Simplified Swarm Optimization for Surrogate-Assisted Reliability Design of Insulated-Gate Bipolar Transistor Power Modules Using an Open-Source Process Finite-Element Model

Transformer-based surrogate models are increasingly used to replace expensive first-principles simulation in engineering design. But conventional transformer architectures are often over parameterized for the small, low-dimensional datasets typical of engineering design spaces, where large simulation data is expensive to generate. Under these conditions, excess parameter capacity leads to overfitting rather than improved accuracy, while also incurring unnecessary memory and compute overhead. This motivates a shift towards architectures that focus on additional compute rather than additional learnable parameters. This paper presents a hardware-aware evaluation of three recursive transformer paradigms for surrogate thermo-mechanical analysis of advanced packages: a)Tiny Recursive Model, b) our proposed Depth Recursive transformer, c) and a simple recursive transformer. We systematically compare their predictive performance (Recall, Mean Reciprocal Rank), parameter count, computational complexity (FLOPs), providing practical design guidelines for selecting recursive transformer architectures under resource-constrained scenarios. We validate this principle on two low-dimensional engineering prediction tasks: 1) thermo-mechanical reliability analysis of advanced semiconductor packages, where stress and warpage from thermal cycling must be evaluated repeatedly across a design-of-experiments sweep under costly finite element analysis (FEA). 2) Laplace PDE iterative numerical solver for capacitance field. Overall, recursive weight-sharing transformers provide an effective and generalizable trade-off between prediction accuracy, parameter efficiency, and computational cost for small data engineering surrogate modeling.

This work presents a deterministic, machine-assisted framework for SI-compliant PCB design based on the Earth Mover's Distance (EMD). In contrast to conventional surrogate-based optimization methods that rely on iterative black-box search procedures, the proposed approach follows an interpretable, sequential evaluation strategy. Neural surrogate models are first used to efficiently predict waveform describing features from topology-dependent design parameters. A decision tree then acts as a physically motivated quality gate that identifies SI-compliant waveforms according to predefined SI criteria. Within the resulting valid solution space, the Earth Mover's Distance is employed as a similarity metric to rank candidate designs according to their proximity to an ideal reference signal. This enables not only the deterministic identification of admissible parameter regions but also a transparent prioritization of physically superior solutions without inverse modeling or stochastic search procedures. The methodology is demonstrated using a large-scale set of simulated DDR3 fly-by waveforms. By combining surrogate prediction, interpretable classification, and EMD-based waveform evaluation, the framework provides an explainable and computationally efficient alternative to conventional optimization strategies for supporting PCB development with AI-based methods.

Interior permanent magnet synchronous motor (IPMSM) design requires balancing conflicting objectives and multi-physics constraints, while modern optimization workflows face three bottlenecks: manual problem setup, high finite element analysis (FEA) cost, and unreliable surrogate-based search in sparse or out-of-distribution regions. To address these limitations, we propose an end-to-end automated IPMSM design optimization framework that integrates retrieval-augmented generation (RAG) for structured problem definition with an uncertainty-aware FEA-AI hybrid optimization pipeline. A Design agent, connected to a motor textbook through RAG, provides domain-knowledge-based options and engineering tips, and compiles an optimization card and a design-of-experiments plan for AI-model training. A Training agent automates electromagnetic FEA, records geometry-validation and solver-failure logs, analyzes failed geometries using ANOVA-based data analysis and LLM reasoning, and invokes a Design Sampling agent to redefine the design space and generate additional samples. An Optimization agent performs GA-based search with uncertainty-driven switching: low-uncertainty candidates are evaluated by AI-surrogate inference, whereas high-uncertainty and reliability-critical Pareto-front or top-K candidates are corrected by high-fidelity FEA and reused for iterative retraining. The framework converts manual, experience-dependent configuration into a reproducible workflow that balances computational cost and prediction reliability. Experimental results under a matched high-fidelity FEA budget show that the proposed hybrid approach achieves better objective performance while maintaining low and further reducible predictive uncertainty, outperforming FEA-only search, which is limited by early budget exhaustion, and AI-only search, which converges to a low-confidence optimum.