# Tools to Explain Neural Networks for Power System Dynamics

arXiv: https://arxiv.org/abs/2608.08048 · HTML: https://mlsanity.com/paper/2608.08048/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 17 references that are in the map.
- First posted on arXiv 8 Aug 2026.

## Builds on (most cited first, 11 of 11)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [KAN: Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2404.19756/) (2024)
- [When and why PINNs fail to train: A neural tangent kernel perspective](https://mlsanity.com/paper/2007.14527/) (2020)
- [SOAP: Improving and Stabilizing Shampoo using Adam](https://mlsanity.com/paper/2409.11321/) (2024)
- [Understanding and mitigating gradient pathologies in physics-informed neural networks](https://mlsanity.com/paper/2001.04536/) (2020)
- [Neural Networks Fail to Learn Periodic Functions and How to Fix It](https://mlsanity.com/paper/2006.08195/) (2020)
- [Physics-Informed Neural Networks for Power Systems](https://mlsanity.com/paper/1911.03737/) (2019)
- [Physics-Informed Neural Networks for Time-Domain Simulations: Accuracy, Computational Cost, and Flexibility](https://mlsanity.com/paper/2303.08994/) (2023)
- [Revisiting Power Systems Time-domain Simulation Methods and Models](https://mlsanity.com/paper/2301.10043/) (2023)
- [Acceleration of Power System Dynamic Simulations using a Deep Equilibrium Layer and Neural ODE Surrogate](https://mlsanity.com/paper/2405.06827/) (2024)

## Abstract (arXiv)

This paper presents, for the first time in power systems literature to our knowledge, analytical tools to explain the training performance of machine learning surrogate models for power system dynamics. Power system simulations are increasingly challenged by stiff and multi-timescale dynamics arising from converter-interfaced resources and fast control loops. Machine learning surrogates emerge as promising tools to handle this complexity and accelerate dynamic simulations. However, their performance remains difficult to interpret, which limits their adoption. Building on the small-signal eigenvalue analysis in power systems, this paper uses the Neural Tangent Kernel (NTK) method. NTK delivers a modal interpretation of the learning performance, identifying error modes that decay rapidly versus others that converge slowly. This connection explains how physical stiffness and timescale separation in power system dynamic models appear as optimization stiffness during Neural Network (NN) training. Based on this analysis, we develop adaptive loss-weighting strategies to improve and explain why structure-aware neural architectures, such as ActNet, perform better than vanilla NNs. We assess the proposed approach on physics-informed machine learning surrogate models of acpSM and power electronic converters. The methods introduced in this paper can deliver the necessary analytical tools to interpret and improve the performance of machine learning surrogates, paving the way for the systematic, physics-aware design of NN architectures and training strategies. By moving beyond trial-and-error development, these tools reveal training dynamics and failure modes, support more reliable design decisions, and strengthen confidence in machine-learning surrogates for engineering applications.