An adaptive high-order discontinuous Galerkin method with error control for the Hamilton-Jacobi equations. Part I: The one-dimensional steady state case. - Yanlai Chen; Bernardo Cockburn (J. Comput. Phys., 2007)

Certified Reduced Basis Methods and Output Bounds for the Harmonic Maxwell's Equations. - Yanlai Chen; Jan S. Hesthaven; Yvon Maday; Jerónimo Rodríguez (SIAM J. Sci. Comput., 2010)

Reduced Collocation Methods: Reduced Basis Methods in the Collocation Framework. - Yanlai Chen; Sigal Gottlieb (J. Sci. Comput., 2013)

Analysis of variable-degree HDG methods for Convection-Diffusion equations. Part II: Semimatching nonconforming meshes. - Yanlai Chen; Bernardo Cockburn (Math. Comput., 2014)

Using visualization and analysis with efficient dimension Reduction to determine underlying factors in hospital inpatient procedure costs. - Miriam Perkins; Yanlai Chen (VAST, 2015)

Reduced basis decomposition: A certified and fast lossy data compression algorithm. - Yanlai Chen (Comput. Math. Appl., 2015)

A Reduced Radial Basis Function Method for Partial Differential Equations on Irregular Domains. - Yanlai Chen; Sigal Gottlieb; Alfa R. H. Heryudono; Akil Narayan 001 (J. Sci. Comput., 2016)

A Goal-Oriented Reduced Basis Methods-Accelerated Generalized Polynomial Chaos Algorithm. - Jiahua Jiang; Yanlai Chen; Akil Narayan 001 (SIAM/ASA J. Uncertain. Quantification, 2016)

Superconvergent HDG methods for linear, stationary, third-order equations in one-space dimension. - Yanlai Chen; Bernardo Cockburn; Bo Dong (Math. Comput., 2016)

Offline-Enhanced Reduced Basis Method Through Adaptive Construction of the Surrogate Training Set. - Jiahua Jiang; Yanlai Chen; Akil Narayan 001 (J. Sci. Comput., 2017)

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 (J. Sci. Comput., 2018)

A robust error estimator and a residual-free error indicator for reduced basis methods. - Yanlai Chen; Jiahua Jiang; Akil Narayan 001 (Comput. Math. Appl., 2019)

L1-ROC and R2-ROC: L1- and R2-based Reduced Over-Collocation methods for parametrized nonlinear partial differential equations. - Yanlai Chen; Sigal Gottlieb; Lijie Ji; Yvon Maday; Zhenli Xu (CoRR, 2019)

Multi-level adaptive greedy algorithms for the reduced basis method. - Jiahua Jiang; Yanlai Chen (CoRR, 2019)

Certified Offline-Free Reduced Basis (COFRB) Methods for Stochastic Differential Equations Driven by Arbitrary Types of Noise. - Yong Liu 019; Tianheng Chen; Yanlai Chen; Chi-Wang Shu (J. Sci. Comput., 2019)

Reduced Basis Methods for Fractional Laplace Equations via Extension. - Harbir Antil; Yanlai Chen; Akil Narayan 001 (SIAM J. Sci. Comput., 2019)

Fast L2 optimal mass transport via reduced basis methods for the Monge-Ampère equation. - Shijin Hou; Yanlai Chen; Yinhua Xia (CoRR, 2021)

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 (J. Comput. Phys., 2021)

L1-Based Reduced Over Collocation and Hyper Reduction for Steady State and Time-Dependent Nonlinear Equations. - Yanlai Chen; Lijie Ji; Akil Narayan 001; Zhenli Xu (J. Sci. Comput., 2021)

A new conservative discontinuous Galerkin method via implicit penalization for the generalized KdV equation. - Yanlai Chen; Bo Dong; Rebecca Pereira (CoRR, 2022)

A hyper-reduced MAC scheme for the parametric Stokes and Navier-Stokes equations. - Yanlai Chen; Lijie Ji; Zhu Wang 003 (J. Comput. Phys., 2022)

A Reduced Basis Method for Radiative Transfer Equation. - Zhichao Peng; Yanlai Chen; Yingda Cheng; Fengyan Li (J. Sci. Comput., 2022)

Fast $L^2$ Optimal Mass Transport via Reduced Basis Methods for the Monge-Ampère Equation. - Shijin Hou; Yanlai Chen; Yinhua Xia (SIAM J. Sci. Comput., 2022)

A New Conservative Discontinuous Galerkin Method via Implicit Penalization for the Generalized Korteweg-de Vries Equation. - Yanlai Chen; Bo Dong; Rebecca Pereira (SIAM J. Numer. Anal., 2022)

GPT-PINN: Generative Pre-Trained Physics-Informed Neural Networks toward non-intrusive Meta-learning of parametric PDEs. - Yanlai Chen; Shawn Koohy (CoRR, 2023)

MCMS-RBM: Multi-Component Multi-State Reduced Basis Method toward Efficient Transition Pathway Identification for Crystals and Quasicrystals. - Yajie Ji; Lijie Ji; Yanlai Chen; Zhenli Xu (CoRR, 2023)

A reduced basis warm-start iterative solver for the parameterized systems. - Shijin Hou; Yanlai Chen; Yinhua Xia (CoRR, 2023)

TGPT-PINN: Nonlinear model reduction with transformed GPT-PINNs. - Yanlai Chen; Yajie Ji; Akil Narayan 001; Zhenli Xu (CoRR, 2024)

AAROC: Reduced Over-Collocation Method with Adaptive Time Partitioning and Adaptive Enrichment for Parametric Time-Dependent Equations. - Lijie Ji; Zhichao Peng; Yanlai Chen (CoRR, 2024)

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 J. Sci. Comput., 2024)

A Micro-Macro Decomposed Reduced Basis Method for the Time-Dependent Radiative Transfer Equation. - Zhichao Peng; Yanlai Chen; Yingda Cheng; Fengyan Li (Multiscale Model. Simul., 2024)

VGPT-PINN: Viscosity-enhanced Generative Pre-Trained Physics Informed Neural Networks for parameterized nonlinear conservation laws. - Yajie Ji; Yanlai Chen; Zhenli Xu (CoRR, 2025)

S2GPT-PINNs: Sparse and Small models for PDEs. - Yajie Ji; Yanlai Chen; Shawn Koohy (CoRR, 2025)