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07/14/2023
Generalized Finite Difference Method on unknown manifolds
In this paper, we extend the Generalized Finite Difference Method (GFDM)...
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10/19/2022
Spectral methods for solving elliptic PDEs on unknown manifolds
In this paper, we propose a mesh-free numerical method for solving ellip...
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08/17/2022
Radial basis approximation of tensor fields on manifolds: From operator estimation to manifold learning
We study the Radial Basis Function (RBF) approximation to differential o...
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10/13/2021
Spectral Convergence of Symmetrized Graph Laplacian on manifolds with boundary
We study the spectral convergence of a symmetrized Graph Laplacian matri...
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09/09/2021
Stationary Density Estimation of Itô Diffusions Using Deep Learning
In this paper, we consider the density estimation problem associated wit...
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06/12/2021
Graph-based Prior and Forward Models for Inverse Problems on Manifolds with Boundaries
This paper develops manifold learning techniques for the numerical solut...
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06/12/2021
Solving PDEs on Unknown Manifolds with Machine Learning
This paper proposes a mesh-free computational framework and machine lear...
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05/28/2021
Kernel-based methods for Solving Time-Dependent Advection-Diffusion Equations on Manifolds
In this paper, we extend the class of kernel methods, the so-called diff...
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05/21/2021
Error Bounds of the Invariant Statistics in Machine Learning of Ergodic Itô Diffusions
This paper studies the theoretical underpinnings of machine learning of ...
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07/08/2020
Kernel-based Prediction of Non-Markovian Time Series
A nonparametric method to predict non-Markovian time series of partially...
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06/07/2020
Ghost Point Diffusion Maps for solving elliptic PDE's on Manifolds with Classical Boundary Conditions
In this paper, we extend the class of kernel methods, the so-called diff...
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02/18/2020
Bridging data science and dynamical systems theory
This short review describes mathematical techniques for statistical anal...
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12/23/2019
Kernel Embedding Linear Response
In the paper, we study the problem of estimating linear response statist...
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10/30/2019
Linear Response Based Parameter Estimation in the Presence of Model Error
Recently, we proposed a method to estimate parameters in stochastic dyna...
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10/23/2019
Kernel Methods for Bayesian Elliptic Inverse Problems on Manifolds
This paper investigates the formulation and implementation of Bayesian i...
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10/13/2019
Machine Learning for Prediction with Missing Dynamics
This article presents a general framework for recovering missing dynamic...
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05/17/2019
