% This file was created with JabRef 2.10. % Encoding: Cp1252 @String { AIAA = {AIAA Journal} } @String { APPNUMERMATH = {Appl. Numer. Math.} } @String { ARMA = {Arch. Rat. Mech. Anal.} } @String { CMA = {Comput. Mech. Advances} } @String { CMAME = {Comput. Methods Appl. Mech. Engrg.} } @String { COMPGEO = {Comp. Geosci.} } @String { CPAM = {Comm. Pure and Appl. Math.} } @String { CRAS = {C. R. Acad. Sci. Paris, S\'erie I Math.} } @String { DGM = {Discontinuous {G}alerkin Methods. Theory, Computation and Applications} } @String { EASTWEST = {East West J. Num. Math.} } @String { IJMS = {Internat. J. Mech. Sci.} } @String { IJNME = {Internat. J. Numer. Methods Engrg.} } @String { IJNMF = {Internat. J. Numer. Methods Fluids} } @String { IMAJNA = {IMA J. Num. Anal.} } @String { JAM = {J. Appl. Mech.} } @String { JCP = {J. Comput. Phys.} } @String { JDE = {J. Differential Equations} } @String { JNNFM = {J. Non-Newt. Fluid Mech.} } @String { JSC = {J. Sci. Comput.} } @String { LNCSE = {Lect. Notes Comput. Sci. Engrg.} } @String { MA2N = {Mod\'el. Math. Anal. Num\'er. } } @String { MAC = {Mat. Apl. Comput.} } @String { MATHCOMP = {Math. Comp.} } @String { NLAA = {Numer. Linear Alg. Appl.} } @String { NMPDE = {Numer. Methods Partial Differential Equations.} } @String { NUMERMATH = {Numer. Math.} } @String { PAGES = {255-261} } @String { RAIRO = {RAIRO Mod\'el. Math. Anal. Num\'er. } } @String { SIMATH = {SIAM J. Math. Anal.} } @String { SINUM = {SIAM J. Numer. Anal.} } @String { SISC = {SIAM J. Sci. Comput.} } @String { THIS = {this volume} } @String { VOLUME = {11} } @Article{Chen2015_NNSCM, Title = {A Certified Natural-Norm Successive Constraint Method for Parametric Inf-Sup Lower Bounds}, Author = {Y.~Chen}, Journal = {Applied Numer. Math.}, Year = {2016}, Pages = {98--108}, Volume = {99} } @Article{Chen2015_RBD, Title = {Reduced Basis Decomposition: a Certified and Fast Lossy Data Compression Algorithm}, Author = {Y.~Chen}, Journal = {Computers and Mathematics with Applications}, Year = {2015}, Pages = {2566 -- 2574}, Volume = {70} } @Article{ChenCockburnHDG_II, Title = {Analysis of variable-degree {HDG} methods for Convection-Diffusion equations. {Part II}: Semimatching nonconforming meshes}, Author = {Y. Chen and B. Cockburn}, Journal = {Math. Comp.}, Year = {2014}, Number = {285}, Pages = {87 -- 111}, Volume = {83} } @Article{ChenCockburnHDG_I, Title = {Analysis of variable-degree {HDG} methods for convection-diffusion equations. {Part I}: {G}eneral nonconforming meshes}, Author = {Y.~Chen and B.~Cockburn}, Journal = {IMA J. Numer. Anal.}, Year = {2012}, Number = {4}, Pages = {1267 -- 1293}, Volume = {32} } @Article{ChenCockburn07, Title = {An adaptive high order discontinuous {G}alerkin method with error control for the {H}amilton-{J}acobi Equations. {P}art {I}: {T}he one-dimensional steady state case}, Author = {Y.~Chen and B.~Cockburn}, Journal = JCP, Year = {2007}, Number = {1}, Pages = {1027--1058}, Volume = {226} } @Article{ChenCockburnDong14, Title = {Superconvergent HDG methods for linear, stationary, third-order equations in one-space dimension}, Author = {Y.~Chen and B.~Cockburn and B.~Dong}, Journal = {Math. Comp.}, Year = {2016}, Note = {Accepted.}, Pages = {2715-2742}, Volume = {85} } @Article{ChenCockburnDong15, Title = {A new discontinuous Galerkin method, conserving the discrete H2-norm, for third-order linear equations in one space dimension}, Author = {Y.~Chen and B.~Cockburn and B.~Dong}, Journal = IMAJNA, volume = {36}, number = {4}, pages = {1570-1598}, year = {2016}, month = {04}, issn = {0272-4979}, doi = {10.1093/imanum/drv070}, url = {https://doi.org/10.1093/imanum/drv070} } @Article{ChenGottlieb, Title = {Reduced Collocation Methods: Reduced Basis Methods in the Collocation Framework.}, Author = {Y. Chen and S. Gottlieb}, Journal = {J. Sci. Comput.}, Year = {2013}, Number = {3}, Pages = {718--737}, Volume = {55}, Owner = {YChen5admin}, Timestamp = {2011.08.05} } @Article{ChenGottliebHeryudonoNarayan, Title = {A reduced radial basis function method for partial differential equations on irregular domains}, Author = {Y.~Chen and S.~Gottlieb and A.~Heryudono and A.~Narayan}, Journal = {J. Sci. Comput.}, Year = {2016}, Number = {1}, Pages = {67-90}, Volume = {66}, Owner = {ylchen}, Timestamp = {2014.07.15} } @Article{ChenGottliebMaday, Title = {Parametric Analytical Preconditioning and its Applications to the Reduced Collocation Methods.