My research integrates mathematical modeling, scientific computing, and data-driven methods to study complex biological and multiphysics systems. The publications below are organized around five interconnected research directions:
Thermodynamic modeling, interfacial dynamics, and structure-preserving computation
Neurovascular, ocular, and physiological transport
Scientific machine learning and biomedical data science
Soft matter, cell mechanics, and computational biophysics
Homogenization, mathematical analysis, and multiscale methods
Corresponding author † First author
My work develops thermodynamically consistent mathematical models and structure-preserving numerical methods for ionic transport, semi-permeable and reactive interfaces, electrohydrodynamics, active membrane transport, and complex fluids.
Selected publications:
• Energy Variational Approach for Ions Transport.
Communications in Mathematical Sciences, 12(4), 779–789, 2014.
• A Phase Field Model for Mass Transport with Semi-Permeable Interfaces.
Journal of Computational Physics, 464, 111334, 2022.
• Thermodynamically Consistent Modeling and Energy-Stable LDG Schemes for Semi-Permeable Interface Flows.
Journal of Computational Physics, 562, 115036, 2026.
• Thermodynamically Consistent Modeling and Stable ALE Approximations of Reactive Semi-Permeable Interfaces.
Computer Methods in Applied Mechanics and Engineering, 448, 118512, 2026.
I develop multidomain physiological models that integrate fluid flow, electrodiffusion, oxygen transport, osmotic water transport, and cellular regulation. Applications include optic-nerve microcirculation, potassium clearance, glymphatic transport, lens homeostasis, and neurovascular dysfunction.
Selected publications:
• Tridomain Model for Potassium Clearance in Optic Nerve of Necturus.
Biophysical Journal, 120(15), 3008–3027, 2021.
• Optic Nerve Microcirculation: Fluid Flow and Electrodiffusion.
Physics of Fluids, 33, 041906, 2021.
• A Multidomain Model for Microcirculation in Optic Nerve: Blood Flow and Oxygen Transport.
Physica D: Nonlinear Phenomena, 134272, 2024.
• Glymphatic Clearance in the Optic Nerve: A Multidomain Electro-Osmotic Model.
Entropy, 27(11), 1174, 2025.
My research develops robust, interpretable, and mechanism-informed learning methods for imbalanced scientific data, physics-informed neural networks, biomedical signal reconstruction, retinal-image analysis, clinical risk assessment, and parameter inference.
Selected publications:
• NCART: Neural Classification and Regression Tree for Tabular Data.
Pattern Recognition, 110578, 2024.
• VSG-GAN: A High-Fidelity Image Synthesis Method with Semantic Manipulation in Retinal Fundus Images.
Biophysical Journal, 123(17), 2815–2829, 2024.
• An Imbalanced Learning-Based Sampling Method for Physics-Informed Neural Networks.
Journal of Computational Physics, 534, 114010, 2025.
• CLEP-GAN: An Innovative Approach to Subject-Independent ECG Reconstruction from PPG Signals.
BMC Bioinformatics, 26, 306, 2025.
I combine continuum mechanics, mesoscale modeling, and biological mechanisms to investigate blood-clot mechanics, cell aggregation, lipid membranes, polymeric fluids, and cellular morphogenesis.
Selected publications:
• Deformation, Embolization, and Permeability of Partially Obstructive Blood Clots under Shear Flow.
Journal of the Royal Society Interface, 14, 20170441, 2017.
• Diffuse Interface Model for Cell Interaction and Aggregation with Lennard-Jones-Type Potential.
Computer Methods in Applied Mechanics and Engineering, 415, 116257, 2023.
• Study of Impacts of Two Types of Cellular Aging on Yeast Bud Morphogenesis.
PLOS Computational Biology, 20(9), e1012491, 2024.
• Micro-Macro Modeling of Polymeric Fluids and Shear-Induced Microscopic Behaviors with Bond-Breaking.
Physical Review Fluids, 9, 103301, 2024.
