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 R