DOI10.1007/978-3-642-41095-6_4zbMath1302.65004arXiv1304.5472OpenAlexW2949063410MaRDI QIDQ2926211
Michael B. Giles
Publication date: 31 October 2014
Published in: Acta Numerica, Springer Proceedings in Mathematics & Statistics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1304.5472
Space-time multilevel Monte Carlo methods and their application to cardiac electrophysiology,
The role of adaptivity in a numerical method for the Cox-Ingersoll-Ross model,
A generalized approximate control variate framework for multifidelity uncertainty quantification,
Coupling the reduced-order model and the generative model for an importance sampling estimator,
Numerical analysis of lognormal diffusions on the sphere,
Physics-informed machine learning with conditional Karhunen-Loève expansions,
Multilevel asymptotic-preserving Monte Carlo for kinetic-diffusive particle simulations of the Boltzmann-BGK equation,
On the optimization of approximate control variates with parametrically defined estimators,
Approximation of probability density functions by the multilevel Monte Carlo maximum entropy method,
Multilevel estimation of normalization constants using ensemble Kalman-Bucy filters,
Uncertainty quantification in littoral erosion,
Chebyshev interpolation for parametric option pricing,
An EMC-HDG scheme for the convection-diffusion equation with random diffusivity,
A multi-fidelity ensemble Kalman filter with hyperreduced reduced-order models,
The deep parametric PDE method and applications to option pricing,
An importance sampling technique in Monte Carlo methods for SDEs with a.s. stable and mean-square unstable equilibrium,
Global sensitivity analysis for multivariate outputs using polynomial chaos-based surrogate models,
Uncertainty quantification analysis in discrete fracture network flow simulations,
Stochastic turbulence modeling in RANS simulations via multilevel Monte Carlo,
Optimal unbiased estimation for expected cumulative discounted cost,
Stress-based topology optimization under uncertainty via simulation-based Gaussian process,
Multilevel and multifidelity uncertainty quantification for cardiovascular hemodynamics,
A bi-fidelity surrogate modeling approach for uncertainty propagation in three-dimensional hemodynamic simulations,
Strong convergence rates for Cox-Ingersoll-Ross processes -- full parameter range,
A low-rank control variate for multilevel Monte Carlo simulation of high-dimensional uncertain systems,
Assessment of multilevel ensemble-based data assimilation for reservoir history matching,
A highly parallel algorithm for computing the action of a matrix exponential on a vector based on a multilevel Monte Carlo method,
Coupling sample paths to the thermodynamic limit in Monte Carlo estimators with applications to gene expression,
Adaptive Euler-Maruyama method for SDEs with nonglobally Lipschitz drift,
Quantifying uncertain system outputs via the multilevel Monte Carlo method. I: Central moment estimation,
Multilevel Monte Carlo and improved timestepping methods in atmospheric dispersion modelling,
On coupling particle filter trajectories,
Multilevel particle filters: normalizing constant estimation,
Goal-oriented adaptive modeling of random heterogeneous media and model-based multilevel Monte Carlo methods,
Multilevel and multi-index Monte Carlo methods for the McKean-Vlasov equation,
Multilevel particle filters for the non-linear filtering problem in continuous time,
Importance sampling for a robust and efficient multilevel Monte Carlo estimator for stochastic reaction networks,
Multilevel Monte Carlo by using the Halton sequence,
The parallel finite element system M++ with integrated multilevel preconditioning and multilevel Monte Carlo methods,
Weak error for nested multilevel Monte Carlo,
Multi-scale control variate methods for uncertainty quantification in kinetic equations,
High-dimensional and higher-order multifidelity Monte Carlo estimators,
Random bit quadrature and approximation of distributions on Hilbert spaces,
An efficient multi-level high-order algorithm for simulation of a class of Allen-Cahn stochastic systems,
A parallel dynamic asynchronous framework for uncertainty quantification by hierarchical Monte Carlo algorithms,
Multilevel Monte Carlo for computing the SCR with the standard formula and other stress tests,
