Reduced-Order Modeling with Time-Dependent Bases for PDEs with Stochastic Boundary Conditions

DOI10.1137/21m1468097arXiv2112.14326MaRDI QIDQ6177923

Prerna Patil, Hessam Babaee

Publication date: 31 August 2023

Published in: SIAM/ASA Journal on Uncertainty Quantification (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2112.14326

zbMATH Keywords

variational principleuncertainty quantificationreduced-order modelingstochastic boundary conditionstime-dependent bases

Mathematics Subject Classification ID

Analysis of algorithms and problem complexity (68Q25) Graph theory (including graph drawing) in computer science (68R10) Computer graphics; computational geometry (digital and algorithmic aspects) (68U05)

Cites Work

• On the equivalence of dynamically orthogonal and bi-orthogonal methods: theory and numerical simulations
• Fundamental limitations of polynomial chaos for uncertainty quantification in systems with intermittent instabilities
• A dynamically bi-orthogonal method for time-dependent stochastic partial differential equations. II: Adaptivity and generalizations
• A dynamically bi-orthogonal method for time-dependent stochastic partial differential equations. I: Derivation and algorithms
• Adaptive ANOVA decomposition of stochastic incompressible and compressible flows
• Multi-level Monte Carlo finite element method for elliptic PDEs with stochastic coefficients
• Control of linear instabilities by dynamically consistent order reduction on optimally time-dependent modes
• Galerkin methods for linear and nonlinear elliptic stochastic partial differential equations
• Dynamically orthogonal field equations for continuous stochastic dynamical systems
• Multi-element probabilistic collocation method in high dimensions
• The multi-element probabilistic collocation method (ME-PCM): Error analysis and applications
• Long-term behavior of polynomial chaos in stochastic flow simulations
• Polynomial chaos representation of spatio-temporal random fields from experimental measurements
• Mean field dynamics of fermions and the time-dependent Hartree-Fock equation
• Sparse finite elements for elliptic problems with stochastic loading
• Spectral polynomial chaos solutions of the stochastic advection equation
• A robust bi-orthogonal/dynamically-orthogonal method using the covariance pseudo-inverse with application to stochastic flow problems
• Dual dynamically orthogonal approximation of incompressible Navier Stokes equations with random boundary conditions
• Finite elements for elliptic problems with stochastic coefficients
• Modeling uncertainty in flow simulations via generalized polynomial chaos.
• Real-time reduced-order modeling of stochastic partial differential equations via time-dependent subspaces
• On-the-fly reduced order modeling of passive and reactive species via time-dependent manifolds
• Sparse grid collocation schemes for stochastic natural convection problems
• An adaptive multi-element generalized polynomial chaos method for stochastic differential equations
• Adaptive sparse interpolation for accelerating nonlinear stochastic reduced-order modeling with time-dependent bases
• Dynamical Tensor Approximation
• Stochastic Domain Decomposition via Moment Minimization
• Multilevel Monte Carlo Path Simulation
• Multi-Element Generalized Polynomial Chaos for Arbitrary Probability Measures
• Mixture Kalman Filters
• Reduced-order description of transient instabilities and computation of finite-time Lyapunov exponents
• Gaussian fields and random flow
• The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
• Quasi-Monte Carlo Finite Element Methods for a Class of Elliptic Partial Differential Equations with Random Coefficients
• Computing Sensitivities in Evolutionary Systems: A Real-Time Reduced Order Modeling Strategy
• An observation-driven time-dependent basis for a reduced description of transient stochastic systems
• A minimization principle for the description of modes associated with finite-time instabilities
• Uncertainty propagation in CFD using polynomial chaos decomposition
• Dynamical Low‐Rank Approximation
• High-Order Collocation Methods for Differential Equations with Random Inputs
• Spectral/hp Element Methods for Computational Fluid Dynamics
• A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data
• A stochastic projection method for fluid flow. I: Basic formulation

This page was built for publication: Reduced-Order Modeling with Time-Dependent Bases for PDEs with Stochastic Boundary Conditions