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

Area of Science:

• Computational Electromagnetics
• Numerical Methods for EM Wave Propagation

Background:

• Accurate truncation of unbounded domains is critical in time-domain electromagnetic (EM) simulations.
• Conventional Perfectly Matched Layers (PMLs) require multiple grid layers and auxiliary variables, increasing computational expense.

Purpose of the Study:

• To introduce a computationally efficient, single-layer neural complete radiation boundary condition (NP-SSM-CRBC).
• To replace traditional thick absorbing boundaries with a one-cell model for improved performance.

Main Methods:

• Employs a neural state-space model (SSM) to predict boundary ghost-cell responses directly.
• Learns a time-causal boundary operator, avoiding explicit evolution of auxiliary fields.
• Incorporates explicit physical constraints for long-term stability.

Main Results:

• Achieves low reflection levels comparable to conventional methods.
• Demonstrates substantially reduced computational overhead (runtime and memory).
• Validates the effectiveness of the single-layer neural boundary condition.

Conclusions:

• The NP-SSM-CRBC offers a promising alternative to traditional PMLs for EM simulations.
• The method provides a foundation for extension to larger 3D problems and complex geometries.
• Significant reduction in computational cost without compromising accuracy.