Physics-informed time series analysis with Kolmogorov-Arnold Networks under Ehrenfest constraints
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , , , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866914052010147840 |
|---|---|
| author | Sen, Abhijit Lukin, Illya V. Jacobs, Kurt Kaplan, Lev Sotnikov, Andrii G. Bondar, Denys I. |
| author_facet | Sen, Abhijit Lukin, Illya V. Jacobs, Kurt Kaplan, Lev Sotnikov, Andrii G. Bondar, Denys I. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_18483 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Physics-informed time series analysis with Kolmogorov-Arnold Networks under Ehrenfest constraints Sen, Abhijit Lukin, Illya V. Jacobs, Kurt Kaplan, Lev Sotnikov, Andrii G. Bondar, Denys I. Machine Learning Quantum Physics 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. |
| title | Physics-informed time series analysis with Kolmogorov-Arnold Networks under Ehrenfest constraints |
| topic | Machine Learning Quantum Physics |
| url | https://arxiv.org/abs/2509.18483 |