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

• URL: http://arxiv.org/abs/2509.18483v1
• Date: Tue, 23 Sep 2025 00:37:04 GMT
• Title: Physics-informed time series analysis with Kolmogorov-Arnold Networks under Ehrenfest constraints
• Authors: Abhijit Sen, Illya V. Lukin, Kurt Jacobs, Lev Kaplan, Andrii G. Sotnikov, Denys I. Bondar,
• Abstract summary: Predictions of quantum dynamical responses lie at the heart of modern physics.<n>Quantum dynamics presents a fundamentally different challenge: forecasting the entire temporal evolution of quantum systems.<n>We introduce a fundamentally new approach: Kolmogorov Arnold Networks (KANs) augmented with physics-informed loss functions that enforce the Ehrenfest theorems.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 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.

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