Related papers: Stochastic hierarchical data-driven optimization: …

A widely used heuristic for solving stochastic optimization problems is to use a deterministic rolling horizon procedure, which has been modified to handle uncertainty (e.g. buffer stocks, schedule slack). This approach has been criticized…

In this paper we present a data driven approach for approximating dynamical systems. A dynamics is approximated using basis functions, which are derived from maximization of the information-theoretic entropy, and can be generated directly…

In this paper, a shape optimization problem constrained by a random elliptic partial differential equation with a pure Neumann boundary is presented. The model is motivated by applications in interface identification, where we assume…

Large scale models of physical phenomena demand the development of new statistical and computational tools in order to be effective. Many such models are `sloppy', i.e., exhibit behavior controlled by a relatively small number of parameter…

Stochastic sequential decision making often requires hierarchical structure in the problem where each high-level action should be further planned with primitive states and actions. In addition, many real-world applications require a plan…

A version of the time-parallel algorithm parareal is analyzed and applied to stochastic models in chemical kinetics. A fast predictor at the macroscopic scale (evaluated in serial) is available in the form of the usual reaction rate…

Stochastic models of biochemical reaction networks are widely used to capture intrinsic noise in cellular systems. The typical formulation of these models are based on Markov processes for which there is extensive research on efficient…

Stochastic optimization algorithms update models with cheap per-iteration costs sequentially, which makes them amenable for large-scale data analysis. Such algorithms have been widely studied for structured sparse models where the sparsity…

We address the question of parameterizing the subgrid scales in simulations of geophysical flows by applying stochastic mode reduction to the one-dimensional stochastically forced shallow water equations. The problem is formulated in…

Nonlinear differential equations rarely admit closed-form solutions, thus requiring numerical time-stepping algorithms to approximate solutions. Further, many systems characterized by multiscale physics exhibit dynamics over a vast range of…

We develop a non-empirical scheme to search for the minimum-energy escape paths from the minima of the potential surface to unknown saddle points nearby. A stochastic algorithm is constructed to move the walkers up the surface through the…

This paper concerns models and convergence principles for dealing with stochasticity in a wide range of algorithms arising in nonlinear analysis and optimization in Hilbert spaces. It proposes a flexible geometric framework within which…

We present a new method for stochastic shape optimisation of engineering structures. The method generalises an existing deterministic scheme, in which the structure is represented and evolved by a level-set method coupled with mathematical…

We present a novel approach to investigate the long-time stochastic dynamics of multi-dimensional classical systems, in contact with a heat-bath. When the potential energy landscape is rugged, the kinetics displays a decoupling of short and…

Quantifying uncertainty in predictive simulations for real-world problems is of paramount importance - and far from trivial, mainly due to the large number of stochastic parameters and significant computational requirements. Adaptive sparse…

Stochasticity plays a fundamental role in various biochemical processes, such as cell regulatory networks and enzyme cascades. Isothermal, well-mixed systems can be modelled as Markov processes, typically simulated using the Gillespie…

The simulation of complex stochastic network dynamics arising, for instance, from models of coupled biomolecular processes remains computationally challenging. Often, the necessity to scan a models' dynamics over a large parameter space…

We focus on improving the accuracy of an approximate model of a multiscale dynamical system that uses a set of parameter-dependent terms to account for the effects of unresolved or neglected dynamics on resolved scales. We start by…

Stochastic Spatio-Temporal processes are prevalent across domains ranging from modeling of plasma to the turbulence in fluids to the wave function of quantum systems. This letter studies a measure-theoretic description of such systems by…

Finding parameters that minimise a loss function is at the core of many machine learning methods. The Stochastic Gradient Descent algorithm is widely used and delivers state of the art results for many problems. Nonetheless, Stochastic…