Physics-Informed Neural Network with Residual Correction Architecture for Hybrid Feedforward-Feedback Temperature...

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.