A blackbox yield estimation workflow with Gaussian process regression applied to the design of electromagnetic devices,
Implementable coupling of Lévy process and Brownian motion,
Multi-fidelity uncertainty quantification method with application to nonlinear structural response analysis,
Antithetic multilevel sampling method for nonlinear functionals of measure,
Application of quasi-Monte Carlo methods to elliptic PDEs with random diffusion coefficients: a survey of analysis and implementation,
Goal-oriented error estimation and adaptivity for elliptic PDEs with parametric or uncertain inputs,
A data-driven framework for sparsity-enhanced surrogates with arbitrary mutually dependent randomness,
Limit theorems for weighted and regular multilevel estimators,
Parallel tensor sampling in the hierarchical Tucker format,
General multilevel adaptations for stochastic approximation algorithms. II: CLTs,
M-PCM-OFFD: an effective output statistics estimation method for systems of high dimensional uncertainties subject to low-order parameter interactions,
An FEM-MLMC algorithm for a moving shutter diffraction in time stochastic model,
Analysis and computation of the elastic wave equation with random coefficients,
Determining optimal multilevel Monte Carlo parameters with application to fault tolerance,
A two-stage surrogate model for neo-Hookean problems based on adaptive proper orthogonal decomposition and hierarchical tensor approximation,
Data fusion for uncertainty quantification with non-intrusive polynomial chaos,
Random bit multilevel algorithms for stochastic differential equations,
Central limit theorems for multilevel Monte Carlo methods,
Strong convergence analysis of iterative solvers for random operator equations,
Decision-theoretic sensitivity analysis for reservoir development under uncertainty using multilevel quasi-Monte Carlo methods,
Multilevel sequential Monte Carlo for Bayesian inverse problems,
Multilevel Monte Carlo simulation of Coulomb collisions,
A multilevel Monte Carlo method for asymptotic-preserving particle schemes in the diffusive limit,
Uncertainty quantification of spatially uncorrelated loads with a reduced-order stochastic isogeometric method,
Multilevel Monte Carlo acceleration of seismic wave propagation under uncertainty,
A probabilistic linear solver based on a multilevel Monte Carlo method,
Strong convergence rates of probabilistic integrators for ordinary differential equations,
A modern retrospective on probabilistic numerics,
Multi-level Monte Carlo methods for the approximation of invariant measures of stochastic differential equations,
Numerical methods for conservation laws with rough flux,
Second order linear differential equations with analytic uncertainties: stochastic analysis via the computation of the probability density function,
Quantifying the uncertainty in a hyperelastic soft tissue model with stochastic parameters,
Multilevel Monte Carlo method for topology optimization of flexoelectric composites with uncertain material properties,
Isogeometric multilevel quadrature for forward and inverse random acoustic scattering,
On the optimal design of the randomized unbiased Monte Carlo estimators,
Accelerating Monte Carlo estimation with derivatives of high-level finite element models,
A multigrid multilevel Monte Carlo method for Stokes-Darcy model with random hydraulic conductivity and Beavers-Joseph condition,
Slow-scale split-step tau-leap method for stiff stochastic chemical systems,
Markov chain simulation for multilevel Monte Carlo,
A multilevel approach to stochastic trace estimation,
Unbiased estimation of the solution to Zakai's equation,
Multilevel Monte Carlo methods and lower-upper bounds in initial margin computations,
A generalized probabilistic learning approach for multi-fidelity uncertainty quantification in complex physical simulations,
Decision-making under uncertainty: using MLMC for efficient estimation of EVPPI,
Optimized parametric inference for the inner loop of the multigrid ensemble Kalman filter,
Solving BSDEs based on novel multi-step schemes and multilevel Monte Carlo,
Well-posedness and tamed schemes for McKean-Vlasov equations with common noise,
Constructing unbiased gradient estimators with finite variance for conditional stochastic optimization,