• Thermodynamically Consistent Modeling and Energy-Stable LDG Schemes for Semi-Permeable Interface Flows.
Ruihan Guo, Jie Shen, Shixin Xu*, and Xianmin Xu. Journal of Computational Physics, 562, 115036, 2026.
• Thermodynamically Consistent Phase-Field Modeling for Mass Transport with Interfacial Reaction.
Zhaoyang Wang, Huaxiong Huang, Ping Lin, and Shixin Xu. Physics of Fluids, 38(7), 2026.
• Active Interfacial Ion Transport Modulates Droplet Electrohydrodynamics: Deformation, Pinch-Off, and Recoalescence.
Yuzhe Qin, Huaxiong Huang, Zilong Song, and Shixin Xu*. Physical Review Fluids, 11, 053702, 2026.
• Thermodynamically Consistent Modeling and Stable ALE Approximations of Reactive Semi-Permeable Interfaces.
Weidong Shi, Shixin Xu*, Zhen Zhang, and Quan Zhao. Computer Methods in Applied Mechanics and Engineering, 448, 118512, 2026.
• Coupled Chemical Reactions: Effects of Electric Field, Diffusion, and Boundary Control.
Shixin Xu, Robert Eisenberg, Zilong Song, and Huaxiong Huang. Physical Review E, 108, 064413, 2023.
• Mathematical Model for Chemical Reactions in Electrolytes Applied to Cytochrome c Oxidase: An Electro-Osmotic Approach.
Shixin Xu†, Robert Eisenberg, Zilong Song, and Huaxiong Huang. Computation, 11(12), 253, 2023.
• Droplet Dynamics: A Phase-Field Model of Mobile Charges, Polarization, and Its Leaky-Dielectric Approximation.
Yuzhe Qin, Huaxiong Huang, Zilong Song, and Shixin Xu*. Physics of Fluids, 35, 2023.
• A Level-Set Method for the Simulation of Moving Contact Lines in Three Dimensions.
Shixin Xu and Quan Zhao. Communications in Computational Physics, 32(5), 2022.
• A Phase Field Model for Mass Transport with Semi-Permeable Interfaces.
Yuzhe Qin, Huaxiong Huang, Yi Zhu, Chun Liu, and Shixin Xu*. Journal of Computational Physics, 464, 111334, 2022.
• A Phase Field Model for Compressible Immiscible Fluids with a New Equation of State.
Hao Dai, Zhiliang Xu, Ning Zhao, Chengxiang Zhu, Chunling Zhu, and Shixin Xu. International Journal of Multiphase Flow, 149, 103937, 2022.
• An Energy-Stable Finite Element Scheme for a Phase-Field Model of Vesicle Motion and Deformation.
Lingyue Shen, Zhiliang Xu, Ping Lin, Huaxiong Huang, and Shixin Xu*. SIAM Journal on Scientific Computing, 44(1), B122–B145, 2022.
• An Energy-Stable C⁰ Finite Element Scheme for a Quasi-Incompressible Phase-Field Model of Moving Contact Lines with Variable Density.
Lingyue Shen, Huaxiong Huang, Ping Lin, Zilong Song, and Shixin Xu*. Journal of Computational Physics, 405, 109179, 2020.
• Non-Stokes Drag Coefficient in Single-Particle Electrophoresis: New Insights on a Classical Problem.
Maijia Liao, Ming-Tzo Wei, H. Daniel Ou-Yang, Ping Sheng, and Shixin Xu. Chinese Physics B, 28(8), 084701, 2019.
• Reinitialization of the Level-Set Function in Three-Dimensional Simulations of Moving Contact Lines.
Shixin Xu† and Weiqing Ren. Communications in Computational Physics, 20(5), 1163–1182, 2016.
• The Poisson–Boltzmann Equation and the Charge-Separation Phenomenon at the Silica–Water Interface: A Holistic Approach.
Maijia Liao, Li Wan, Chun Liu, Ping Sheng, and Shixin Xu. Annals of Mathematical Sciences and Applications, 1, 217–249, 2016.
