All Outputs (21)

Neural variance reduction for stochastic differential equations (2023)
Journal Article

Variance reduction techniques are of crucial importance for the efficiency of Monte Carlo simulations in finance applications. We propose the use of neural SDEs, with control variates parameterized by neural networks, in order to learn approximately... Read More about Neural variance reduction for stochastic differential equations.

Deep Learning of Transition Probability Densities for Stochastic Asset Models with Applications in Option Pricing (2023)
Journal Article

Transition probability density functions (TPDFs) are fundamental to computational finance, including option pricing and hedging. Advancing recent work in deep learning, we develop novel neural TPDF generators through solving backward Kolmogorov equat... Read More about Deep Learning of Transition Probability Densities for Stochastic Asset Models with Applications in Option Pricing.

Simplest random walk for approximating Robin boundary value problems and ergodic limits of reflected diffusions (2023)
Journal Article

A simple-to-implement weak-sense numerical method to approximate reflected stochastic differential equations (RSDEs) is proposed and analysed. It is proved that the method has the first order of weak convergence. Together with the Monte Carlo techniq... Read More about Simplest random walk for approximating Robin boundary value problems and ergodic limits of reflected diffusions.

Consensus-based optimization via jump-diffusion stochastic differential equations (2023)
Journal Article

We introduce a new consensus-based optimization (CBO) method where an interacting particle system is driven by jump-diffusion stochastic differential equations (SDEs). We study well-posedness of the particle system as well as of its mean-field limit.... Read More about Consensus-based optimization via jump-diffusion stochastic differential equations.

Ensemble Kalman inversion for magnetic resonance elastography. (2022)
Journal Article

Magnetic Resonance Elastography (MRE) is an MRI-based diagnostic method for measuring mechanical properties of biological tissues. MRE measurements are processed by an inversion algorithm to produce a map of the biomechanical properties. In this pape... Read More about Ensemble Kalman inversion for magnetic resonance elastography..

Controlling resin flow in Liquid Composite Moulding processes through localized irradiation with ultraviolet light (2022)
Journal Article

A vacuum infusion process was implemented to produce composite specimens from a random glass filament mat and an acrylic modified polyester resin curable upon irradiation with ultraviolet (UV) light. Through localized irradiation with UV light during... Read More about Controlling resin flow in Liquid Composite Moulding processes through localized irradiation with ultraviolet light.

Random walk algorithm for the Dirichlet problem for parabolic integro-differential equation (2021)
Journal Article

We consider stochastic differential equations driven by a general Lévy processes (SDEs) with infinite activity and the related, via the Feynman–Kac formula, Dirichlet problem for parabolic integro-differential equation (PIDE). We approximate the solu... Read More about Random walk algorithm for the Dirichlet problem for parabolic integro-differential equation.

Bayesian inversion algorithm for estimating local variations in permeability and porosity of reinforcements using experimental data (2021)
Journal Article

Mean-square approximation of Navier-Stokes equations with additive noise in vorticity-velocity formulation (2020)
Journal Article

We consider a time discretization of incompressible Navier-Stokes equations with spatial periodic boundary conditions and additive noise in the vorticity-velocity formulation. The approximation is based on freezing the velocity on time subintervals r... Read More about Mean-square approximation of Navier-Stokes equations with additive noise in vorticity-velocity formulation.

Effect of random forcing on fluid lubricated bearing (2019)
Journal Article

A model for a fluid lubricated bearing is derived for operation under conditions where external forces are subject to random fluctuations that may act to destabilise the bearing. The fluid flow through the bearing is described by a Reynolds equation... Read More about Effect of random forcing on fluid lubricated bearing.

Mutation and Selection in Bacteria: Modelling and Calibration (2018)
Journal Article

© 2018, The Author(s). Temporal evolution of a clonal bacterial population is modelled taking into account reversible mutation and selection mechanisms. For the mutation model, an efficient algorithm is proposed to verify whether experimental data ca... Read More about Mutation and Selection in Bacteria: Modelling and Calibration.

Bayesian inversion in resin transfer molding (2018)
Journal Article

We study a Bayesian inverse problem arising in the context of Resin Transfer Molding (RTM), which is a process commonly used for the manufacturing of fiber- reinforced composite materials. The forward model is described by a moving boundary problem i... Read More about Bayesian inversion in resin transfer molding.

Evaluation of the minimum face clearance of a high speed gas lubricated bearing with Navier slip boundary conditions under random excitations (2018)
Journal Article

Motivated by ongoing developments in aero-engine technology, a model for a coupled gas lubricated bearing is developed in terms of an extended dynamical system. A slip boundary condition, characterised by a slip length, is incorporated on the bearing... Read More about Evaluation of the minimum face clearance of a high speed gas lubricated bearing with Navier slip boundary conditions under random excitations.

Geometric integrator for Langevin systems with quaternion-based rotational degrees of freedom and hydrodynamic interactions (2017)
Journal Article

We introduce new Langevin-type equations describing the rotational and translational motion of rigid bodies interacting through conservative and non-conservative forces, and hydrodynamic coupling. In the absence of non-conservative forces the Langevi... Read More about Geometric integrator for Langevin systems with quaternion-based rotational degrees of freedom and hydrodynamic interactions.

Uncertainty in geometry of fibre preforms manufactured with Automated Dry Fibre Placement and its effects on permeability (2017)
Journal Article

© 2017, The Author(s) 2017. Resin transfer moulding is one of several processes available for manufacturing fibre-reinforced composites from dry fibre reinforcement. Recently, dry reinforcements made with Automated Dry Fibre Placement have been intro... Read More about Uncertainty in geometry of fibre preforms manufactured with Automated Dry Fibre Placement and its effects on permeability.

Stochastic resin transfer molding process (2017)
Journal Article

We consider one-dimensional and two-dimensional models of the stochastic resin transfer molding process, which are formulated as random moving boundary problems. We study their properties, analytically in the one-dimensional case and numerically in t... Read More about Stochastic resin transfer molding process.

Layer methods for stochastic Navier–Stokes equations using simplest characteristics (2016)
Journal Article

We propose and study a layer method for stochastic Navier-Stokes equations (SNSE) with spatial periodic boundary conditions and additive noise. The method is constructed using conditional probabilistic representations of solutions to SNSE and exploit... Read More about Layer methods for stochastic Navier–Stokes equations using simplest characteristics.

New Langevin and gradient thermostats for rigid body dynamics (2015)
Journal Article

Wiener chaos versus stochastic collocation methods for linear advection-diffusion-reaction equations with multiplicative white noise (2015)
Journal Article

We compare Wiener chaos and stochastic collocation methods for linear advection-reaction-diffusion equations with multiplicative white noise. Both methods are constructed based on a recursive multistage algorithm for long-time integration. We derive... Read More about Wiener chaos versus stochastic collocation methods for linear advection-diffusion-reaction equations with multiplicative white noise.

A recursive sparse grid collocation method for differential equations with white noise (2014)
Journal Article

We consider a sparse grid collocation method in conjunction with a time discretization of the differential equations for computing expectations of functionals of solutions to differential equations perturbed by time-dependent white noise. We first an... Read More about A recursive sparse grid collocation method for differential equations with white noise.