}, Author = {Y. Chen and S. Gottlieb and Y. Maday}, Journal = {C. R. Acad. Sci. Paris, Ser. I}, Year = {2014}, Pages = {661 - 666}, Volume = {352}, Doi = {10.1016/j.crma.2014.06.001}, Owner = {ylchen}, Timestamp = {2014.07.15} } @InProceedings{CHM, Title = {A Seamless Reduced Basis Element Methods for 2D Maxwell's Problem: An Introduction}, Author = {Y. Chen and J.S. Hesthaven and Y. Maday}, Booktitle = {{Spectral and High Order Methods for Partial Differential Equations, }}, Year = {2011}, Editor = {J.S. Hesthaven and E.M. R${\textnormal \o}$nquist}, Number = {76}, Pages = {141--152}, Series = {Lecture Notes in Computational Science and Engineering} } @Article{CHMR_Sisc, Title = {Certified reduced basis methods and output bounds for the harmonic {M}axwell's equations}, Author = {Y. Chen and J. S. Hesthaven and Y. Maday and J. Rodr\'{i}guez}, Journal = {Siam J. Sci. Comput.}, Year = {2010}, Number = {2}, Pages = {970--996}, Volume = {32} } @Article{CHMR-M2an, Title = {Improved Successive Constraint Method Based A Posteriori Error Estimate for Reduced Basis Approximation of 2D Maxwell's Problem}, Author = {Y. Chen and J. S. Hesthaven and Y. Maday and J. Rodr\'{i}guez}, Journal = {M2AN}, Year = {2009}, Pages = {1099--1116}, Volume = {43} } @Article{CHMR-Cras, Title = {A Monotonic Evaluation of Lower Bounds for Inf-Sup Stability Constants in the Frame of Reduced Basis Approximations}, Author = {Y. Chen and J. S. Hesthaven and Y. Maday and J. Rodr\'{i}guez}, Journal = {C. R. Acad. Sci. Paris, Ser. I}, Year = {2008}, Pages = {1295--1300}, Volume = {346} } @Article{CHM_JCP, Title = {Certified Reduced Basis Method for Electromagnetic Scattering and Radar Cross Section Estimation}, Author = {Y. Chen and J. S. Hesthaven and Y. Maday and J. Rodr\'{i}guez and X. Zhu}, Journal = {CMAME}, Year = {2012}, Pages = {92--108}, Volume = {233} } @Article{HKCHP, Title = {A Natural-Norm Successive Constraint Method for Inf-Sup Lower Bounds}, Author = {D.B.P. Huynh and D.J. Knezevic and Y. Chen and J.S. Hesthaven and A.T. Patera}, Journal = {CMAME}, Year = {2010}, Pages = {1963--1975}, Volume = {199} } @Article{JiangChenNarayan, Title = {{A goal-oriented RBM-Accelerated generalized polynomial chaos algorithm}}, Author = {J. Jiang and Y. Chen and A. Narayan}, Journal = {SIAM/ASA JUQ}, Year = {2016}, Number = {1}, Pages = {1398--1420}, Volume = {4} } @Article{JiangChenNarayan2019, issn = "0898-1221", doi = "https://doi.org/10.1016/j.camwa.2018.11.032", url = "http://www.sciencedirect.com/science/article/pii/S0898122118306850", author = "Yanlai Chen and Jiahua Jiang and Akil Narayan", Title = {{A robust error estimator and a residual-free error indicator for reduced basis methods}}, Author = {Y. Chen and J. Jiang and A. Narayan}, Journal = {Computers \& Mathematics with Applications}, Year = {2019}, Volume = {77}, Issue = {7}, Pages = {1963--1979} } @article{ChenDongJiang2018, author = {Chen, Yanlai and Dong, Bo and Jiang, Jiahua}, title = {Optimally convergent hybridizable discontinuous Galerkin method for fifth-order Korteweg-de Vries type equations}, DOI= "10.1051/m2an/2018037", url= "https://doi.org/10.1051/m2an/2018037", journal = {ESAIM: M2AN}, year = 2018, volume = 52, number = 6, pages = "2283-2306", } @Article{LiuChenChenShu2019, author="Liu, Yong and Chen, Tianheng and Chen, Yanlai and Shu, Chi-Wang", title="Certified Offline-Free Reduced Basis (COFRB) Methods for Stochastic Differential Equations Driven by Arbitrary Types of Noise", journal="Journal of Scientific Computing", year="2019", month="May", day="16", abstract="In this paper, we propose, analyze, and implement a new reduced basis method (RBM) tailored for the linear (ordinary and partial) differential equations driven by arbitrary (i.e. not necessarily Gaussian) types of noise. There are four main ingredients of our algorithm. First, we propose a new space-time-like treatment of time in the numerical schemes for ODEs and PDEs. The second ingredient is an accurate yet efficient compression technique for the spatial component of the space-time snapshots that the RBM is adopting as bases. The third ingredient is a non-conventional ``parameterization'' of a non-parametric problem. The last is a RBM that is free of any dedicated offline procedure yet is still efficient online. The numerical experiments verify the effectiveness and robustness of our algorithms for both types of differential equations.", issn="1573-7691", doi="10.1007/s10915-019-00976-5", url="https://doi.org/10.1007/s10915-019-00976-5" } @Article{AntilChenNarayan2018, Title = {Certified reduced basis methods for fractional Laplace equations via extension}, Author = {Antil, Harbir and Chen, Yanlai and Narayan, Akil}, Journal = {Siam J. Sci. Comput.}, volume = {41}, number = {6}, pages = {A3552-A3575}, year = {2019}, doi = {10.1137/18M1204802}, URL = { https://doi.org/10.1137/18M1204802 }, eprint = { https://doi.org/10.1137/18M1204802 } } @Article{JiChenXu2018, author = {Lijie Ji and Yanlai Chen and Zhenli Xu}, title = {A Reduced Basis Method for the Nonlinear Poisson-Boltzmann Equation}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2019}, volume = {11}, number = {5}, pages = {1200--1218}, abstract = {

