Publications of Yanlai Chen

Yanlai Chen is a Professor of Mathematics at the University of Massachusetts Dartmouth whose research centers on numerical analysis, scientific computing, and scientific machine learning. His work advances high-order discontinuous Galerkin methods, finite element and structure preserving formulations, reduced basis methods, uncertainty quantification, and scientific machine learning notably the GPT-PINN family of physics-informed neural networks. Consistently funded by federal agencies including the NSF and AFOSR, Dr. Chen's research tackles major challenges in linear and nonlinear model order reduction toward fast and reliable numerical methods for partial differential equations and scalable simulations for complex physical systems. He also leads the research enterprise at UMass Dartmouth.

51 items, newest first. Also available as BibTeX; full list on Google Scholar.

2026

Reduced basis methods for parametric steady-state radiative transfer equation
Kimberly Matsuda, Yanlai Chen, Yingda Cheng, Fengyan Li
Journal of Computational Physics, Vol. 548, pp. 114597 (2026). DOI
Derivative-informed Graph Convolutional Autoencoder with Phase Classification for the Lifshitz-Petrich Model
Yanlai Chen, Yajie Ji, Zhenli Xu
CSIAM Transactions on Applied Mathematics (2026). DOI
S²GPT-PINN: Reduced basis and hyper reduction-driven double reduction for Physics-Informed Neural Networks
Yajie Ji, Yanlai Chen, Shawn Koohy
Communications in Computational Physics, Vol. 40, No. 4, pp. 1293–1316 (2026). DOI
EGPT-PINN: Entropy-regularized generative pre-trained physics informed neural networks for parameterized nonlinear conservation laws
Yajie Ji, Yanlai Chen, Zhenli Xu
Computers & Mathematics with Applications, Vol. 222, pp. 223–243 (2026). DOI
Nonlinear Model Order Reduction on Quadratic Manifolds via Greedy Algorithms with Dimension-Dependent Regularization Preprint
Lijie Ji, S. Rashid, Yanlai Chen, Zhu Wang
Submitted (2026).
High-order Conservative Discontinuous Galerkin Methods via Implicit Penalization for the Generalized Korteweg–de Vries Equation and the Hirota–Satsuma KdV System Preprint
Muhammad Shan Tariq, Yanlai Chen, Bo Dong
Submitted (2026).

2025

ReBaNO: Reduced Basis Neural Operator Mitigating Generalization Gaps and Achieving Discretization Invariance Preprint
Haolan Zheng, Yanlai Chen, J. Han, Y. Yu
arXiv preprint arXiv:2509.09611 (2025). arXiv
AAROC: Reduced Over-Collocation Method With Adaptive Time Partitioning and Adaptive Enrichment for Parametric Time-Dependent Equations
Lijie Ji, Zhichao Peng, Yanlai Chen
Numerical Methods for Partial Differential Equations, Vol. 41, No. 5, pp. e70031 (2025). DOI
A reduced basis warm-start iterative solver for the parameterized linear systems
Shijin Hou, Yanlai Chen, Yinhua Xia
Beijing Journal of Pure and Applied Mathematics, Vol. 2, No. 1, pp. 123–146 (2025). DOI
Greedy Rational Approximation for Frequency-Domain Model Reduction of Parametric LTI Systems Preprint
Filip Bělík, Yanlai Chen, Akil Narayan
arXiv preprint arXiv:2512.23814 (2025). arXiv

2024

GPT-PINN: Generative Pre-Trained Physics-Informed Neural Networks toward non-intrusive Meta-learning of parametric PDEs
Yanlai Chen, Shawn Koohy
Finite Elements in Analysis and Design, Vol. 228, pp. 104047 (2024). DOI
Design of Experiments via Multi-Fidelity Surrogates and Statistical Sensitivity Measures
David J. Gillcrist, Negin Alemazkoor, Yanlai Chen, Mazdak Tootkaboni
Journal of Machine Learning for Modeling and Computing, Vol. 5, No. 4, pp. 95–121 (2024). DOI
TGPT-PINN: Nonlinear model reduction with transformed GPT-PINNs
Yanlai Chen, Yajie Ji, Akil Narayan, Zhenli Xu
Computer Methods in Applied Mechanics and Engineering, Vol. 430, pp. 117198 (2024). DOI
MCMS-RBM: Multicomponent Multistate Reduced Basis Method Toward Rapid Generation of Phase Diagrams for the Lifshitz–Petrich Model
Yajie Ji, Lijie Ji, Yanlai Chen, Zhenli Xu
SIAM Journal on Scientific Computing, Vol. 46, No. 6, pp. B785-B805 (2024). DOI
A Micro-Macro Decomposed Reduced Basis Method for the Time-Dependent Radiative Transfer Equation
Zhichao Peng, Yanlai Chen, Yingda Cheng, Fengyan Li
Multiscale Modeling & Simulation, Vol. 22, No. 1, pp. 639–666 (2024). DOI

