Physics-Informed Neural Network with Residual Correction Architecture for Hybrid Feedforward–Feedback Temperature Control of DFB Semiconductor Lasers

Wavelength stability of distributed feedback (DFB) semiconductor lasers in dense wavelength division multiplexing (DWDM) systems hinges on sub-millikelvin temperature regulation, a task complicated by the nonlinear, multi-node dynamics of the thermoelectric cooler (TEC) and the purely reactive nature of conventional proportional–integral–derivative (PID) control. We present a physics-informed neural network (PINN) built around a residual correction architecture for hybrid feedforward–feedback TEC temperature control. Rather than penalizing physics-residual violations in the loss function, the architecture wires a simplified one-node thermal model directly into the network graph as a frozen baseline. A trainable branch then learns only the residual mismatch. Temporal lag features are appended to the input so that the network can reconstruct unmeasured internal thermal states from the cold-side temperature history, which proves essential for overcoming the partial-observability bottleneck inherent in multi-node TEC packages. Ablation experiments on a high-fidelity three-node TEC simulator show that all model variants (PINN, physics-feature-augmented NN, and pure NN) exceed R2 = 0.993 when trained on the full dataset, yet the PINN’s advantage becomes pronounced under data scarcity. At a 3% training budget, it reaches R2 = 0.966 versus 0.930 for the pure NN, implying an approximately 5.4× reduction in the data needed to reach a given accuracy target. In closed-loop validation, the PINN+PID hybrid settles 60% faster than standalone PID. Tracking RMSE drops by 69%, and peak disturbance deviation falls by 74%, across step, multi-setpoint, and current-perturbation scenarios. All results reported here are obtained in simulations. Experimental validation on physical DFB-TEC hardware is left to future work.