In numerical simulations of many charged systems at the micro/nano scale, a common theme is the repeated {resolution} of the Poisson-Boltzmann equation. This task proves challenging, if not entirely infeasible, largely due to the nonlinearity of the equation and the high dimensionality of the physical and parametric domains with the latter emulating the system configuration. In this paper, we for the first time adapt a mathematically rigorous and computationally efficient model order reduction paradigm, the so-called reduced basis method (RBM), to mitigate this challenge. We adopt a finite difference method as the mandatory underlying scheme to produce the {high-fidelity numerical solutions of the Poisson-Boltzmann equation}  upon which the fast {RBM} algorithm is built and its performance is measured against. Numerical tests presented in this paper demonstrate the high efficiency and accuracy of the fast algorithm, the reliability of its error estimation, as well as its capability in effectively capturing the boundary layer.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2018-0188}, url = {http://global-sci.org/intro/article_detail/aamm/13207.html} } @Article{NguyenChen2018, Title = {Reduced-basis method for the iterative solution of parametrized symmetric positive-definite linear systems}, Author = {Nguyen, Cuong and Chen, Yanlai}, Journal = {arXiv:1804.06363}, Year = {2018}, Url = {} } @article{JiangChen2019, author = {Jiang, Jiahua and Chen, Yanlai}, title = {Adaptive greedy algorithms based on parameter-domain decomposition and reconstruction for the reduced basis method}, journal = {International Journal for Numerical Methods in Engineering}, volume = {121}, number = {23}, pages = {5426-5445}, keywords = {Greedy algorithm, reduced basis method}, doi = {https://doi.org/10.1002/nme.6544}, url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/nme.6544}, eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6544}, abstract = {Abstract The reduced basis method (RBM) empowers repeated and rapid evaluation of parametrized partial differential equations through an offline–online decomposition, a.k.a. a learning-execution process. A key feature of the method is a greedy algorithm repeatedly scanning the training set, a fine discretization of the parameter domain, to identify the next dimension of the parameter-induced solution manifold along which we expand the surrogate solution space. Although successfully applied to problems with fairly high parametric dimensions, the challenge is that this scanning cost dominates the offline cost due to it being proportional to the cardinality of the training set which is exponential with respect to the parameter dimension. In this work, we review three recent attempts in effectively delaying this curse of dimensionality, and propose two new hybrid strategies through successive refinement and multilevel maximization of the error estimate over the training set. All five offline-enhanced methods and the original greedy algorithm are tested and compared on two types of problems: the thermal block problem and the geometrically parameterized Helmholtz problem.}, year = {2020} } @Article{CGJMX2019, Title = {L1-ROC and R2-ROC: L1- and R2-based Reduced Over-Collocation methods for parametrized nonlinear partial differential equations}, Author = {Chen, Yanlai and Gottlieb, Sigal and Ji, Lijie and Maday, Yvon and Xu, Zhenli}, Journal = {arXiv:1906.07349}, Year = {2019}, Url = {} } @article{ChenJiNarayanXu2021, author = {Yanlai Chen and Lijie Ji and Akil Narayan and Zhenli Xu}, title = {L1-based reduced over collocation and hyper reduction for steady state and time-dependent nonlinear equations}, journal = {J. Sci. Compt.}, volume = {87}, pages = {10}, year = {2021}, doi={10.1007/s10915-021-01416-z} } @article{ChenSigalJiMaday2021, title = {An EIM-degradation free reduced basis method via over collocation and residual hyper reduction-based error estimation}, journal = {Journal of Computational Physics}, volume = {444}, pages = {110545}, year = {2021}, issn = {0021-9991}, doi = {https://doi.org/10.1016/j.jcp.2021.110545}, url = {https://www.sciencedirect.com/science/article/pii/S002199912100440X}, author = {Yanlai Chen and Sigal Gottlieb and Lijie Ji and Yvon Maday}, keywords = {Reduced basis method, Empirical interpolation method, Generalized empirical interpolation method, Collocation, Over Collocation, Hyper reductions, Greedy algorithm}, abstract = {The need for multiple interactive, real-time simulations using different