Related papers: Consensus-based optimization with $\alpha$-stable …
Stochastic bilevel optimization (SBO) has been integrated into many machine learning paradigms recently, including hyperparameter optimization, meta learning, and reinforcement learning. Along with the wide range of applications, there have…
We derive general properties of anomalous diffusion and nonexponential relaxation from the theory of tempered \alpha-stable processes. Its most important application is to overcome the infinite-moment difficulty for the \alpha-stable random…
This paper presents and analyzes the compensated projected Euler-Maruyama method for stochastic differential equations with jumps under a global monotonicity condition. Compared with existing conditions, this condition allows the…
This paper is concerned with the numerical approximation of stochastic ordinary differential equations, which satisfy a global monotonicity condition. This condition includes several equations with super-linearly growing drift and diffusion…
We calibrate parameters of neural networks that model forces in interaction dynamics with the help of the Consensus-based global optimization method (CBO). We state the general framework of interaction particle systems driven by neural…
We analyse the convergence and stability of a micro-macro acceleration algorithm for Monte Carlo simulations of stiff stochastic differential equations with a time-scale separation between the fast evolution of the individual stochastic…
We propose a piecewise deterministic Markovian jump process in Hilbert space such that the covariance matrix of this stochastic process solves the thermodynamic quantum master equation. The proposed stochastic process is particularly simple…
This paper addresses the question of whether it can be beneficial for an optimization algorithm to follow directions of negative curvature. Although prior work has established convergence results for algorithms that integrate both descent…
Diffusion of particles in velocity space undergoing turbulent field was extensively studied in the problem of warm beam relaxation. Under low field intensities the diffusion is described by the Fokker-Planck equation with the diffusion…
Stochastic thermodynamics investigates energetic and entropic bounds in small systems. Foundational results, e.g., the first and second laws, predominantly rely on the Markov (memoryless) assumption. Although physicists recognise that the…
We analyze the fluctuation-driven escape of particles from a metastable state under the influence of a weak periodic force. We develop an asymptotic method to solve the appropriate Fokker-Planck equation with mixed natural and absorbing…
This paper discusses tractable development and statistical estimation of a continuous time stochastic process with a finite state space having non-Markov property. The process is formed by a finite mixture of right-continuous Markov jump…
Stochastic reaction-diffusion equations are a popular modelling approach for studying interacting populations in a heterogeneous environment under the influence of environmental fluctuations. Although the theoretical basis of alternative…
This paper develops solutions of fractional Fokker-Planck equations describing subdiffusion of probability densities of stochastic dynamical systems driven by non-Gaussian L\'evy processes, with space-time-dependent drift, diffusion and…
We study Markov processes associated with stochastic differential equations, whose non-linearities are gradients of convex functionals. We prove a general result of existence of such Markov processes and a priori estimates on the transition…
In this paper, a physics-oriented stochastic kinetic scheme will be developed that includes random inputs from both flow and electromagnetic fields via a hybridization of stochastic Galerkin and collocation methods. Based on the BGK-type…
Bi-level optimization problems, where one wishes to find the global minimizer of an upper-level objective function over the globally optimal solution set of a lower-level objective, arise in a variety of scenarios throughout science and…
Computational multi-scale methods capitalize on a large time-scale separation to efficiently simulate slow dynamics over long time intervals. For stochastic systems, one often aims at resolving the statistics of the slowest dynamics. This…
This work develops Monte Carlo Euler adaptive time stepping methods for the weak approximation problem of jump diffusion driven stochastic differential equations. The main result is the derivation of a new expansion for the omputational…
We analyze convergence rates of stochastic optimization procedures for non-smooth convex optimization problems. By combining randomized smoothing techniques with accelerated gradient methods, we obtain convergence rates of stochastic…