Search algorithm and sampling algorithm using nonlinear dynamics

I am studying the use of complexity that is found in large-scale nonlinear dynamical systems for information processing and problem-solving. Modern computation and information processing are performed more diversely, for example, with specialized devices such as GPUs and quantum computers. In addition, other than in artificial computational devices, information processing can be found in other places such as brain activity and intracellular information transmission. Computation and information processing are realized in various forms, but all of which are supported by nonlinear and dynamic phenomena. By studying nonlinear dynamical systems for computation and information processing through mathematical models, I expect that we can obtain a model of dynamics that guides the designing of new computational devices or is itself useful as an algorithm through efficient numerical simulations. Specifically, I am working on optimization problems such as the satisfiability problem and Ising problem, and numerical integration for complex probability distributions. For these problems, I am developing search and sampling algorithms, analyzing their performance, and studying numerical methods. These problems are important because they frequently appear as mathematical expressions of engineering problems and they are also known as problems for which simple and regular enumeration and search become inefficient. For this reason, it is popular using stochastic noise to increase the complexity of the search, and I believe that using the complex behavior of nonlinear dynamical systems is effective for such problems.