parameter values has driven the design of fast numerical algorithms with certifiable accuracies. The reduced basis method (RBM) presents itself as such an option. RBM features a mathematically rigorous error estimator which drives the construction of a low-dimensional subspace. A surrogate solution is then sought in this low-dimensional space approximating the parameter-induced high fidelity solution manifold. However when the system is nonlinear or its parameter dependence nonaffine, this efficiency gain degrades tremendously, an inherent drawback of the application of the empirical interpolation method (EIM). In this paper, we augment and extend the EIM approach as a direct solver, as opposed to an assistant, for solving nonlinear partial differential equations on the reduced level. The resulting method, called Reduced Over-Collocation method (ROC), is stable and capable of avoiding the efficiency degradation. Two critical ingredients of the scheme are collocation at about twice as many locations as the number of basis elements for the reduced approximation space, and an efficient error indicator for the strategic building of the reduced solution space. The latter, the main contribution of this paper, results from an adaptive hyper reduction of the residuals for the reduced solution. Together, these two ingredients render the proposed R2-ROC scheme both offline- and online-efficient. A distinctive feature is that the efficiency degradation appearing in traditional RBM approaches that utilize EIM for nonlinear and nonaffine problems is circumvented, both in the offline and online stages. Numerical tests on different families of time-dependent and steady-state nonlinear problems demonstrate the high efficiency and accuracy of our R2-ROC and its superior stability performance.} } @Article{JiangChenNarayan2017, Title = {{Offline-Enhanced reduced basis method through adaptive construction of the surrogate training set.}}, Author = {J. Jiang and Y. Chen and A. Narayan}, Journal = {J. Sci. Comput.}, year="2017", month="Dec", day="01", volume="73", number="2", pages="853--875", } @Article{PerkinsChen2015, Title = {Using Visualization and Analysis with Efficient Dimension Reduction Techniques to Determine Underlying Factors in Hospital Inpatient Procedure Costs}, Author = {M. Perkins and Y. Chen}, Journal = {2015 IEEE Conference on Visual Analytics Science and Technology (VAST)}, Volume ={00}, Pages ={205-206}, Year = {2015} } @Article{CSUMS3, Title = {Transformation of a Mathematics Department's Teaching and Research Through a Focus on Computational Science}, Author = {Y. Chen, G. Davis, S. Gottlieb, A. Hausknecht, A. Heryudono, and S.Kim}, Journal = {JOCSE}, Year = {2013}, Number = {1}, Pages = {24-29}, Volume = {4}, Owner = {ychen5}, Timestamp = {2014.11.05} } @article{chen2023gpt, title = {GPT-PINN: Generative Pre-Trained Physics-Informed Neural Networks toward non-intrusive Meta-learning of parametric PDEs}, journal = {Finite Elements in Analysis and Design}, volume = {228}, pages = {104047}, year = {2024}, issn = {0168-874X}, doi = {https://doi.org/10.1016/j.finel.2023.104047}, url = {https://www.sciencedirect.com/science/article/pii/S0168874X23001403}, author = {Yanlai Chen and Shawn Koohy}, keywords = {Physics-Informed Neural Networks, Meta-learning, model order reduction, Network of networks, Non-intrusive learning, Parametric PDEs}, abstract = {Physics-Informed Neural Network (PINN) has proven itself a powerful tool to obtain the numerical solutions of nonlinear partial differential equations (PDEs) leveraging the expressivity of deep neural networks and the computing power of modern heterogeneous hardware. However, its training is still time-consuming, especially in the multi-query and real-time simulation settings, and its parameterization often overly excessive. In this paper, we propose the Generative Pre-Trained PINN (GPT-PINN) to mitigate both challenges in the setting of parametric PDEs. GPT-PINN represents a brand-new meta-learning paradigm for parametric systems. As a network of networks, its outer-/meta-network is hyper-reduced with only one hidden layer having significantly reduced number of neurons. Moreover, its activation function at each hidden neuron is a (full) PINN pre-trained at a judiciously selected system configuration. The meta-network adaptively “learns” the parametric dependence of the system and “grows” this hidden layer one neuron at a time. In the end, by encompassing a very small number of networks trained at this set of adaptively-selected parameter values, the meta-network is capable of generating surrogate solutions for the parametric system across the entire parameter domain accurately and efficiently.