A variance-reduced direct Monte Carlo simulation method for solving the Boltzmann equation over a wide range of rarefaction,
Multilevel Monte Carlo estimators for elliptic PDEs with Lévy-type diffusion coefficient,
Improved efficiency of multilevel Monte Carlo for stochastic PDE through strong pairwise coupling,
An MLMCE-HDG method for the convection diffusion equation with random diffusivity,
Bayesian parameter inference for partially observed stochastic differential equations driven by fractional Brownian motion,
Bi-fidelity reduced polynomial chaos expansion for uncertainty quantification,
Efficient derivative-free Bayesian inference for large-scale inverse problems,
Ensemble Approximate Control Variate Estimators: Applications to MultiFidelity Importance Sampling,
Collocation Methods and Beyond in Non-linear Mechanics,
Unbiased filtering of a class of partially observed diffusions,
Multilevel Monte Carlo method for ergodic SDEs without contractivity,
Connecting the Dots: Numerical Randomized Hamiltonian Monte Carlo with State-Dependent Event Rates,
Tensor-Based Numerical Method for Stochastic Homogenization,
VAE-KRnet and Its Applications to Variational Bayes,
Nonasymptotic bounds for sampling algorithms without log-concavity,
A Fully Parallelizable Space-Time Multilevel Monte Carlo Method for Stochastic Differential Equations with Additive Noise,
Adaptive Multilevel Monte Carlo Methods for Stochastic Variational Inequalities,
Asymptotically Compatible Schemes for Stochastic Homogenization,
Rapid Bayesian Inference for Expensive Stochastic Models,
Efficient Steady-State Simulation of High-Dimensional Stochastic Networks,
Unbiased MLMC-based Variational Bayes for Likelihood-Free Inference,
Multilevel Monte Carlo for Smoothing via Transport Methods,
Multilevel Monte Carlo for exponential Lévy models,
Adaptive Multilevel Monte Carlo for Probabilities,
A survey of unsupervised learning methods for high-dimensional uncertainty quantification in black-box-type problems,
A Multilevel Approach to Variance Reduction in the Stochastic Estimation of the Trace of a Matrix,
Multilevel Ensemble Kalman–Bucy Filters,
A weak-intrusive stochastic finite element method for stochastic structural dynamics analysis,
Multifidelity multilevel Monte Carlo to accelerate approximate Bayesian parameter inference for partially observed stochastic processes,
Simulation of the drawdown and its duration in Lévy models via stick-breaking Gaussian approximation,
Quantifying uncertainties in contact mechanics of rough surfaces using the Multilevel Monte Carlo method,
Recovery of Sobolev functions restricted to iid sampling,
Goal-oriented adaptive finite element multilevel Monte Carlo with convergence rates,
The cardiovascular system: Mathematical modelling, numerical algorithms and clinical applications,
Quantitative bounds for concentration-of-measure inequalities and empirical regression: the independent case,
Construction of a Mean Square Error Adaptive Euler–Maruyama Method With Applications in Multilevel Monte Carlo,
Non-nested Adaptive Timesteps in Multilevel Monte Carlo Computations,
A Seamless Multilevel Ensemble Transform Particle Filter,
Full-field order-reduced Gaussian process emulators for nonlinear probabilistic mechanics,
Multilevel Particle Filters,
Mixing LSMC and PDE Methods to Price Bermudan Options,
Fast Euler-Maruyama method for weakly singular stochastic Volterra integral equations with variable exponent,
Hyperbolic Conservation Laws with Stochastic Discontinuous Flux Functions,
Multilevel Quasi-Monte Carlo Uncertainty Quantification for Advection-Diffusion-Reaction,
Stochastic Methods for Solving High-Dimensional Partial Differential Equations,
A Multilevel Monte Carlo Asymptotic-Preserving Particle Method for Kinetic Equations in the Diffusion Limit,
Rapid Covariance-Based Sampling of Linear SPDE Approximations in the Multilevel Monte Carlo Method,
A Multilevel Monte Carlo Algorithm for Parabolic Advection-Diffusion Problems with Discontinuous Coefficients,
Numerical methods for the deterministic second moment equation of parabolic stochastic PDEs,
Resource-Constrained Model Selection for Uncertainty Propagation and Data Assimilation,
