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

• URL: http://arxiv.org/abs/2508.21559v1
• Date: Fri, 29 Aug 2025 12:15:32 GMT
• Title: Limitations of Physics-Informed Neural Networks: a Study on Smart Grid Surrogation
• Authors: Julen Cestero, Carmine Delle Femine, Kenji S. Muro, Marco Quartulli, Marcello Restelli,
• Abstract summary: PINNs present a transformative approach for smart grid modeling by integrating physical laws directly into learning frameworks.<n>This paper evaluates PINNs' capabilities as surrogate models for smart grid dynamics.<n>We demonstrate PINNs' superior generalization, outperforming data-driven models in error reduction.
• Score: 29.49941497527361
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

Related papers

• Improving Long-Range Interactions in Graph Neural Simulators via Hamiltonian Dynamics [71.53370807809296]
  Recent Graph Neural Simulators (GNSs) accelerate simulations by learning dynamics on graph-structured data.<n>We propose Information-preserving Graph Neural Simulators (IGNS), a graph-based neural simulator built on the principles of Hamiltonian dynamics.<n>IGNS consistently outperforms state-of-the-art GNSs, achieving higher accuracy and stability under challenging and complex dynamical systems.
  arXiv  Detail & Related papers  (2025-11-11T12:53:56Z)
• Physics-Informed Neural Network Frameworks for the Analysis of Engineering and Biological Dynamical Systems Governed by Ordinary Differential Equations [0.0]
  PINNs offer a powerful approach for handling challenging numerical scenarios.<n> PINNs can achieve superior results by embedding physical laws directly into the learning process.
  arXiv  Detail & Related papers  (2025-10-28T04:00:59Z)
• Learning Satellite Attitude Dynamics with Physics-Informed Normalising Flow [0.26217304977339473]
  We investigate the benefits of incorporating Physics-Informed Neural Networks into the learning of spacecraft attitude dynamics.<n>We train several models on simulated data generated with the Basilisk simulator.<n>We find that PINN-based models consistently outperform their purely data-driven counterparts in terms of control accuracy and robustness.
  arXiv  Detail & Related papers  (2025-08-11T10:50:49Z)
• Improving physics-informed neural network extrapolation via transfer learning and adaptive activation functions [44.44497277876625]
  Physics-Informed Neural Networks (PINNs) are deep learning models that incorporate the governing physical laws of a system into the learning process.<n>We introduce a transfer learning (TL) method to improve the extrapolation capability of PINNs.<n>We demonstrate that our method achieves an average of 40% reduction in relative L2 error and an average of 50% reduction in mean absolute error.
  arXiv  Detail & Related papers  (2025-07-16T22:19:53Z)
• PI-WAN: A Physics-Informed Wind-Adaptive Network for Quadrotor Dynamics Prediction in Unknown Environments [3.4802474792943805]
  We introduce the Physics-Informed Wind-Adaptive Network (PI-WAN), which embeds physical constraints directly into the training process for robust quadrotor dynamics learning.<n>Specifically, PI-WAN employs a Temporal Convolutional Network (TCN) architecture that efficiently captures temporal dependencies from historical flight data.<n>By incorporating real-time prediction results into a model predictive control (MPC) framework, we achieve improvements in closed-loop tracking performance.
  arXiv  Detail & Related papers  (2025-07-01T14:48:22Z)
• Physics-Informed Neural Networks for Electrical Circuit Analysis: Applications in Dielectric Material Modeling [0.0]
  Physics-Informed Neural Networks (PINNs) offer a promising approach by incorporating physical laws directly into the learning process. This article explores the capabilities and limitations of the DeepXDE framework, a tool specifically designed for implementing PINNs. We show that applying a logarithmic transformation to the current (ln(I)) significantly enhances the stability and accuracy of PINN predictions.
  arXiv  Detail & Related papers  (2024-11-13T19:08:36Z)
• DeltaPhi: Physical States Residual Learning for Neural Operators in Data-Limited PDE Solving [54.605760146540234]
  DeltaPhi is a novel learning framework that transforms the PDE solving task from learning direct input-output mappings to learning the residuals between similar physical states.<n>Extensive experiments demonstrate consistent and significant improvements across diverse physical systems.
  arXiv  Detail & Related papers  (2024-06-14T07:45:07Z)
• Knowledge-Based Convolutional Neural Network for the Simulation and Prediction of Two-Phase Darcy Flows [3.5707423185282656]
  Physics-informed neural networks (PINNs) have gained significant prominence as a powerful tool in the field of scientific computing and simulations. We propose to combine the power of neural networks with the dynamics imposed by the discretized differential equations. By discretizing the governing equations, the PINN learns to account for the discontinuities and accurately capture the underlying relationships between inputs and outputs.
  arXiv  Detail & Related papers  (2024-04-04T06:56:32Z)
• Physics-Informed Deep Learning of Rate-and-State Fault Friction [0.0]
  We develop a multi-network PINN for both the forward problem and for direct inversion of nonlinear fault friction parameters. We present the computational PINN framework for strike-slip faults in 1D and 2D subject to rate-and-state friction. We find that the network for the parameter inversion at the fault performs much better than the network for material displacements to which it is coupled.
  arXiv  Detail & Related papers  (2023-12-14T23:53:25Z)
• ConCerNet: A Contrastive Learning Based Framework for Automated Conservation Law Discovery and Trustworthy Dynamical System Prediction [82.81767856234956]
  This paper proposes a new learning framework named ConCerNet to improve the trustworthiness of the DNN based dynamics modeling. We show that our method consistently outperforms the baseline neural networks in both coordinate error and conservation metrics.
  arXiv  Detail & Related papers  (2023-02-11T21:07:30Z)
• Physics-Inspired Temporal Learning of Quadrotor Dynamics for Accurate Model Predictive Trajectory Tracking [76.27433308688592]
  Accurately modeling quadrotor's system dynamics is critical for guaranteeing agile, safe, and stable navigation. We present a novel Physics-Inspired Temporal Convolutional Network (PI-TCN) approach to learning quadrotor's system dynamics purely from robot experience. Our approach combines the expressive power of sparse temporal convolutions and dense feed-forward connections to make accurate system predictions.
  arXiv  Detail & Related papers  (2022-06-07T13:51:35Z)
• Characterizing possible failure modes in physics-informed neural networks [55.83255669840384]
  Recent work in scientific machine learning has developed so-called physics-informed neural network (PINN) models. We demonstrate that, while existing PINN methodologies can learn good models for relatively trivial problems, they can easily fail to learn relevant physical phenomena even for simple PDEs. We show that these possible failure modes are not due to the lack of expressivity in the NN architecture, but that the PINN's setup makes the loss landscape very hard to optimize.
  arXiv  Detail & Related papers  (2021-09-02T16:06:45Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.