Accurate traffic forecasting is essential for network capacity planning, traffic engineering, and congestion management. Deep learning models such as LSTMs and Temporal Convolutional Networks (TCNs) achieve low prediction error but ignore link capacity limits, often leading to forecasts that are physically unrealistic. Physics-informed neural networks (PINNs) offer a way to include domain constraints, but naive formulations may reduce accuracy. We propose Soft-PINN, a physics-informed model that adds a differentiable penalty for exceeding link capacities, allowing a flexible trade-off between accuracy and feasibility. Evaluated on the Abilene backbone for forecasting horizons \(H \in {1,6,12}\) , Soft-PINN significantly reduces capacity violations—often to near zero—while maintaining accuracy comparable to strong neural baselines. These results show that Soft-PINN is a practical approach for capacity-aware traffic forecasting in backbone networks.