An overview on deep learning-based approximation methods for partial differential equations,
Multilevel Markov chain Monte Carlo for Bayesian inverse problem for Navier-Stokes equation,
Bayesian Static Parameter Estimation for Partially Observed Diffusions via Multilevel Monte Carlo,
Problem Statement for Preparing a Single Batch of End Product Under Uncertainty,
Multilevel Monte Carlo Approximation of Functions,
Uncertainty Quantification for Low-Frequency, Time-Harmonic Maxwell Equations with Stochastic Conductivity Models,
Multilevel Estimation of Expected Exit Times and Other Functionals of Stopped Diffusions,
Efficient White Noise Sampling and Coupling for Multilevel Monte Carlo with Nonnested Meshes,
Continuous Level Monte Carlo and Sample-Adaptive Model Hierarchies,
Multilevel QMC with Product Weights for Affine-Parametric, Elliptic PDEs,
MLMC for Nested Expectations,
Modern Monte Carlo Variants for Uncertainty Quantification in Neutron Transport,
Adaptive Quasi-Monte Carlo Methods for Cubature,
Low-Rank Tensor Approximation for Chebyshev Interpolation in Parametric Option Pricing,
A Multilevel Monte Carlo Estimator for Matrix Multiplication,
Multilevel higher-order quasi-Monte Carlo Bayesian estimation,
Multilevel Monte Carlo Estimation of the Expected Value of Sample Information,
On Multilevel Best Linear Unbiased Estimators,
Renormalization Based MLMC Method for Scalar Elliptic SPDE,
Multilevel Monte Carlo estimation of expected information gains,
Thinning and multilevel Monte Carlo methods for piecewise deterministic (Markov) processes with an application to a stochastic Morris–Lecar model,
Stochastic Resin Transfer Molding Process,
Multilevel Sequential Importance Sampling for Rare Event Estimation,
Unbiased multi-index Monte Carlo,
Multilevel Hierarchical Decomposition of Finite Element White Noise with Application to Multilevel Markov Chain Monte Carlo,
Unnamed Item,
Importance Sampling for Pathwise Sensitivity of Stochastic Chaotic Systems,
A Distributed Optimal Control Problem with Averaged Stochastic Gradient Descent,
Analysis and Application of Single Level, Multi-Level Monte Carlo and Quasi-Monte Carlo Finite Element Methods for Time-Dependent Maxwell's Equations with Random Inputs,
Multilevel Control Variates for Uncertainty Quantification in Simulations of Cloud Cavitation,
On Large Lag Smoothing for Hidden Markov Models,
Pricing American options by exercise rate optimization,
Multilevel Ensemble Transform Particle Filtering,
Multilevel Monte Carlo Covariance Estimation for the Computation of Sobol' Indices,
Multifidelity Approximate Bayesian Computation,
Statistical Treatment of Inverse Problems Constrained by Differential Equations-Based Models with Stochastic Terms,
Flow state estimation in the presence of discretization errors,
Bias behaviour and antithetic sampling in mean-field particle approximations of SDEs nonlinear in the sense of McKean,
Multilevel Quadrature for Elliptic Parametric Partial Differential Equations in Case of Polygonal Approximations of Curved Domains,
Unbiased Estimators and Multilevel Monte Carlo,
Multilevel Higher Order QMC Petrov--Galerkin Discretization for Affine Parametric Operator Equations,
Multilevel approximation of parametric and stochastic PDES,
Multiscale Variance Reduction Methods Based on Multiple Control Variates for Kinetic Equations with Uncertainties,
A Walk Outside Spheres for the fractional Laplacian: Fields and first eigenvalue,
Robust Optimization of PDEs with Random Coefficients Using a Multilevel Monte Carlo Method,
Multilevel Designed Quadrature for Partial Differential Equations with Random Inputs,
A Multifidelity Ensemble Kalman Filter with Reduced Order Control Variates,
Multilevel Hierarchical Decomposition of Finite Element White Noise with Application to Multilevel Markov Chain Monte Carlo,
MG/OPT and Multilevel Monte Carlo for Robust Optimization of PDEs,
Asymptotic Analysis of Multilevel Best Linear Unbiased Estimators,
Multilevel Quasi Monte Carlo Methods for Elliptic PDEs with Random Field Coefficients via Fast White Noise Sampling,
A multi-level procedure for enhancing accuracy of machine learning algorithms,
Algorithms for solving high dimensional PDEs: from nonlinear Monte Carlo to machine learning,
A Bandit-Learning Approach to Multifidelity Approximation,