} } @article{MATSUDA2026114597, title = {Reduced basis methods for parametric steady-state radiative transfer equation}, journal = {Journal of Computational Physics}, volume = {548}, pages = {114597}, year = {2026}, issn = {0021-9991}, doi = {https://doi.org/10.1016/j.jcp.2025.114597}, url = {https://www.sciencedirect.com/science/article/pii/S0021999125008794}, author = {Kimberly Matsuda and Yanlai Chen and Yingda Cheng and Fengyan Li}, keywords = {Model order reduction, Reduced basis method, Least-squares Petrov-Galerkin, Radiative transfer, Transport model, High dimension}, abstract = {The radiative transfer equation (RTE) is a fundamental mathematical model to describe physical phenomena involving the propagation of radiation and its interactions with the host medium, and it arises in many applications. Deterministic methods can produce accurate solutions without any statistical noise, yet often at a price of expensive computational costs originating from the intrinsic high dimensionality of the model. This is more prominent in multi-query tasks, e.g., inverse problems and optimal design, when the RTE needs to be solved repeatedly. This motivates the developments of dimensionality and model order reduction techniques for such transport models. With this work, we present the first systematic investigation of projection-based reduced order models (ROMs) following the reduced basis method (RBM) framework to simulate the parametric steady-state RTE with isotropic scattering and one energy group. The use of RBM compared to standard proper orthogonal decomposition (POD) is well motivated, especially considering that a large number of degrees of freedom is needed by full order models to solve high dimensional transport models like RTE. Four ROMs are designed, with each defining a nested family of reduced surrogate solvers of different resolution/fidelity. They are based on either a Galerkin or least-squares Petrov-Galerkin projection and utilize either an L1 or residual-based importance/error indicator. Two of the proposed ROMs are certified in the setting when the absorption cross section is positively bounded below uniformly. One technical focus and contribution lie in the proposed implementation strategies under the affine assumption of the parameter dependence of the model. These well-crafted broadly applicable strategies not only ensure the efficiency and accuracy of the offline training stage and the online prediction of reduced surrogate solvers, they also take into account the conditioning of the reduced systems as well as the stagnation-free residual evaluation for numerical robustness. Computational complexities are derived for both the offline training and online prediction stages of the proposed model order reduction strategies, and they are demonstrated numerically along with the accuracy and robustness of the reduced surrogate solvers. Numerically we observe four to six orders of magnitude speedup of our ROMs compared to full order models for some 2D2v examples.} } @article{chen2025derivative, title={Derivative-informed Graph Convolutional Autoencoder with Phase Classification for the Lifshitz-Petrich Model}, author={Chen, Yanlai and Ji, Yajie and Xu, Zhenli}, journal={CSIAM Transactions on Applied Mathematics}, year={2026}, doi={10.4208/csiam-am.so-2025-0089}, url={https://arxiv.org/abs/2509.11293} } @article{zheng2025rebano, title={{ReBaNO}: Reduced Basis Neural Operator Mitigating Generalization Gaps and Achieving Discretization Invariance}, author={Zheng, Haolan and Chen, Yanlai and Han, J. and Yu, Y.}, journal={arXiv preprint arXiv:2509.09611}, year={2025}, url={https://arxiv.org/abs/2509.09611} } @article{ji2025s2gpt, title={{S$^2$GPT-PINN}: Reduced basis and hyper reduction-driven double reduction for Physics-Informed Neural Networks}, author={Ji, Yajie and Chen, Yanlai and Koohy, Shawn}, journal={Communications in Computational Physics}, volume={40}, number={4}, pages={1293--1316}, year={2026}, doi={10.4208/cicp.OA-2025-0152}, url={https://arxiv.org/abs/2506.15687} } @article{chen2025egpt, title={{EGPT-PINN}: Entropy-regularized generative pre-trained physics informed neural networks for parameterized nonlinear conservation laws}, author={Ji, Yajie and Chen, Yanlai and Xu, Zhenli}, journal={Computers \& Mathematics with Applications}, volume={222}, pages={223--243}, year={2026}, doi={10.1016/j.camwa.2026.09.017}, url={https://papers.ssrn.com/sol3/papers.cfm?abstract_id=5216939} } @article{Ji2025AAROC, author = {Ji, Lijie and Peng, Zhichao and Chen, Yanlai}, title = {AAROC: Reduced Over-Collocation Method With Adaptive Time Partitioning and Adaptive Enrichment for Parametric Time-Dependent Equations}, journal = {Numerical Methods