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

Abhijit Sen1,*, Illya V. Lukin2,3,†, Kurt Jacobs4,5,‡, Lev Kaplan1,§, Andrii G. Sotnikov2,3,∥, and Denys I. Bondar1,¶

  • *Contact author: abhijit913@gmail.com
  • †Contact author: illya.lukin11@gmail.com
  • ‡Contact author: dr.kurt.jacobs@gmail.com
  • §Contact author: lkaplan@tulane.edu
  • ∥Contact author: a_sotnikov@kipt.kharkov.ua
  • Contact author: dbondar@tulane.edu
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Phys. Rev. Research 8, 023018 – Published 6 April, 2026

DOI: https://doi.org/10.1103/84vm-tvzm

Abstract

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 an 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% of the samples (200) compared to temporal convolution networks (3700). We further introduce the chain of KANs, an 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.

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Phys. Rev. Research 8, 023018– Published 6 April, 2026
  • Received 24 September 2025
  • Accepted 11 March 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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