Machine learning with hard constraints: Neural Differential-Algebraic Equations (DAEs) as a general formalism

Neural differential-algebraic equations (DAEs) allow imposing hard constraints on machine learning models for dynamical systems. This approach combines neural networks with algebraic constraints to enforce physical laws or other requirements. Different formulations exist, including fully implicit DAEs, mass matrix DAEs, and manifold projection methods, each with tradeoffs in generality, computational efficiency, and constraint preservation.