for Partial Differential Equations}, volume = {41}, number = {5}, pages = {e70031}, keywords = {basis adaptivity, empirical interpolation method, model order reduction, nonlinear and nonaffine partial differential equations, reduced over collocation}, doi = {https://doi.org/10.1002/num.70031}, url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/num.70031}, eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/num.70031}, abstract = {ABSTRACT Nonlinear and nonaffine terms in parametric partial differential equations can potentially lead to a computational cost of a reduced-order model (ROM) that is comparable to the cost of the original full-order model (FOM). To address this, the Reduced Residual Reduced Over-Collocation method (R2-ROC) is developed as a hyper-reduction method within the framework of the reduced basis method in the collocation setting. R2-ROC greedily selects two sets of reduced collocation points based on the (generalized) empirical interpolation method for both solution snapshots and residuals, thereby avoiding the computational inefficiency. The vanilla R2-ROC method can face instability when applied to parametric fluid dynamic problems. To address this, an adaptive enrichment strategy has been proposed to stabilize the ROC method. However, this strategy can involve an excessive number of reduced collocation points, thereby negatively impacting online efficiency. To ensure both efficiency and accuracy, we propose an adaptive time partitioning and adaptive enrichment strategy-based ROC method (AAROC). The adaptive time partitioning dynamically captures the low-rank structure, necessitating fewer reduced collocation points being sampled in each time segment. Numerical experiments on the parametric viscous Burgers' equation and lid-driven cavity problems demonstrate the efficiency, enhanced stability, and accuracy of the proposed AAROC method.}, year = {2025} } @article{Gillcrist_2024, author = {David J. Gillcrist and Negin Alemazkoor and Yanlai Chen and Mazdak Tootkaboni}, title = {Design of Experiments via Multi-Fidelity Surrogates and Statistical Sensitivity Measures}, journal = {Journal of Machine Learning for Modeling and Computing}, issn = {2689-3967}, year = {2024}, volume = {5}, number = {4}, URL = {https://dl.begellhouse.com/journals/558048804a15188a,6ea623526214d90d,3f8883e81a37d18c.html}, pages = {95--121}, DOI = {10.1615/JMachLearnModelComput.2024055261}, } @article{chen2024tgpt, title={{TGPT-PINN}: Nonlinear model reduction with transformed {GPT-PINNs}}, author={Chen, Yanlai and Ji, Yajie and Narayan, Akil and Xu, Zhenli}, journal={Computer Methods in Applied Mechanics and Engineering}, volume={430}, pages={117198}, year={2024}, doi={10.1016/j.cma.2024.117198} } @article{hou2023reduced, title={A reduced basis warm-start iterative solver for the parameterized linear systems}, author={Hou, Shijin and Chen, Yanlai and Xia, Yinhua}, journal={Beijing Journal of Pure and Applied Mathematics}, year={2025}, volume = {2}, number = {1}, pages={123--146}, doi={10.4310/BPAM.250414231722} } @article{JiJiChenXu2024, author = {Ji, Yajie and Ji, Lijie and Chen, Yanlai and Xu, Zhenli}, title = {MCMS-RBM: Multicomponent Multistate Reduced Basis Method Toward Rapid Generation of Phase Diagrams for the Lifshitz–Petrich Model}, journal = {SIAM Journal on Scientific Computing}, volume = {46}, number = {6}, pages = {B785-B805}, year = {2024}, doi = {10.1137/23M1596831}, URL = { https://doi.org/10.1137/23M1596831 }, eprint = { https://doi.org/10.1137/23M1596831 } , abstract = { Abstract. Due to quasicrystals having long-range orientational order but without translational symmetry, traditional numerical methods usually suffer when applied as is. In the past decade, the projection method has emerged as a prominent solver for quasiperiodic problems. Transforming them into higher-dimensional but periodic ones, the projection method facilitates the application of the fast Fourier transform. However, the computational complexity inevitably becomes high, which significantly impedes, e.g., the generation of the phase diagram since a high-fidelity simulation of a problem whose dimension is doubled must be performed for numerous times. To address the computational challenge of quasiperiodic problems based on the projection method, this paper proposes a multicomponent multistate reduced basis method (MCMS-RBM). Featuring multiple components with each providing reduction functionality for one branch of the problem induced by one part of the parameter domain, the MCMS-RBM does not resort to the parameter domain configurations (e.g., phase diagrams) a priori. It enriches each component in a greedy fashion via a phase transition guided exploration