The simulation of matter by direct computation of individual atomic motions has become an important element in the design of new drugs and in the construction of new materials. This book demonstrates how to implement the numerical techniques needed for such simulation, thereby aiding the design of new, faster, and more robust solution schemes. Clear explanations and many examples and exercises will ensure the value of this text for students, professionals, and researchers.

In this book the authors describe the principles and methods behind probabilistic forecasting and Bayesian data assimilation. Instead of focusing on particular application areas, the authors adopt a general dynamical systems approach, with a profusion of low-dimensional, discrete-time numerical examples designed to build intuition about the subject. Part I explains the mathematical framework of ensemble-based probabilistic forecasting and uncertainty quantification. Part II is devoted to Bayesian filtering algorithms, from classical data assimilation algorithms such as the Kalman filter,...

This book contains two review articles on nonlinear data assimilation that deal with closely related topics but were written and can be read independently. Both contributions focus on so-called particle filters.

The first contribution by Jan van Leeuwen focuses on the potential of proposal densities. It discusses the issues with present-day particle filters and explorers new ideas for proposal densities to solve them, converging to particle filters that work well in systems of any dimension, closing the contribution with a high-dimensional example. The second contribution by Cheng and Reich...