Learning stable radiation boundaries for wave simulations via passive neural state-space models.

Overview

1. School of Science, Qingdao University of Technology, Qingdao 266520, China
2. School of Information and Control Engineering, Qingdao University of Technology, Qingdao 266520, China

Abstract

Accurate truncation of unbounded domains is a central challenge in time-domain electromagnetic (EM) systems. While perfectly matched layers (PMLs) can deliver excellent absorption, they typically require multiple grid layers and auxiliary variables, increasing runtime and memory costs. This work introduces a single-layer neural complete radiation boundary condition (NP-SSM-CRBC) that replaces a thick absorbing boundary with a one-cell boundary model. Instead of explicitly evolving auxiliary fields as in conventional PML or convolutional PMLs (CPMLs) formulations, the proposed approach employs a neural state-space model to predict the boundary ghost-cell responses directly. The method learns an effective, time-causal boundary operator and is designed to remain stable over long time horizons through explicit physical constraints. Experimental results demonstrate that the proposed method achieves low reflection levels with substantially reduced computational overhead. These results provide a foundation for extension to larger three-dimensional problems and more complex boundary geometries.

Reproduced under the paper's license (CC BY), from the paper cited above.

Code

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The paper's code and data availability statement is in the Data section.

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Data

Datasets cited

• data.mendeley.com/datasets/khzkt7pn6p, at Mendeley Data; found in “Data and code availability”

Data and code availability

• The datasets used for the experiments have been deposited at Mendeley Data: https://data.mendeley.com/datasets/khzkt7pn6p/1 and are publicly available as of the date of publication. • The original code is available on GitHub: https://github.com/Blizzard-Passage-Lab/NP-SSM–CRBC (https://github.com/Blizzard-Passage-Lab/NP-SSM_CRBC). • Any additional information required to reanalyze the data reported in this study is available from the lead contact upon request.

Reproduced under the paper's license (CC BY), from the paper cited above.

Versions

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Version 1, 27 September 2026: the first record

Recorded: type, language, journal, volume, issue, pages, dates, 4 authors, 3 keywords, 9 references.

Cite

This paper

Li, A., Wang, X., Wang, Y., & Wang, S. (2026). Learning stable radiation boundaries for wave simulations via passive neural state-space models. iScience, 29(6), 116116. https://doi.org/10.1016/j.isci.2026.116116

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