Deep learning models are increasingly deployed in safety-critical tasks where predictions must satisfy hard constraints, such as physical laws, fairness requirements, or safety limits. However, standard architectures lack built-in mechanisms to enforce such constraints, and existing approaches based on regularization or projection are often limited to simple constraints, computationally expensive, or lack feasibility guarantees. This paper proposes a model-agnostic framework for enforcing input-dependent linear equality and inequality constraints on neural network outputs. The architecture combines a task network trained for prediction accuracy with a safe network trained using decision rules from the stochastic and robust optimization literature to ensure feasibility across the entire input space. The final prediction is a convex combination of the two subnetworks, guaranteeing constraint satisfaction during both training and inference without iterative procedures or runtime optimization. We prove that the architecture is a universal approximator of constrained functions and derive computationally tractable formulations based on linear decision rules. Empirical results on benchmark regression tasks show that our method consistently satisfies constraints while maintaining competitive accuracy and low inference latency.

Natural-gas and power systems are increasingly interdependent due to the integration of an increasing number of combined cycle gas turbines in the power generation mix. However, natural gas and power systems are generally independently operated. This is the result of history and the fact that natural gas has not been important for electricity production until recently. Adopting a power system perspective, this article reviews in a tutorial manner models for the operations and long-term expansion planning of interdependent but independently operated natural-gas and power systems.