
- Traditional models show erratic performance in extreme regimes.

## Abstract

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.