2022

A New Conservative Discontinuous Galerkin Method via Implicit Penalization for the Generalized Korteweg–de Vries Equation
Yanlai Chen, Bo Dong, Rebecca Pereira
SIAM Journal on Numerical Analysis, Vol. 60, No. 6, pp. 3078-3098 (2022). DOI
Fast L² Optimal Mass Transport via Reduced Basis Methods for the Monge–Ampère Equation
Shijin Hou, Yanlai Chen, Yinhua Xia
SIAM Journal on Scientific Computing, Vol. 44, No. 6, pp. A3536-A3559 (2022). DOI
A hyper-reduced MAC scheme for the parametric Stokes and Navier-Stokes equations
Yanlai Chen, Lijie Ji, Zhu Wang
Journal of Computational Physics, Vol. 466, pp. 111412 (2022). DOI
A reduced basis method for radiative transfer equation
Zhichao Peng, Yanlai Chen, Yingda Cheng, Fengyan Li
Journal of Scientific Computing, Vol. 91, No. 5, pp. 24 (2022). DOI
Model reduction for fractional elliptic problems using Kato's formula
Huy Dinh, Harbir Antil, Yanlai Chen, Elena Cherkaev, Akil Narayan
Mathematical Control and Related Fields, Vol. 12, No. 1, pp. 115-146 (2022). DOI

2021

L1-based reduced over collocation and hyper reduction for steady state and time-dependent nonlinear equations
Yanlai Chen, Lijie Ji, Akil Narayan, Zhenli Xu
J. Sci. Compt., Vol. 87, pp. 10 (2021). DOI
An EIM-degradation free reduced basis method via over collocation and residual hyper reduction-based error estimation
Yanlai Chen, Sigal Gottlieb, Lijie Ji, Yvon Maday
Journal of Computational Physics, Vol. 444, pp. 110545 (2021). DOI

2020

Adaptive greedy algorithms based on parameter-domain decomposition and reconstruction for the reduced basis method
Jiahua Jiang, Yanlai Chen
International Journal for Numerical Methods in Engineering, Vol. 121, No. 23, pp. 5426-5445 (2020). DOI

2019

A robust error estimator and a residual-free error indicator for reduced basis methods
Y. Chen, J. Jiang, A. Narayan
Computers & Mathematics with Applications, Vol. 77, pp. 1963–1979 (2019). DOI
Certified Offline-Free Reduced Basis (COFRB) Methods for Stochastic Differential Equations Driven by Arbitrary Types of Noise
Yong Liu, Tianheng Chen, Yanlai Chen, Chi-Wang Shu
Journal of Scientific Computing (2019). DOI
Certified reduced basis methods for fractional Laplace equations via extension
Harbir Antil, Yanlai Chen, Akil Narayan
Siam J. Sci. Comput., Vol. 41, No. 6, pp. A3552-A3575 (2019). DOI
A Reduced Basis Method for the Nonlinear Poisson-Boltzmann Equation
Lijie Ji, Yanlai Chen, Zhenli Xu
Advances in Applied Mathematics and Mechanics, Vol. 11, No. 5, pp. 1200–1218 (2019). DOI
L1-ROC and R2-ROC: L1- and R2-based Reduced Over-Collocation methods for parametrized nonlinear partial differential equations Preprint
Yanlai Chen, Sigal Gottlieb, Lijie Ji, Yvon Maday, Zhenli Xu
arXiv:1906.07349 (2019).

2018

Optimally convergent hybridizable discontinuous Galerkin method for fifth-order Korteweg-de Vries type equations
Yanlai Chen, Bo Dong, Jiahua Jiang
ESAIM: M2AN, Vol. 52, No. 6, pp. 2283-2306 (2018). DOI
Reduced-basis method for the iterative solution of parametrized symmetric positive-definite linear systems Preprint
Cuong Nguyen, Yanlai Chen
arXiv:1804.06363 (2018).
A Foreword to the Special Issue in Honor of Professor Bernardo Cockburn on His 60th Birthday: A Life Time of Discontinuous Schemings
Yanlai Chen, Bo Dong, Chi-Wang Shu
Journal of Scientific Computing, Vol. 77, No. 3, pp. 1303–1309 (2018).

2017

Offline-Enhanced reduced basis method through adaptive construction of the surrogate training set.
J. Jiang, Y. Chen, A. Narayan
J. Sci. Comput., Vol. 73, No. 2, pp. 853–875 (2017).

