Flexible piecewise approximations based on partition of unity. - Weimin Han; Wing Kam Liu (Adv. Comput. Math., 2005)

Rheology of red blood cell aggregation by computer simulation. - Yaling Liu; Wing Kam Liu (J. Comput. Phys., 2006)

Domain reduction method for atomistic simulations. - Sergey N. Medyanik; Eduard G. Karpov; Wing Kam Liu (J. Comput. Phys., 2006)

A pseudo-spectral multiscale method: Interfacial conditions and coarse grid equations. - Shaoqiang Tang; Thomas Y. Hou 001; Wing Kam Liu (J. Comput. Phys., 2006)

Maximum principle and convergence analysis for the meshfree point collocation method. - Do Wan Kim; Wing Kam Liu (SIAM J. Numer. Anal., 2006)

Extrinsic meshfree approximation using asymptotic expansion for interfacial discontinuity of derivative. - Do Wan Kim; Young-Cheol Yoon; Wing Kam Liu; Ted Belytschko (J. Comput. Phys., 2007)

On computational issues of immersed finite element methods. - X. Sheldon Wang; Lucy T. Zhang; Wing Kam Liu (J. Comput. Phys., 2009)

Erratum to "On computational issues of immersed finite element methods" [J. Comput. Phys 228 (2009) 2535-2551]. - X. Sheldon Wang; Lucy T. Zhang; Wing Kam Liu (J. Comput. Phys., 2009)

Electric Field Guided Assembly of One-Dimensional Nanostructures for High Performance Sensors. - Devon A. Brown; Jong-Hoon Kim; Hyun-Boo Lee; Gareth Fotouhi; Kyong-Hoon Lee; Wing Kam Liu; Jae-Hyun Chung (Sensors, 2012)

Computational microstructure characterization and reconstruction for stochastic multiscale material design. - Yu Liu; M. Steven Greene; Wei Chen 041; Dmitriy A. Dikin; Wing Kam Liu (Comput. Aided Des., 2013)

Intersection-free tetrahedral meshing from volumetric images. - Jin Qian; Yongjie Zhang 001; Devin Thomas O'Connor; M. Steven Greene; Wing Kam Liu (Comput. methods Biomech. Biomed. Eng. Imaging Vis., 2013)

HiDeNN-PGD: reduced-order hierarchical deep learning neural networks. - Lei Zhang 164; Ye Lu; Shaoqiang Tang; Wing Kam Liu (CoRR, 2021)

Eighty Years of the Finite Element Method: Birth, Evolution, and Future. - Wing Kam Liu; Shaofan Li; Harold Park (CoRR, 2021)

Stochastic additive manufacturing simulation: from experiment to surface roughness and porosity prediction. - Yangfan Li; Ye Lu; Abdullah Al Amin; Wing Kam Liu (CoRR, 2022)

Deep Learning Discrete Calculus (DLDC): A Family of Discrete Numerical Methods by Universal Approximation for STEM Education to Frontier Research. - Sourav Saha; Chanwook Park; Stefan Knapik; Jiachen Guo; Owen Huang; Wing Kam Liu (CoRR, 2022)

An Introduction to Kernel and Operator Learning Methods for Homogenization by Self-consistent Clustering Analysis. - Owen Huang; Sourav Saha; Jiachen Guo; Wing Kam Liu (CoRR, 2022)

Next-generation prognosis framework for pediatric spinal deformities using bio-informed deep learning networks. - Mahsa Tajdari; Farzam Tajdari; Pouyan Shirzadian; Aishwarya Pawar; Mirwais Wardak; Sourav Saha; Chanwook Park; Toon Huysmans; Yu Song 003; Yongjie Jessica Zhang; John F. Sarwark; Wing Kam Liu (Eng. Comput., 2022)

Physics-based Data-Augmented Deep Learning for Enhanced Autogenous Shrinkage Prediction on Experimental Dataset. - Vishu Gupta; Yuhui Lyu; Derick Suarez; Yuwei Mao; Wei-Keng Liao; Alok N. Choudhary; Wing Kam Liu; Gianluca Cusatis; Ankit Agrawal 001 (IC3, 2023)

Extended tensor decomposition model reduction methods: training, prediction, and design under uncertainty. - Ye Lu; Satyajit Mojumder; Jiachen Guo; Yangfan Li; Wing Kam Liu (CoRR, 2023)

Statistical Parameterized Physics-Based Machine Learning Digital Twin Models for Laser Powder Bed Fusion Process. - Yangfan Li; Satyajit Mojumder; Ye Lu; Abdullah Al Amin; Jiachen Guo; Xiaoyu Xie; Wei Chen 041; Gregory J. Wagner; Jian Cao; Wing Kam Liu (CoRR, 2023)

JAX-FEM: A differentiable GPU-accelerated 3D finite element solver for automatic inverse design and mechanistic data science. - Tianju Xue; Shuheng Liao; Zhengtao Gan; Chanwook Park; Xiaoyu Xie; Wing Kam Liu; Jian Cao (Comput. Phys. Commun., 2023)

Engineering software 2.0 by interpolating neural networks: unifying training, solving, and calibration. - Chanwook Park; Sourav Saha; Jiachen Guo; Xiaoyu Xie; Satyajit Mojumder; Miguel A. Bessa; Dong Qian; Wei Chen 041; Gregory J. Wagner; Jian Cao; Wing Kam Liu (CoRR, 2024)

Simulation-Free Determination of Microstructure Representative Volume Element Size via Fisher Scores. - Wei Liu; Satyajit Mojumder; Wing Kam Liu; Wei Chen; Daniel W. Apley (CoRR, 2024)

Multi-Patch Isogeometric Convolution Hierarchical Deep-learning Neural Network. - Lei Zhang; Chanwook Park; T. J. R. Hughes; Wing Kam Liu (CoRR, 2024)

Convolutional Hierarchical Deep Learning Neural Networks-Tensor Decomposition (C-HiDeNN-TD): a scalable surrogate modeling approach for large-scale physical systems. - Jiachen Guo; Chanwook Park; Xiaoyu Xie; Zhongsheng Sang; Gregory J. Wagner; Wing Kam Liu (CoRR, 2024)

Interpolation Neural Network-Tensor Decomposition (INN-TD): a scalable and interpretable approach for large-scale physics-based problems. - Jiachen Guo; Xiaoyu Xie; Chanwook Park; Hantao Zhang; Matthew Politis; Gino Domel; Thomas J. R. Hughes; Wing Kam Liu (CoRR, 2025)

Tensor-decomposition-based A Priori Surrogate (TAPS) modeling for ultra large-scale simulations. - Jiachen Guo; Gino Domel; Chanwook Park; Hantao Zhang; Ozgur Can Gumus; Ye Lu; Gregory J. Wagner; Dong Qian; Jian Cao; Thomas J. R. Hughes; Wing Kam Liu (CoRR, 2025)

Explainable Hierarchical Deep Learning Neural Networks (Ex-HiDeNN). - Reza T. Batley; Chanwook Park; Wing Kam Liu; Sourav Saha (CoRR, 2025)