Unbiased MLMC Stochastic Gradient-Based Optimization of Bayesian Experimental Designs,
Multi-level Monte Carlo methods with the truncated Euler–Maruyama scheme for stochastic differential equations,
Statistical Finite Elements via Langevin Dynamics,
Computing quantum dynamics in the semiclassical regime,
An ensemble scheme for the numerical solution of a random transient heat equation with uncertain inputs,
Strong error analysis of Euler methods for overdamped generalized Langevin equations with fractional noise: Nonlinear case,
A Simple, Bias-free Approximation of Covariance Functions by the Multilevel Monte Carlo Method Having Nearly Optimal Complexity,
Advanced Multilevel Monte Carlo Methods,
A multilevel Monte Carlo ensemble and hybridizable discontinuous Galerkin method for a stochastic parabolic problem,
Gradient-based optimisation of the conditional-value-at-risk using the multi-level Monte Carlo method,
Multifidelity approaches for uncertainty quantification,
A non‐intrusive domain‐decomposition model reduction method for linear steady‐state partial differential equations with random coefficients,
Multi-output multilevel best linear unbiased estimators via semidefinite programming,
Bayesian inversion of log-normal eikonal equations,
Maximizing the service level on the makespan in the stochastic flexible job-shop scheduling problem,
Weak variable step-size schemes for stochastic differential equations based on controlling conditional moments,
Stacking Designs: Designing Multifidelity Computer Experiments with Target Predictive Accuracy,
Multilevel quasi-Monte Carlo for optimization under uncertainty,
Multilevel Monte Carlo simulation for the Heston stochastic volatility model,
On the Selection of Random Field Evaluation Points in the p-MLQMC Method,
Multilevel Monte Carlo using approximate distributions of the CIR process,
A flux reconstruction stochastic Galerkin scheme for hyperbolic conservation laws,
An ensemble Monte Carlo HDG method for parabolic PDEs with random coefficients,
A Multilevel Stochastic Collocation Method for Schrödinger Equations with a Random Potential,
Multilevel Delayed Acceptance MCMC,
Multi-index antithetic stochastic gradient algorithm,
A randomized multi-index sequential Monte Carlo method,
Learning-based importance sampling via stochastic optimal control for stochastic reaction networks,
Accelerated Simulation of Boltzmann-BGK Equations near the Diffusive Limit with Asymptotic-Preserving Multilevel Monte Carlo,
A Multilevel Method for Many-Electron Schrödinger Equations Based on the Atomic Cluster Expansion,
Learning the random variables in Monte Carlo simulations with stochastic gradient descent: Machine learning for parametric PDEs and financial derivative pricing,
Unbiased optimal stopping via the MUSE,
Space-time Multilevel Quadrature Methods and their Application for Cardiac Electrophysiology,
A Monte Carlo algorithm for the extrema of tempered stable processes,
Efficient multifidelity likelihood-free Bayesian inference with adaptive computational resource allocation,
A Multi-Index Quasi--Monte Carlo Algorithm for Lognormal Diffusion Problems,
On Local Fourier Analysis of Multigrid Methods for PDEs with Jumping and Random Coefficients,
Adaptive multilevel splitting: Historical perspective and recent results,
Multilevel Monte Carlo in approximate Bayesian computation,
Numerical Solution of Scalar Conservation Laws with Random Flux Functions,
Multilevel Monte Carlo Method for Path-Dependent Barrier Interest Rate Derivatives,
Constructing Sampling Schemes via Coupling: Markov Semigroups and Optimal Transport,
Multilevel Nested Simulation for Efficient Risk Estimation,
Adaptive multiscale predictive modelling,
A Domain Decomposition Model Reduction Method for Linear Convection-Diffusion Equations with Random Coefficients,
Implied stopping rules for American basket options from Markovian projection,
Recycling Samples in the Multigrid Multilevel (Quasi-)Monte Carlo Method,
Gaussian Quadrature and Polynomial Approximation for One-Dimensional Ridge Functions,
Numerical approximation of stochastic time-fractional diffusion,
Analysis of Nested Multilevel Monte Carlo Using Approximate Normal Random Variables,
A multilevel approach for stochastic nonlinear optimal control