Related papers: Moment Analysis of Stochastic Hybrid Systems Using…
We present an adjoint sensitivity method for hybrid discrete -- continuous systems, extending previously published forward sensitivity methods. We treat ordinary differential equations and differential-algebraic equations of index up to two…
Many stochastic differential equations (SDEs) in the literature have a superlinearly growing nonlinearity in their drift or diffusion coefficient. Unfortunately, moments of the computationally efficient Euler-Maruyama approximation method…
A moment body is a linear projection of the spectraplex, the convex set of trace-one positive semidefinite matrices. Determining whether a given point lies within a given moment body is a problem with numerous applications in quantum state…
Adaptive moment methods have been remarkably successful in deep learning optimization, particularly in the presence of noisy and/or sparse gradients. We further the advantages of adaptive moment techniques by proposing a family of double…
The moment quantities associated with the nonlinear Schrodinger equation offer important insights towards the evolution dynamics of such dispersive wave partial differential equation (PDE) models. The effective dynamics of the moment…
We propose a methodology to address two analysis problems concerning complex systems, namely bounding state functionals of stochastic differential equations (SDEs) and verifying set avoidance of systems described by partial differential…
Magnetohydrodynamics (MHD) describes the interaction between electrically conducting fluids and electromagnetic fields. We propose and analyze a symplectic, second-order algorithm for the evolutionary MHD system in Els\"asser variables. We…
The derivation of dynamical laws for general observables (or moments) from the master equation for the probability distribution remains a challenging problem in statistical physics. Here, we present an alternative formulation of the general…
In this paper, we study numerical approximations for optimal control of a class of stochastic partial differential equations with partial observations. The system state evolves in a Hilbert space, whereas observations are given in…
This paper is concerned with stochastic incompressible Navier-Stokes equations with multiplicative noise in two dimensions with respect to periodic boundary conditions. Based on the Helmholtz decomposition of the multiplicative noise,…
A step-search sequential quadratic programming method is proposed for solving nonlinear equality constrained stochastic optimization problems. It is assumed that constraint function values and derivatives are available, but only stochastic…
We present a systematic study of moment evolution in multidimensional stochastic difference systems, focusing on characterizing systems whose low-order moments diverge in the neighborhood of a stable fixed point. We consider systems with a…
We analyze a simple randomized subgradient method for approximating solutions to stochastic systems of convex functional constraints, the only input to the algorithm being the size of minibatches. By introducing a new notion of what is…
We study statistical model checking of continuous-time stochastic hybrid systems. The challenge in applying statistical model checking to these systems is that one cannot simulate such systems exactly. We employ the multilevel Monte Carlo…
Fractional statistical moments are utilized for various tasks of uncertainty quantification, including the estimation of probability distributions. However, an estimation of fractional statistical moments of costly mathematical models by…
We consider stochastic convex optimization problems where the objective is an expectation over smooth functions. For this setting we suggest a novel gradient estimate that combines two recent mechanism that are related to notion of…
Stochastic gradient descent with momentum (SGDM) is the dominant algorithm in many optimization scenarios, including convex optimization instances and non-convex neural network training. Yet, in the stochastic setting, momentum interferes…
We propose a hybrid algorithm for the time integration of large sets of rate equations coupled by a relatively small number of degrees of freedom. A subset containing fast degrees of freedom evolves deterministically, while the rest of the…
Simulation of stochastic spatially-extended systems is a challenging problem. The fundamental quantities in these models are individual entities such as molecules, cells, or animals, which move and react in a random manner. In big systems,…
A novel class of non-reversible Markov chain Monte Carlo schemes relying on continuous-time piecewise-deterministic Markov Processes has recently emerged. In these algorithms, the state of the Markov process evolves according to a…