8 citations · 8 across the 8 of their papers we have counts for
10 papers
A Local Sinkhorn Framework for Conditional Distribution Reconstruction of Multidimensional Random Fields
Mingtao Xia, Qijing Shen
In this paper, we propose a local Sinkhorn divergence framework for conditional distribution reconstruction of multidimensional random fields. By utilizing the debiased Sinkhorn di…
Hierarchical RBF-KAN and RBF-SKAN Architectures for Multidimensional Function Approximation and Random Field Learning
Mingtao Xia, Qijing Shen
In this manuscript, we propose and analyze hierarchical Kolmogorov--Arnold neural network architectures employing radial basis functions as activation functions for approximating d…
An adaptive radial basis function approach for efficiently solving multidimensional spatiotemporal integrodifferential equations
Mingtao Xia, Qijing Shen
In this work, we propose an adaptive radial basis function (RBF) approach for the efficient solution of multidimensional spatiotemporal integrodifferential equations. Our approach…
Efficient reconstruction of multidimensional random field models with heterogeneous data using stochastic neural networks
Mingtao Xia, Qijing Shen
In this paper, we analyze the scalability of a recent Wasserstein-distance approach for training stochastic neural networks (SNNs) to reconstruct multidimensional random field mode…
A generalized Wasserstein-2 distance approach for efficient reconstruction of random field models using stochastic neural networks
Mingtao Xia, Qijing Shen
In this work, we propose a novel generalized Wasserstein-2 distance approach for efficiently training stochastic neural networks to reconstruct random field models, where the targe…
A new local time-decoupled squared Wasserstein-2 method for training stochastic neural networks to reconstruct uncertain parameters in dynamical systems
Mingtao Xia, Qijing Shen, Philip Maini +2
In this work, we propose and analyze a new local time-decoupled squared Wasserstein-2 method for reconstructing the distribution of unknown parameters in dynamical systems. Specifi…
A local squared Wasserstein-2 method for efficient reconstruction of models with uncertainty
Mingtao Xia, Qijing Shen
In this paper, we propose a local squared Wasserstein-2 (W_2) method to solve the inverse problem of reconstructing models with uncertain latent variables or parameters. A key adva…
An efficient Wasserstein-distance approach for reconstructing jump-diffusion processes using parameterized neural networks
Mingtao Xia, Xiangting Li, Qijing Shen +1
We analyze the Wasserstein distance (-distance) between two probability distributions associated with two multidimensional jump-diffusion processes. Specifically, we analyze a t…
Squared Wasserstein-2 Distance for Efficient Reconstruction of Stochastic Differential Equations
Mingtao Xia, Xiangting Li, Qijing Shen +1
We provide an analysis of the squared Wasserstein-2 () distance between two probability distributions associated with two stochastic differential equations (SDEs). Based on th…
A Spectral Approach for Learning Spatiotemporal Neural Differential Equations
Mingtao Xia, Xiangting Li, Qijing Shen +1
Rapidly developing machine learning methods has stimulated research interest in computationally reconstructing differential equations (DEs) from observational data which may provid…