2025
DUE: A Deep Learning Framework and Library for Modeling Unknown Equations.
CoRR, April, 2025
Multi-fidelity Parameter Estimation Using Conditional Diffusion Models.
CoRR, April, 2025
On Enforcing Nonnegativity in Polynomial Approximations in High Dimensions.
SIAM J. Sci. Comput., 2025
2024
Learning stochastic dynamical system via flow map operator.
J. Comput. Phys., 2024
Deep learning for model correction of dynamical systems with data scarcity.
CoRR, 2024
A Training-Free Conditional Diffusion Model for Learning Stochastic Dynamical Systems.
CoRR, 2024
Chebyshev Feature Neural Network for Accurate Function Approximation.
CoRR, 2024
Data-driven Effective Modeling of Multiscale Stochastic Dynamical Systems.
CoRR, 2024
Modeling Unknown Stochastic Dynamical System Subject to External Excitation.
CoRR, 2024
On enforcing non-negativity in polynomial approximations in high dimensions.
CoRR, 2024
2023
DNN modeling of partial differential equations with incomplete data.
J. Comput. Phys., November, 2023
Robust modeling of unknown dynamical systems via ensemble averaged learning.
J. Comput. Phys., February, 2023
Modeling Unknown Stochastic Dynamical System via Autoencoder.
CoRR, 2023
Flow Map Learning for Unknown Dynamical Systems: Overview, Implementation, and Benchmarks.
CoRR, 2023
2022
Construction of discontinuity detectors using convolutional neural networks.
J. Sci. Comput., 2022
Deep neural network modeling of unknown partial differential equations in nodal space.
J. Comput. Phys., 2022
Learning Fine Scale Dynamics from Coarse Observations via Inner Recurrence.
CoRR, 2022
Deep Learning of Chaotic Systems from Partially-Observed Data.
CoRR, 2022
Modeling unknown dynamical systems with hidden parameters.
CoRR, 2022
2021
Data-Driven Learning of Nonautonomous Systems.
SIAM J. Sci. Comput., 2021
On generalized residual network for deep learning of unknown dynamical systems.
J. Comput. Phys., 2021
2020
Structure-Preserving Method for Reconstructing Unknown Hamiltonian Systems From Trajectory Data.
SIAM J. Sci. Comput., 2020
Methods to Recover Unknown Processes in Partial Differential Equations Using Data.
J. Sci. Comput., 2020
Data-driven deep learning of partial differential equations in modal space.
J. Comput. Phys., 2020
Data-driven learning of non-autonomous systems.
CoRR, 2020
Learning reduced systems via deep neural networks with memory.
CoRR, 2020
A Non-Intrusive Correction Algorithm for Classification Problems with Corrupted Data.
CoRR, 2020
On generalized residue network for deep learning of unknown dynamical systems.
CoRR, 2020
2019
Numerical aspects for approximating governing equations using data.
J. Comput. Phys., 2019
Data driven governing equations approximation using deep neural networks.
J. Comput. Phys., 2019
Energy conserving Galerkin approximation of two dimensional wave equations with random coefficients.
J. Comput. Phys., 2019
Uncertainty quantification of discontinuous outputs via a non-intrusive bifidelity strategy.
J. Comput. Phys., 2019
A neural network approach for uncertainty quantification for time-dependent problems with random parameters.
CoRR, 2019
2018
Parameter uncertainty quantification using surrogate models applied to a spatial model of yeast mating polarization.
PLoS Comput. Biol., 2018
Sequential function approximation on arbitrarily distributed point sets.
J. Comput. Phys., 2018
Sequential function approximation with noisy data.
J. Comput. Phys., 2018
An Explicit Neural Network Construction for Piecewise Constant Function Approximation.
CoRR, 2018
Reducing Parameter Space for Neural Network Training.
CoRR, 2018
2017
Sparse Approximation using ℓ<sub>1-ℓ<sub>2</sub></sub> Minimization and Its Application to Stochastic Collocation.
SIAM J. Sci. Comput., 2017
A Randomized Tensor Quadrature Method for High Dimensional Polynomial Approximation.
SIAM J. Sci. Comput., 2017
A Randomized Algorithm for Multivariate Function Approximation.
SIAM J. Sci. Comput., 2017
Multi-fidelity stochastic collocation method for computation of statistical moments.
J. Comput. Phys., 2017
A stochastic Galerkin method for first-order quasilinear hyperbolic systems with uncertainty.
J. Comput. Phys., 2017
2016
Correcting Data Corruption Errors for Multivariate Function Approximation.
SIAM J. Sci. Comput., 2016
Nonadaptive Quasi-Optimal Points Selection for Least Squares Linear Regression.
