Adaptive stepsize and instabilities in complex Langevin dynamics

Current-induced atomic dynamics, instabilities, and Raman signals: Quasiclassical Langevin equation approach

Dynamics of Langevin Simulations

This chapter reviews numerical simulations of quantum field theories based on stochastic quantization and the Langevin equation. The topics discussed include renormalization of finite stepsize algorithms, Fourier acceleration, and the relation of the Langevin equation to hybrid stochastic algorithms and hybrid Monte Carlo. Invited chapter to appear in the special supplement “Stochastic Quantiza...

Mirrored Langevin Dynamics

We generalize the Langevin Dynamics through the mirror descent framework for first-order sampling. The näıve approach of incorporating Brownian motion into the mirror descent dynamics, which we refer to as Symmetric Mirrored Langevin Dynamics (S-MLD), is shown to connected to the theory of Weighted Hessian Manifolds. The S-MLD, unfortunately, contains the hard instance of Cox–Ingersoll–Ross pro...

Stepsize control for adaptive multiprecision path tracking

Numerical difficulties encountered when following paths using methods such as homotopy continuation may be overcome by combining adaptive stepsize and adaptive multiprecision. In the paper Adaptive multiprecision path tracking [1], precision and stepsize are adapted separately. This can lead to suboptimal performance and even failure in certain circumstances. This paper presents a strategy for ...

Instabilities in population dynamics

Biologists have long known that the smaller the population, the more susceptible it is to extinction from various causes. Biologists define minimum viable population size (MVP), which is the critical population size, below which the population has a very small chance to survive. There are several theoretical models for predicting the probability that a small population will become extinct. But ...