# Physics-Guided Neural Surrogate Model with Particle Swarm-Based Multi-Objective Optimization for Quasi-Coaxial TSV Interconnect Design

## TL;DR

This paper introduces a physics-informed neural model and optimization framework to improve high-frequency signal performance in microsystem interconnects.

## Contribution

A physics-constrained neural surrogate model and PSO-based multi-objective optimization framework for TSV interconnect design.

## Key findings

- The model enforces causality and passivity through regularization, improving accuracy in predicting S-parameters.
- Optimized parameters achieved deviations below 1 dB and an average prediction error of 2.11%.
- The PSO framework effectively balances multiple performance targets for TSV structures.

## Abstract

In reconfigurable radio frequency (RF) microsystems, the interconnect structure critically affects high-frequency signal integrity, and the accuracy of electromagnetic (EM) modeling directly determines the overall system performance. Conventional neural network-based surrogate models mainly focus on minimizing numerical errors, while neglecting essential physical constraints, such as causality and passivity, thereby limiting their applicability in both time and frequency domains. This paper proposes a physics-constrained Neuro-Transfer surrogate model with a broadband output architecture to directly predict S-parameters over the 1–50 GHz range. Causality and passivity are enforced through dedicated regularization terms during training. Furthermore, a particle swarm optimization (PSO)-based multi-objective intelligent optimization framework is developed, incorporating fixed-weight normalization and a linearly decreasing inertia weight strategy to simultaneously optimize the S11, S21, and S22 performance of a quasi-coaxial TSV composite structure. Target values are set to −25 dB, −0.54 dB, and −24 dB, respectively. The optimized structural parameters yield prediction-to-simulation deviations below 1 dB, with an average prediction error of 2.11% on the test set.