Appropriate noise addition to metaheuristic algorithms can enhance their performance.

Nature-inspired swarm-based algorithms are increasingly applied to tackle high-dimensional and complex optimization problems across disciplines. They are general purpose optimization algorithms, easy to implement and assumption-free. Some common drawbacks of these algorithms are their premature convergence and the solution found may not be a global optimum.

Concrete ensemble Kalman filters with rigorous catastrophic filter divergence.

The ensemble Kalman filter and ensemble square root filters are data assimilation methods used to combine high-dimensional, nonlinear dynamical models with observed data. Ensemble methods are indispensable tools in science and engineering and have enjoyed great success in geophysical sciences, because they allow for computationally cheap low-ensemble-state approximation for extremely high-dimensional turbulent forecast models. From a theoretical perspective, the dynamical properties of these methods are poorly understood.