A Physics-Informed Neural Network Surrogate for Runtime PDN and Dynamic Droop Prediction in 2.5-D Chiplet Integration

By Xi Chen, Northwestern University

Power delivery network (PDN) analysis has become increasingly critical in heterogeneous 2.5-D chiplet systems, where reduced supply voltages and complex interposer-package structures amplify both resistive and inductive droop effects. Traditional circuit solvers provide accurate results but are prohibitively slow for large-scale transient simulations, while purely data-driven neural networks (NNs) lack physical consistency and often require excessive training data. This work introduces a physics-informed NN (PINN) framework that embeds circuit constraints into training, enforcing current and voltage constraints while reducing dependence on labeled data. The framework is extended to multilayer 2.5-D PDNs by spatially labeling chiplet and interposer, with vertical links modeled through partial differential equation (PDE) residuals. Boundary/initial conditions (ICs), workload encoding, and step-load superposition enable efficient modeling of realistic transient supply profiles. Loss normalization and adaptive reweighting in multiobjective optimization (MOO) improve convergence stability, enabling accurate training under limited simulation data. Experiments on 2.5-D chiplets with RISC- V processors and convolutional NN (CNN) accelerators show that the framework achieves sub-mV accuracy with up to 80% fewer simulations compared to conventional NNs and nearly 300× runtime reduction compared with commercial solvers. Experimental results also demonstrate generalization to out-of-distribution (OOD) workloads, reducing worst case droop error by up to 35 mV compared with conventional NNs. Relative to recent CNN-based IR-drop estimators, the proposed PINN achieves 1.5× higher accuracy and 7× lower inference latency.