2016

A Certified Natural-Norm Successive Constraint Method for Parametric Inf-Sup Lower Bounds
Y. Chen
Applied Numer. Math., Vol. 99, pp. 98–108 (2016).
Superconvergent HDG methods for linear, stationary, third-order equations in one-space dimension
Y. Chen, B. Cockburn, B. Dong
Math. Comp., Vol. 85, pp. 2715-2742 (2016).
A new discontinuous Galerkin method, conserving the discrete H2-norm, for third-order linear equations in one space dimension
Y. Chen, B. Cockburn, B. Dong
IMA J. Num. Anal., Vol. 36, No. 4, pp. 1570-1598 (2016). DOI
A reduced radial basis function method for partial differential equations on irregular domains
Y. Chen, S. Gottlieb, A. Heryudono, A. Narayan
J. Sci. Comput., Vol. 66, No. 1, pp. 67-90 (2016).
A goal-oriented RBM-Accelerated generalized polynomial chaos algorithm
J. Jiang, Y. Chen, A. Narayan
SIAM/ASA JUQ, Vol. 4, No. 1, pp. 1398–1420 (2016).

2015

Reduced Basis Decomposition: a Certified and Fast Lossy Data Compression Algorithm
Y. Chen
Computers and Mathematics with Applications, Vol. 70, pp. 2566–2574 (2015).
Using Visualization and Analysis with Efficient Dimension Reduction Techniques to Determine Underlying Factors in Hospital Inpatient Procedure Costs
M. Perkins, Y. Chen
2015 IEEE Conference on Visual Analytics Science and Technology (VAST), Vol. 00, pp. 205-206 (2015).

2014

Analysis of variable-degree HDG methods for Convection-Diffusion equations. Part II: Semimatching nonconforming meshes
Y. Chen, B. Cockburn
Math. Comp., Vol. 83, No. 285, pp. 87–111 (2014).
Parametric Analytical Preconditioning and its Applications to the Reduced Collocation Methods.
Y. Chen, S. Gottlieb, Y. Maday
C. R. Acad. Sci. Paris, Ser. I, Vol. 352, pp. 661-666 (2014). DOI

2013

Reduced Collocation Methods: Reduced Basis Methods in the Collocation Framework.
Y. Chen, S. Gottlieb
J. Sci. Comput., Vol. 55, No. 3, pp. 718–737 (2013).
Transformation of a Mathematics Department's Teaching and Research Through a Focus on Computational Science
Y. Chen, G. Davis, S. Gottlieb, A. Hausknecht, A. Heryudono, S. Kim
JOCSE, Vol. 4, No. 1, pp. 24-29 (2013).

2012

Analysis of variable-degree HDG methods for convection-diffusion equations. Part I: General nonconforming meshes
Y. Chen, B. Cockburn
IMA J. Numer. Anal., Vol. 32, No. 4, pp. 1267–1293 (2012).
Certified Reduced Basis Method for Electromagnetic Scattering and Radar Cross Section Estimation
Y. Chen, J. S. Hesthaven, Y. Maday, J. Rodríguez, X. Zhu
CMAME, Vol. 233, pp. 92–108 (2012).

2011

A Seamless Reduced Basis Element Methods for 2D Maxwell's Problem: An Introduction
Y. Chen, J. S. Hesthaven, Y. Maday
Spectral and High Order Methods for Partial Differential Equations, Lecture Notes in Computational Science and Engineering, No. 76, pp. 141–152 (2011).

2010

Certified reduced basis methods and output bounds for the harmonic Maxwell's equations
Y. Chen, J. S. Hesthaven, Y. Maday, J. Rodríguez
Siam J. Sci. Comput., Vol. 32, No. 2, pp. 970–996 (2010).
A Natural-Norm Successive Constraint Method for Inf-Sup Lower Bounds
D. B. P. Huynh, D. J. Knezevic, Y. Chen, J. S. Hesthaven, A. T. Patera
CMAME, Vol. 199, pp. 1963–1975 (2010).

2009

Improved Successive Constraint Method Based A Posteriori Error Estimate for Reduced Basis Approximation of 2D Maxwell's Problem
Y. Chen, J. S. Hesthaven, Y. Maday, J. Rodríguez
M2AN, Vol. 43, pp. 1099–1116 (2009).

2008

A Monotonic Evaluation of Lower Bounds for Inf-Sup Stability Constants in the Frame of Reduced Basis Approximations
Y. Chen, J. S. Hesthaven, Y. Maday, J. Rodríguez
C. R. Acad. Sci. Paris, Ser. I, Vol. 346, pp. 1295–1300 (2008).

2007

An adaptive high order discontinuous Galerkin method with error control for the Hamilton-Jacobi Equations. Part I: The one-dimensional steady state case
Y. Chen, B. Cockburn
J. Comput. Phys., Vol. 226, No. 1, pp. 1027–1058 (2007).