Yuan Chen

Yuan Chen
Verified
Yuan verified their affiliation via an institutional email.
Verified
Yuan verified their affiliation via an institutional email.
The Ohio State University | OSU

Bachelor of Engineering

About

20
Publications
2,409
Reads
How we measure 'reads'
A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more
59
Citations
Introduction
My research interests fall in the broad areas of scientific computing and numerical analysis. Recently, I'm working on machine learning methods for scientific computing, specifically the data-driven modeling and uncertainty quantification of physical systems governed by (stochastic) differential equations.

Publications

Publications (20)
Article
Full-text available
We present a new deep neural network (DNN) architecture capable of approximating functions up to machine accuracy. Termed the Chebyshev feature neural network (CFNN), the new structure employs Chebyshev functions with learnable frequencies as the first hidden layer, followed by the standard fully connected hidden layers. The learnable frequencies o...
Article
Full-text available
We present a numerical method for learning the dynamics of slow components of unknown multiscale stochastic dynamical systems. While the governing equations of the systems are unknown, bursts of observation data of the slow variables are available. By utilizing the observation data, our proposed method is capable of constructing a generative stocha...
Preprint
This study introduces a training-free conditional diffusion model for learning unknown stochastic differential equations (SDEs) using data. The proposed approach addresses key challenges in computational efficiency and accuracy for modeling SDEs by utilizing a score-based diffusion model to approximate their stochastic flow map. Unlike the existing...
Preprint
Full-text available
We present a new Deep Neural Network (DNN) architecture capable of approximating functions up to machine accuracy. Termed Chebyshev Feature Neural Network (CFNN), the new structure employs Chebyshev functions with learnable frequencies as the first hidden layer, followed by the standard fully connected hidden layers. The learnable frequencies of th...
Preprint
Full-text available
We present a numerical method for learning the dynamics of slow components of unknown multiscale stochastic dynamical systems. While the governing equations of the systems are unknown, bursts of observation data of the slow variables are available. By utilizing the observation data, our proposed method is capable of constructing a generative stocha...
Preprint
Full-text available
We present a numerical method for learning unknown nonautonomous stochastic dynamical system, i.e., stochastic system subject to time dependent excitation or control signals. Our basic assumption is that the governing equations for the stochastic system are unavailable. However, short bursts of input/output (I/O) data consisting of certain known ex...
Article
We present a numerical framework for learning unknown stochastic dynamical systems using measurement data. Termed stochastic flow map learning (sFML), the new framework is an extension of flow map learning (FML) that was developed for learning deterministic dynamical systems. For learning stochastic systems, we define a stochastic flow map that is...
Preprint
Full-text available
Polynomial approximations of functions are widely used in scientific computing. In certain applications, it is often desired to require the polynomial approximation to be non-negative (resp. non-positive), or bounded within a given range, due to constraints posed by the underlying physical problems. Efficient numerical methods are thus needed to en...
Article
Full-text available
We present a numerical method to learn an accurate predictive model for an unknown stochastic dynamical system from its trajectory data. The method seeks to approximate the unknown flow map of the underlying system. It employs the idea of autoencoder to identify the unobserved latent random variables. In our approach, we design an encoding function...
Preprint
Full-text available
We present a numerical method to learn an accurate predictive model for an unknown stochastic dynamical system from its trajectory data. The method seeks to approximate the unknown flow map of the underlying system. It employs the idea of autoencoder to identify the unobserved latent random variables. In our approach, we design an encoding function...
Article
Full-text available
This paper introduces a high-order immersed finite element (IFE) method to solve two- phase incompressible Navier–Stokes equations on interface-unfitted meshes. In spatial discretization, we use the newly developed immersed P2-P1 Taylor-Hood finite element. The unisolvency of new IFE basis functions is theoretically established. We introduce an enh...
Preprint
Full-text available
In this paper, we study ultra-weak discontinuous Galerkin methods with generalized numerical fluxes for multi-dimensional high order partial differential equations on both unstructured simplex and Cartesian meshes. The equations we consider as examples are the nonlinear convection-diffusion equation and the biharmonic equation. Optimal error estima...
Article
In this paper, we present an immersed finite element (IFE) method for solving the elastodynamics interface problems on interface-unfitted meshes. For spatial discretization, we use vector-valued P1 and Q1 IFE spaces. We establish some important properties of these IFE spaces, such as inverse inequalities, which will be crucial in the error analysis...
Article
We present a computational technique for modeling the evolution of partial differential equations (PDEs) with incomplete data. It is a significant extension of the recent work of data driven learning of PDEs, in the sense that we consider two forms of partial data: data are observed only on a subset of the domain, and data are observed only on a su...
Preprint
Full-text available
We present a numerical framework for learning unknown stochastic dynamical systems using measurement data. Termed stochastic flow map learning (sFML), the new framework is an extension of flow map learning (FML) that was developed for learning deterministic dynamical systems. For learning stochastic systems, we define a stochastic flow map that is...
Article
Full-text available
We present a computational technique for modeling the evolution of partial differential equations (PDEs) with incomplete data. It is a significant extension of the recent work of data driven learning of PDEs, in the sense that we consider two forms of partial data: data are observed only on a subset of the domain, and data are observed only on a su...
Article
Full-text available
In this article, we develop a Taylor-Hood immersed finite element (IFE) method to solve two-dimensional Stokes interface problems. The P2-P1 local IFE spaces are constructed using the least-squares approximation on an enlarged fictitious element. The partially penalized IFE method with ghost penalty is employed for solving Stoke interface problems....
Preprint
In this article, we introduce a new partially penalized immersed finite element method (IFEM) for solving elliptic interface problems with multi-domains and triple-junction points. We construct new IFE functions on elements intersected with multiple interfaces or with triple-junction points to accommodate interface jump conditions. For non-homogene...
Article
Full-text available
In this article, we introduce a new partially penalized immersed finite element method (IFEM) for solving elliptic interface problems with multi-domain and triple-junction points. We construct new IFE functions on elements intersected with multiple interfaces or with triple-junction points to accommodate interface jump conditions. For non-homogeneo...
Article
Full-text available
Interface problems have wide applications in modern scientific research. Obtaining accurate numerical solutions of multi-domain problems involving triple junction conditions remains a significant challenge. In this paper, we develop an efficient finite element method based on non-body-fitting meshes for solving multi-domain elliptic interface probl...

Network

Cited By