Closed-Loop Latent Surrogate Modeling of Thermally Coupled VCSEL Dynamics for Waveform-Level Circuit Simulation

Abstract

We present a compact data-driven surrogate model for waveform-level simulation of thermally coupled VCSEL dynamics, motivated by fabrication-stage studies in which repeated transient evaluation with high-fidelity electro-thermal VCSEL models can become costly and cumbersome. The proposed approach identifies an empirical finite-memory representation from simulator-generated waveform data, and then learns a shared nonlinear latent dynamical model with lightweight temperature-specific affine readouts. Training is performed using a closed-loop rollout objective so that the surrogate is optimized for recursive self-generated operation rather than only one-step prediction. Simulation results based on a high-fidelity electro-thermal VCSEL model at 20 Gbaud show that the surrogate can reproduce optical waveforms accurately over 1200-sample free-running rollouts across temperatures from −40°C to 80°C. The learned encoder contains 35,680 trainable parameters, corresponding to approximately 0.136 MB in single precision, while each temperature-specific affine readout adds only 33 parameters. The results further show that a shared latent representation transfers across temperatures through lightweight per-temperature readout calibration, and also transfers effectively across bias conditions with minimal adaptation. These findings support closed-loop latent dynamical surrogate modeling as a compact approach for repeated waveform-level evaluation of thermally coupled VCSEL dynamics.