# Physics-informed time series analysis with Kolmogorov-Arnold Networks under Ehrenfest constraints

arXiv: https://arxiv.org/abs/2509.18483 · HTML: https://mlsanity.com/paper/2509.18483/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 54 references that are in the map.
- First posted on arXiv 23 Sep 2025.

## Builds on (most cited first, 12 of 12)

- [KAN: Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2404.19756/) (2024)
- [Characterizing possible failure modes in physics-informed neural networks](https://mlsanity.com/paper/2109.01050/) (2021)
- [Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next](https://mlsanity.com/paper/2201.05624/) (2022)
- [An Expert's Guide to Training Physics-informed Neural Networks](https://mlsanity.com/paper/2308.08468/) (2023)
- [Wav-KAN: Wavelet Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2405.12832/) (2024)
- [A Survey on Kolmogorov-Arnold Network](https://mlsanity.com/paper/2411.06078/) (2024)
- [Distributed physics informed neural network for data-efficient solution to partial differential equations](https://mlsanity.com/paper/1907.08967/) (2019)
- [Physics Informed Kolmogorov-Arnold Neural Networks for Dynamical Analysis via Efficent-KAN and WAV-KAN](https://mlsanity.com/paper/2407.18373/) (2024)
- [Stochastic Physics-Informed Neural Ordinary Differential Equations](https://mlsanity.com/paper/2109.01621/) (2021)
- [Machine learning applied to single-shot x-ray diagnostics in an XFEL](https://mlsanity.com/paper/1610.03378/) (2016)
- [Deep Learning Reconstruction of Ultra-Short Pulses](https://mlsanity.com/paper/1803.06024/) (2018)
- [Deep learning and high harmonic generation](https://mlsanity.com/paper/2012.10328/) (2020)

## Built on by (most cited first, 5 of 5)

- [Worst-Case Distance-Aware Error Bounds for Neural Networks](https://mlsanity.com/paper/2510.22021/) (2025)
- [Geometric Kolmogorov--Arnold Network (GeoKAN)](https://mlsanity.com/paper/2605.06740/) (2026)
- [K-U-KAN: Koopman-Enhanced U-KAN for 3D Dental Reconstruction from a Single Panoramic X-ray Radiograph](https://mlsanity.com/paper/2605.25163/) (2026)
- [Quantum Kolmogorov--Arnold representation theorem for continuous unitary-valued maps](https://mlsanity.com/paper/2607.03187/) (2026)
- [Digital Twin Modeling of Quantum Dynamical Systems: Dissipative Quantum Reservoir Computing](https://mlsanity.com/paper/2609.36901/) (2026)

## Abstract (arXiv)

The prediction of quantum dynamical responses lies at the heart of modern physics. Yet, modeling these time-dependent behaviors remains a formidable challenge because quantum systems evolve in high-dimensional Hilbert spaces, often rendering traditional numerical methods computationally prohibitive. While large language models have achieved remarkable success in sequential prediction, quantum dynamics presents a fundamentally different challenge: forecasting the entire temporal evolution of quantum systems rather than merely the next element in a sequence. Existing neural architectures such as recurrent and convolutional networks often require vast training datasets and suffer from spurious oscillations that compromise physical interpretability. In this work, we introduce a fundamentally new approach: Kolmogorov Arnold Networks (KANs) augmented with physics-informed loss functions that enforce the Ehrenfest theorems. Our method achieves superior accuracy with significantly less training data: it requires only 5.4 percent of the samples (200) compared to Temporal Convolution Networks (3,700). We further introduce the Chain of KANs, a novel architecture that embeds temporal causality directly into the model design, making it particularly well-suited for time series modeling. Our results demonstrate that physics-informed KANs offer a compelling advantage over conventional black-box models, maintaining both mathematical rigor and physical consistency while dramatically reducing data requirements.