Differential Algebraic Equation

Differential-algebraic equations (DAEs) model dynamic systems subject to both differential and algebraic constraints, often representing physical laws or limitations. Current research focuses on developing efficient and accurate numerical solutions for DAEs, particularly high-index systems, using methods like physics-informed neural networks (PINNs), Gaussian processes, and specialized machine learning algorithms tailored to the DAE structure. These advancements are improving data-driven modeling of complex systems across diverse fields, including multibody dynamics, circuit design, and sustainable energy, by enabling more accurate and computationally tractable simulations. The development of robust identifiability tests for DAE models is also a key area of focus, ensuring reliable parameter estimation from experimental data.