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03/11/2023
An approximate control variates approach to multifidelity distribution estimation
Forward simulation-based uncertainty quantification that studies the dis...
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09/13/2022
Quadrature Sampling of Parametric Models with Bi-fidelity Boosting
Least squares regression is a ubiquitous tool for building emulators (a....
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09/13/2022
Fast Algorithms for Monotone Lower Subsets of Kronecker Least Squares Problems
Approximate solutions to large least squares problems can be computed ef...
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07/08/2022
Nonparametric Embeddings of Sparse High-Order Interaction Events
High-order interaction events are common in real-world applications. Lea...
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05/07/2022
Variational Inference for Nonlinear Inverse Problems via Neural Net Kernels: Comparison to Bayesian Neural Networks, Application to Topology Optimization
Inverse problems and, in particular, inferring unknown or latent paramet...
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04/19/2022
Proximal Implicit ODE Solvers for Accelerating Learning Neural ODEs
Learning neural ODEs often requires solving very stiff ODE systems, prim...
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04/08/2022
Dimensionality Reduction in Deep Learning via Kronecker Multi-layer Architectures
Deep learning using neural networks is an effective technique for genera...
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03/18/2022
Convex Optimization-Based Structure-Preserving Filter For Multidimensional Finite Element Simulations
In simulation sciences, it is desirable to capture the real-world proble...
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02/24/2022
Learning POD of Complex Dynamics Using Heavy-ball Neural ODEs
Proper orthogonal decomposition (POD) allows reduced-order modeling of c...
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02/10/2022
A Stieltjes algorithm for generating multivariate orthogonal polynomials
Orthogonal polynomials of several variables have a vector-valued three-t...
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12/17/2021
GP-HMAT: Scalable, O(nlog(n)) Gaussian Process Regression with Hierarchical Low-Rank Matrices
A Gaussian process (GP) is a powerful and widely used regression techniq...
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11/25/2021
Model Reduction of Linear Dynamical Systems via Balancing for Bayesian Inference
We consider the Bayesian approach to the linear Gaussian inference probl...
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10/26/2021
Physics-Informed Neural Networks (PINNs) for Parameterized PDEs: A Metalearning Approach
Physics-informed neural networks (PINNs) as a means of discretizing part...
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10/16/2021
Meta-Learning with Adjoint Methods
Model Agnostic Meta-Learning (MAML) is widely used to find a good initia...
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08/26/2021
Non-Dissipative and Structure-Preserving Emulators via Spherical Optimization
Approximating a function with a finite series, e.g., involving polynomia...
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06/25/2021
Multifidelity Modeling for Physics-Informed Neural Networks (PINNs)
Multifidelity simulation methodologies are often used in an attempt to j...
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06/15/2021
Structure-preserving Nonlinear Filtering for Continuous and Discontinuous Galerkin Spectral/hp Element Methods
Finite element simulations have been used to solve various partial diffe...
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05/17/2021
Adaptive Density Tracking by Quadrature for Stochastic Differential Equations
Density tracking by quadrature (DTQ) is a numerical procedure for comput...
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05/10/2021
Budget-limited distribution learning in multifidelity problems
Multifidelity methods are widely used for statistical estimation of quan...
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04/22/2021
Hyperbolicity-Preserving and Well-Balanced Stochastic Galerkin Method for Two-Dimensional Shallow Water Equations
Stochastic Galerkin formulations of the two-dimensional shallow water sy...
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04/13/2021
Optimal design for kernel interpolation: applications to uncertainty quantification
The paper is concerned with classic kernel interpolation methods, in add...
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03/29/2021
A bandit-learning approach to multifidelity approximation
Multifidelity approximation is an important technique in scientific comp...
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03/05/2021
Fast Barycentric-Based Evaluation Over Spectral/hp Elements
As the use of spectral/hp element methods, and high-order finite element...
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01/28/2021
On the computation of recurrence coefficients for univariate orthogonal polynomials
Associated to a finite measure on the real line with finite moments are ...
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01/11/2021
Randomized weakly admissible meshes
A weakly admissible mesh (WAM) on a continuum real-valued domain is a se...
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01/05/2021
Kernel optimization for Low-Rank Multi-Fidelity Algorithms
One of the major challenges for low-rank multi-fidelity (MF) approaches ...
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09/08/2020
L1-based reduced over collocation and hyper reduction for steady state and time-dependent nonlinear equations
The task of repeatedly solving parametrized partial differential equatio...
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08/23/2020
Sparse approximation of data-driven Polynomial Chaos expansions: an induced sampling approach
One of the open problems in the field of forward uncertainty quantificat...
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08/19/2020
Structure-preserving function approximation via convex optimization
Approximations of functions with finite data often do not respect certai...
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08/18/2020
Hyperbolicity-Preserving and Well-Balanced Stochastic Galerkin Method for Shallow Water Equations
A stochastic Galerkin formulation for a stochastic system of balanced or...
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08/11/2020
Efficient sampling for polynomial chaos-based uncertainty quantification and sensitivity analysis using weighted approximate Fekete points
Performing uncertainty quantification (UQ) and sensitivity analysis (SA)...
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04/13/2020
Analysis of The Ratio of ℓ_1 and ℓ_2 Norms in Compressed Sensing
We first propose a novel criterion that guarantees that an s-sparse sign...
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10/15/2019
A Robust Hyperviscosity Formulation for Stable RBF-FD Discretizations of Advection-Diffusion-Reaction Equations on Manifolds
We present a new hyperviscosity formulation for stabilizing radial basis...
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12/30/2018
Allocation strategies for high fidelity models in the multifidelity regime
We propose a novel approach to allocating resources for expensive simula...
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08/30/2018
Parametric Topology Optimization with Multi-Resolution Finite Element Models
We present a methodical procedure for topology optimization under uncert...
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07/08/2018
RBF-LOI: Augmenting Radial Basis Functions (RBFs) with Least Orthogonal Interpolation (LOI) for Solving PDEs on Surfaces
We present a new method for the solution of PDEs on manifolds M⊂R^d of c...
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04/17/2018