U-PINet: Physics-Informed Hierarchical Learning for Accurate and Fast 3D RCS Prediction

TL;DR

U-PINet tackles the challenge of fast, accurate 3D RCS prediction by embedding EM physics into a hierarchical deep learning architecture that mirrors MLFMA's near-field and far-field operations. It introduces a MoM-guided near-field graph encoder and a cross-scale, attention-based far-field fusion, optimized with a physics residual loss that enforces the EFIE, enabling end-to-end prediction of bistatic RCS $σ(θ,φ)$. The approach achieves solver-level accuracy with orders-of-magnitude speedups and demonstrates robust generalization to unseen geometries with limited training data. This physics-informed surrogate enables scalable, end-to-end RCS curve modeling for multi-aspect radar analysis and target recognition.

Abstract

Accurate radar cross section (RCS) computation is a fundamental task in radar engineering and electromagnetic (EM) scattering analysis, underpinning target signature characterization, detection, and recognition. Conventional computational electromagnetics (CEM) solvers provide high-fidelity RCS predictions but suffer from prohibitive computational costs when applied to 3-dimensional (3D) targets under multi-aspect configurations. In contrast, purely data-driven neural networks offer high efficiency yet often lack physical consistency and generalization capability. To address these challenges, this paper proposes a U-shaped Physics-Informed Network (U-PINet). To the best of our knowledge, it is the first framework to establish a fully end-to-end, physics-informed hierarchical architecture for fast and accurate RCS computation, grounded in the governing principles of CEM. Inspired by the near-far field decomposition in classical fast solvers, U-PINet explicitly models local EM coupling and long-range radiation effects through a hierarchical operator design. A physics-guided graph construction is further introduced to represent self- and mutual-coupling among mesh elements of complex 3D targets, enabling physically interpretable intermediate representations. By embedding EM governing equations as residual constraints, the proposed framework achieves end-to-end, physically consistent RCS prediction with significantly improved computational efficiency. Extensive numerical experiments demonstrate that U-PINet attains solver-level RCS accuracy with orders-of-magnitude runtime reduction, while exhibiting strong generalization to unseen target geometries under limited training data.

Figures (15)

• Figure 1: Illustration of the RCS calculation for a representative target.
• Figure 2: Framework Comparison for RCS Prediction. The diagram illustrates the pathway to the final RCS calculation ($\sigma$) using the standard MLFMA approach (top) versus the proposed U-PINet method (bottom). U-PINet utilizes physics-informed learning to directly resolve field interactions, bypassing traditional iterative solvers to rapidly determine the scattered field for RCS assessment.
• Figure 3: Workflow of the proposed U-PINet for physics-informed surface current prediction.
• Figure 4: (a) Physics-guided edge attention combining density- and normal-based branches to produce learnable near-field edge weights; (b) GNN block that stacks GAT/GCN layers to iteratively refine the surface current.
• Figure 5: Schematic of the physics-driven pipeline. The predicted current $\mathbf{J}_{\mathrm{pred}}$ bifurcates into two paths: minimizing the EFIE residual $\mathcal{L}_{phys}$ for training (red), and evaluating the RCS $\sigma$ for inference (blue).