of the multiple states inherent to the problem. Adopting the empirical interpolation method, the resulting online-efficient method vastly accelerates the generation of a delicate phase diagram to a matter of minutes for a parametrized two-turn-four dimensional Lifshitz–Petrich model with two length scales. Moreover, it furnishes surrogate and equally accurate field variables anywhere in the parameter domain. } } @article{ChenDongPereira2022, author = {Chen, Yanlai and Dong, Bo and Pereira, Rebecca}, title = {A New Conservative Discontinuous Galerkin Method via Implicit Penalization for the Generalized Korteweg–de Vries Equation}, journal = {SIAM Journal on Numerical Analysis}, volume = {60}, number = {6}, pages = {3078-3098}, year = {2022}, doi = {10.1137/22M1470827}, URL = { https://doi.org/10.1137/22M1470827 }, eprint = { https://doi.org/10.1137/22M1470827 } , abstract = { Abstract. We design, analyze, and implement a new conservative discontinuous Galerkin (DG) method for the simulation of solitary wave solutions to the generalized Korteweg–de Vries (KdV) equation. The key feature of our method is the conservation, at the numerical level, of the mass, energy, and Hamiltonian that are conserved by exact solutions of all KdV equations. To our knowledge, this is the first DG method that conserves all these three quantities, a property critical for the accurate long-time evolution of solitary waves. To achieve the desired conservation properties, our novel idea is to introduce two stabilization parameters in the numerical fluxes as new unknowns, which then allow us to enforce the conservation of energy and Hamiltonian in the formulation of the numerical scheme. We prove the conservation properties of the scheme which are corroborated by numerical tests. This idea of achieving conservation properties by implicitly defining penalization parameters, which are traditionally specified a priori, can serve as a framework for designing physics-preserving numerical methods for other types of problems. } } @article{HouChenXi2022, author = {Hou, Shijin and Chen, Yanlai and Xia, Yinhua}, title = {Fast \$L^2\$ Optimal Mass Transport via Reduced Basis Methods for the Monge--Ampère Equation}, journal = {SIAM Journal on Scientific Computing}, volume = {44}, number = {6}, pages = {A3536-A3559}, year = {2022}, doi = {10.1137/21M1463720}, URL = { https://doi.org/10.1137/21M1463720 }, eprint = { https://doi.org/10.1137/21M1463720 } , abstract = { Repeatedly solving the parameterized optimal mass transport (pOMT) problem is a frequent task in applications such as image registration and adaptive grid generation. It is thus critical to develop a highly efficient reduced solver that is equally accurate as the full order model. In this paper, we propose such a machine learning--like method for pOMT by adapting a new reduced basis (RB) technique specifically designed for nonlinear equations, the reduced residual reduced over-collocation (R2-ROC) approach, to the parameterized Monge--Ampère equation. It builds on top of a narrow-stencil finite difference method (FDM), a so-called truth solver, which we propose in this paper for the Monge--Ampère equation with the transport boundary. Together with the R2-ROC approach, it allows us to handle the strong and unique nonlinearity pertaining to the Monge--Ampère equation achieving online efficiency without resorting to any direct approximation of the nonlinearity. Several challenging numerical tests demonstrate the accuracy and high efficiency of our reduced solver for solving the parameterized Monge--Ampère equation, effectively transporting the nontrivial boundaries. } } @article{CHEN2022111412, title = {A hyper-reduced MAC scheme for the parametric Stokes and Navier-Stokes equations}, journal = {Journal of Computational Physics}, volume = {466}, pages = {111412}, year = {2022}, issn = {0021-9991}, doi = {https://doi.org/10.1016/j.jcp.2022.111412}, url = {https://www.sciencedirect.com/science/article/pii/S0021999122004740}, author = {Yanlai Chen and Lijie Ji and Zhu Wang}, keywords = {Reduced residual reduced over-collocation method, Generalized empirical interpolation method, Hyper-reduced, Adaptive enrichment strategy, Greedy algorithm, Collocation}, abstract = {The need for accelerating the repeated solving of certain parametrized systems motivates the development of more efficient reduced order methods. The classical reduced basis method is popular due to an offline-online decomposition and a mathematically rigorous a posterior error estimator which guides a greedy algorithm offline. For nonlinear and nonaffine problems, hyper reduction techniques have been introduced to make this decomposition efficient. However, they