SIAM J. Sci. Comput., 2016
A Well-Balanced Stochastic Galerkin Method for Scalar Hyperbolic Balance Laws with Random Inputs.
J. Sci. Comput., 2016
On a near optimal sampling strategy for least squares polynomial regression.
J. Comput. Phys., 2016
Numerical strategy for model correction using physical constraints.
J. Comput. Phys., 2016
2015
A Stochastic Galerkin Method for Hamilton-Jacobi Equations with Uncertainty.
SIAM J. Sci. Comput., 2015
Local Polynomial Chaos Expansion for Linear Differential Equations with High Dimensional Random Inputs.
SIAM J. Sci. Comput., 2015
An Efficient Method for Uncertainty Propagation using Fuzzy Sets.
SIAM J. Sci. Comput., 2015
Weighted discrete least-squares polynomial approximation using randomized quadratures.
J. Comput. Phys., 2015
Asymptotic-preserving methods for hyperbolic and transport equations with random inputs and diffusive scalings.
J. Comput. Phys., 2015
2014
A Stochastic Collocation Algorithm with Multifidelity Models.
SIAM J. Sci. Comput., 2014
Surrogate Based Method for Evaluation of Failure Probability under Multiple Constraints.
SIAM J. Sci. Comput., 2014
On Upper and Lower Bounds for Quantity of Interest in Problems Subject to Epistemic Uncertainty.
SIAM J. Sci. Comput., 2014
Computational Aspects of Stochastic Collocation with Multifidelity Models.
SIAM/ASA J. Uncertain. Quantification, 2014
2013
Constructing Nested Nodal Sets for Multivariate Polynomial Interpolation.
SIAM J. Sci. Comput., 2013
Minimal multi-element stochastic collocation for uncertainty quantification of discontinuous functions.
J. Comput. Phys., 2013
A flexible numerical approach for quantification of epistemic uncertainty.
J. Comput. Phys., 2013
2012
Stochastic Collocation Methods on Unstructured Grids in High Dimensions via Interpolation.
SIAM J. Sci. Comput., 2012
Computation of Failure Probability Subject to Epistemic Uncertainty.
SIAM J. Sci. Comput., 2012
Stochastic Collocation for Optimal Control Problems with Stochastic PDE Constraints.
SIAM J. Control. Optim., 2012
Generalised Polynomial Chaos for a Class of Linear Conservation Laws.
J. Sci. Comput., 2012
Sequential data assimilation with multiple models.
J. Comput. Phys., 2012
2011
An efficient surrogate-based method for computing rare failure probability.
J. Comput. Phys., 2011
Characterization of discontinuities in high-dimensional stochastic problems on adaptive sparse grids.
J. Comput. Phys., 2011
2010
Evaluation of failure probability via surrogate models.
J. Comput. Phys., 2010
Numerical approach for quantification of epistemic uncertainty.
J. Comput. Phys., 2010
2009
Efficient stochastic Galerkin methods for random diffusion equations.
J. Comput. Phys., 2009
A generalized polynomial chaos based ensemble Kalman filter with high accuracy.
J. Comput. Phys., 2009
Discontinuity detection in multivariate space for stochastic simulations.
J. Comput. Phys., 2009
2007
Parametric uncertainty analysis of pulse wave propagation in a model of a human arterial network.
J. Comput. Phys., 2007
Guest Editors' Introduction: Stochastic Modeling of Complex Systems.
Comput. Sci. Eng., 2007
2006
Numerical Methods for Differential Equations in Random Domains.
SIAM J. Sci. Comput., 2006
Stochastic analysis of transport in tubes with rough walls.
J. Comput. Phys., 2006
2005
High-Order Collocation Methods for Differential Equations with Random Inputs.
SIAM J. Sci. Comput., 2005
Equation-Free, Multiscale Computation for Unsteady Random Diffusion.
Multiscale Model. Simul., 2005
Strong and Auxiliary Forms of the Semi-Lagrangian Method for Incompressible Flows.
J. Sci. Comput., 2005
An equation-free, multiscale approach to uncertainty quantification.
Comput. Sci. Eng., 2005
2004
Stochastic Solutions for the Two-Dimensional Advection-Diffusion Equation.
SIAM J. Sci. Comput., 2004
A Two-Scale Nonperturbative Approach to Uncertainty Analysis of Diffusion in Random Composites.
Multiscale Model. Simul., 2004
2003
Performance Evaluation of Generalized Polynomial Chaos.
Proceedings of the Computational Science - ICCS 2003, 2003
2002
The Wiener-Askey Polynomial Chaos for Stochastic Differential Equations.
SIAM J. Sci. Comput., 2002
A Semi-Lagrangian Method for Turbulence Simulations Using Mixed Spectral Discretizations.
J. Sci. Comput., 2002