{"ID":2866834,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.18483","arxiv_id":"2509.18483","title":"Physics-informed time series analysis with Kolmogorov-Arnold Networks under Ehrenfest constraints","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.","short_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 languag...","url_abs":"https://arxiv.org/abs/2509.18483","url_pdf":"https://arxiv.org/pdf/2509.18483v1","authors":"[\"Abhijit Sen\",\"Illya V. Lukin\",\"Kurt Jacobs\",\"Lev Kaplan\",\"Andrii G. Sotnikov\",\"Denys I. Bondar\"]","published":"2025-09-23T00:37:04Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"quant-ph\"]","methods":"[\"Language Model\"]","has_code":false}