may be tricky to implement and often degrade the offline and online computational efficiency. To avoid this degradation, reduced residual reduced over-collocation (R2-ROC) was invented. It integrates the empirical interpolation techniques on the solution snapshots and the well-chosen residuals, the collocation philosophy, and the simplicity of evaluating the hyper-reduced well-chosen residuals. In this paper, we introduce an adaptive enrichment strategy for R2-ROC rendering it capable of handling parametric fluid flow problems. Built on top of an underlying Marker and Cell (MAC) scheme, a novel hyper-reduced MAC scheme is therefore presented and tested on lid-driven cavity and flow past a backward-facing step problems demonstrating its high efficiency, stability and accuracy.} } @article{peng2022reduced, title={A reduced basis method for radiative transfer equation}, author={Peng, Zhichao and Chen, Yanlai and Cheng, Yingda and Li, Fengyan}, journal={Journal of Scientific Computing}, volume={91}, number={5}, pages={24}, year={2022}, doi={10.1007/s10915-022-01782-2} } @articleInfo{DinhAntilChenCherkaevNarayan2022, title = {Model reduction for fractional elliptic problems using Kato's formula}, journal = {Mathematical Control and Related Fields}, volume = {12}, number = {1}, pages = {115-146} year = {2022}, issn = {2156-8472}, doi = {10.3934/mcrf.2021004}, url = {https://www.aimsciences.org/article/id/1d28d5fa-c41e-4127-80ef-8907c0fac247}, author = {Huy Dinh and Harbir Antil and Yanlai Chen and Elena Cherkaev and Akil Narayan}, keywords = {Fractional Laplacian, model order reduction, numerical methods}, abstract = {We propose a novel numerical algorithm utilizing model reduction for computing solutions to stationary partial differential equations involving the spectral fractional Laplacian. Our approach utilizes a known characterization of the solution in terms of an integral of solutions to local (classical) elliptic problems. We reformulate this integral into an expression whose continuous and discrete formulations are stable; the discrete formulations are stable independent of all discretization parameters. We subsequently apply the reduced basis method to accomplish model order reduction for the integrand. Our choice of quadrature in discretization of the integral is a global Gaussian quadrature rule that we observe is more efficient than previously proposed quadrature rules. Finally, the model reduction approach enables one to compute solutions to multi-query fractional Laplace problems with orders of magnitude less cost than a traditional solver.} } @article{belik2025greedy, title={Greedy Rational Approximation for Frequency-Domain Model Reduction of Parametric LTI Systems}, author={B{\v{e}}l{\'i}k, Filip and Chen, Yanlai and Narayan, Akil}, journal={arXiv preprint arXiv:2512.23814}, year={2025}, url={https://arxiv.org/abs/2512.23814} } @article{chen2018foreword, title={A Foreword to the Special Issue in Honor of Professor Bernardo Cockburn on His 60th Birthday: A Life Time of Discontinuous Schemings}, author={Chen, Yanlai and Dong, Bo and Shu, Chi-Wang}, journal={Journal of Scientific Computing}, volume={77}, number={3}, pages={1303--1309}, year={2018}, publisher={Springer}, abstract = {We present this special issue of the Journal of Scientific Computing to celebrate Bernardo Cockburn’s sixtieth birthday. The theme of this issue is discontinuous Galerkin methods, a hallmark of Bernardo’s distinguished professional career. This foreword provides an informal but rigorous account of what enabled Bernardo’s achievements, based on the concluding presentation he gave at the the IMA workshop “Recent Advances and Challenges in Discontinuous Galerkin Methods and Related Approaches” on July 1, 2017 which was widely deemed as the best lecture of his career so far.} } @article{peng2024micromacro, title={A Micro-Macro Decomposed Reduced Basis Method for the Time-Dependent Radiative Transfer Equation}, author={Peng, Zhichao and Chen, Yanlai and Cheng, Yingda and Li, Fengyan}, journal={Multiscale Modeling \& Simulation}, volume={22}, number={1}, pages={639--666}, year={2024}, doi={10.1137/22M1533487} } @article{ji2026quadratic, title={Nonlinear Model Order Reduction on Quadratic Manifolds via Greedy Algorithms with Dimension-Dependent Regularization}, author={Ji, Lijie and Rashid, S. and Chen, Yanlai and Wang, Zhu}, journal={Submitted}, year={2026} } @article{tariq2026kdv, title={High-order Conservative Discontinuous {G}alerkin Methods via Implicit Penalization for the Generalized {K}orteweg--de {V}ries Equation and the {H}irota--{S}atsuma {K}d{V} System}, author={Tariq, Muhammad Shan and Chen, Yanlai and Dong, Bo}, journal={Submitted}, year={2026} }