Φ-BO: Physics-Informed Bayesian Optimization for Multi-Port Decoupling Capacitor Placement in 2.5-D Chiplets

Power distribution network (PDN) optimization in 2.5-D chiplet architectures represents a critical bottleneck as designs scale to 100+ integrated chiplets, where decoupling capacitor placement becomes a multi-port optimization challenge requiring millions of expensive electromagnetic (EM) simulations. Current state-of-the-art (SOTA) methods - from genetic algorithms (GA) to reinforcement learning (RL) - treat PDN as black-box functions, failing to exploit inherent physical structure and scaling exponentially with problem complexity. We introduce Φ-BO, the first physics-informed Bayesian optimization (BO) framework specifically designed for multi-port decoupling capacitor placement in 2.5-D chiplet PDN. Our key innovation systematically integrates EM field theory into machine learning (ML) optimization through novel spatial feature transformations and Multi-Port Aware Transformation (MPAT), enabling a paradigm shift from black-box to physics-aware optimization. This approach captures spatial dependencies and port coupling effects, dramatically reducing effective problem dimensionality while enabling intelligent exploration of discrete placement configurations. Demonstrated on a 22-chiplet RISC-V processor design, Φ-BO achieves 23% impedance improvement, and 3 × faster convergence compared to SOTA methods.