Related papers: On the validity of complex Langevin method for pat…
Likelihood profiling is an efficient and powerful frequentist approach for parameter estimation, uncertainty quantification and practical identifiablity analysis. Unfortunately, these methods cannot be easily applied for stochastic models…
Self-interacting scalar quantum field theories possessing $PT$-symmetry are physically admissible since their energy spectrum is real and bounded below. However, models with $PT$-invariant potentials can have complex actions in general and…
Lattice models are valuable tools to gain insight into the statistical physics of heteropolymers. We rigorously map the partition function of these models into a vacuum expectation value of a $\mathbb{Z}_2$ lattice gauge theory (LGT), with…
We derive the linear Langevin equation that describes the behavior of critical fluctuation above the critical temperature of the chiral phase transition in the Nambu-Jona-Lasinio model. The Langevin equation relaxes exhibiting oscillation…
Gaussian variational inference and the Laplace approximation are popular alternatives to Markov chain Monte Carlo that formulate Bayesian posterior inference as an optimization problem, enabling the use of simple and scalable stochastic…
Bayesian inference requires approximation methods to become computable, but for most of them it is impossible to quantify how close the approximation is to the true posterior. In this work, we present a theorem upper-bounding the KL…
Langevin Monte Carlo (LMC) algorithms are popular Markov Chain Monte Carlo (MCMC) methods to sample a target probability distribution, which arises in many applications in machine learning. Inspired by regime-switching stochastic…
The generalized Jeffreys-type law is formulated as a multi-term time-fractional Jeffreys-type equation, whose dynamics exhibit rich scaling crossover phenomena entailing different diffusion mechanisms. In this work, we provide a novel…
The Langevin equation is a common tool to model diffusion at a single-particle level. In non-homogeneous environments, such as aqueous two-phase systems or biological condensates with different diffusion coefficients in different phases,…
Real time evolution of a scalar field theory is investigated. The severe sign problem is circumvented using the Complex Langevin equation. The naive application of the method breaks down for extended real times due to the appearance of…
The exact estimation of latent variable models with big data is known to be challenging. The latents have to be integrated out numerically, and the dimension of the latent variables increases with the sample size. This paper develops a…
We describe a stochastic technique which allows one to compute numerically the coefficients of the weak coupling perturbative expansion of any observable in Lattice Gauge Theory. The idea is to insert the exponential representation of the…
Effective Polyakov line models, derived from SU(3) gauge-matter systems at finite chemical potential, have a sign problem. In this article I solve two such models, derived from SU(3) gauge-Higgs and heavy quark theories by the relative…
Time derivatives of scalar fields occur quadratically in textbook actions. A simple Legendre transformation turns the lagrangian into a hamiltonian that is quadratic in the momenta. The path integral over the momenta is gaussian. Mean…
We propose a new stable Levin method to compute oscillatory integrals with logarithmic singularities and without stationary points. To avoid the singularity, we apply the technique of singularity separation and transform the singular ODE…
The three-dimensional SU(3) spin model is an effective Polyakov loop model for QCD at nonzero temperature and density. It suffers from a sign problem at nonzero chemical potential. We revisit this model using complex Langevin dynamics and…
Stochastic gradient Langevin dynamics (SGLD) is a computationally efficient sampler for Bayesian posterior inference given a large scale dataset. Although SGLD is designed for unbounded random variables, many practical models incorporate…
Simulations of QCD with a finite chemical potential typically lead to a severe sign problem, prohibiting any standard Monte Carlo approach. Complex Langevin simulations provide an alternative to sample path integrals with oscillating weight…
Transition of a system between two states is an important but difficult problem in natural science. In this article we study the transition problem in the framework of transition path ensemble. Using the overdamped Langevin method, we…
We review the critical behaviour of the Driven Lattice Gas (DLG) model. As a result, we obtain a novel Langevin equation for the DLG which depends on the microscopic transition probabilities. We then show how this dependence affects the…