Universal Differential Equation

Universal Differential Equations (UDEs) combine mechanistic models with neural networks to create flexible and data-driven models for complex dynamical systems. Current research focuses on improving UDE robustness through techniques like non-negativity constraints and rigorous uncertainty quantification, as well as extending their applicability to diverse problem domains, including partial differential equations and differential-algebraic equations, often leveraging transformer architectures. This approach offers a powerful tool for scientific discovery by integrating prior knowledge with data-driven learning, enabling improved modeling and prediction across various scientific and engineering fields.