• Derivation of a Continuum Model and the Energy Law for Moving Contact Lines with Insoluble Surfactants.
Zhen Zhang, Shixin Xu, and Weiqing Ren. Physics of Fluids, 26, 062103, 2014.
• Numerical Simulations of Asymmetrical Conductance Changes in Gramicidin Pores.
Shixin Xu†, Minxin Chen, Sheereen Maja, Xingye Yue, and Chun Liu. Molecular Based Mathematical Biology, 2(1), 2014.
• Self-Consistent Approach to Global Charge Neutrality in Electrokinetics: A Surface-Potential-Trap Model.
Shixin Xu†, Li Wan, Maijia Liao, Chun Liu, and Ping Sheng. Physical Review X, 4, 011042, 2014.
• Energy Variational Approach for Ions Transport.
Shixin Xu†, Chun Liu, and Ping Sheng. Communications in Mathematical Sciences, 12(4), 779–789, 2014.
• Glymphatic Clearance in the Optic Nerve: A Multidomain Electro-Osmotic Model.
Shanfeng Xiao, Huaxiong Huang, Robert Eisenberg, Zilong Song, and Shixin Xu*. Entropy, 27(11), 1174, 2025.
• Potassium Clearance in Optic Nerve: A Multidomain Model.
Shanfeng Xiao, Huaxiong Huang, Robert Eisenberg, Zilong Song, and Shixin Xu*. Frontiers in Bioscience–Landmark, 30, 2025.
• A Multidomain Model for Microcirculation in Optic Nerve: Blood Flow and Oxygen Transport.
Shixin Xu, Zilong Song, Robert Eisenberg, and Huaxiong Huang. Physica D: Nonlinear Phenomena, 134272, 2024.
• Tridomain Model for Potassium Clearance in Optic Nerve of Necturus.
Yi Zhu, Shixin Xu*, Robert S. Eisenberg, and Huaxiong Huang. Biophysical Journal, 120(15), 3008–3027, 2021.
• Optic Nerve Microcirculation: Fluid Flow and Electrodiffusion.
Yi Zhu, Robert Eisenberg, Huaxiong Huang, and Shixin Xu*. Physics of Fluids, 33, 041906, 2021.
• Modelling the Linkage between Influenza Infection and Cardiovascular Events via Thrombosis.
Z. McCarthy, A. Rahman, Shixin Xu, and collaborators. Scientific Reports, 10, 14264, 2020.
• A Mathematical Model for Persistent Post-Cortical-Spreading-Depression Vasoconstriction.
Shixin Xu†, Joshua C. Chang, Carson C. Chow, K. C. Brennan, and Huaxiong Huang. PLOS Computational Biology, 16(7), e1007996, 2020.
• A Bidomain Model of Lens Microcirculation.
Yi Zhu, Robert Eisenberg, Huaxiong Huang, and Shixin Xu*. Biophysical Journal, 116(6), 1171–1184, 2019.
2026
Mixing Configurations for Downstream Prediction, Juntang Wang, Hao Wu, Yihan Wang, Dongmian Zou, Shixin Xu*, Proceedings of the 43 rd International Conference on Machine Learning, Seoul, South Korea. PMLR 306, 2026.
StageGuard: Physiologically Constrained Sleep Staging, Juntang Wang, Yihan Wang, Hao Wu, Shixin Xu, Dongmian Zou, Proceedings of the 32nd ACM SIGKDD Conference on Knowledge Discovery and Data Mining V.2 (KDD '26), August 09--13, 2026.
• Robust-GBDT: Leveraging Robust Loss for Noisy and Imbalanced Classification with Gradient-Boosted Decision Trees.
Jiaqi Luo, Yuedong Quan, and Shixin Xu*. Knowledge and Information Systems, 2025.
• Improving GBDT Performance on Imbalanced Datasets: An Empirical Study of Class-Balanced Loss Functions.
Jiaqi Luo, Yuan Yuan, and Shixin Xu*. Neurocomputing, 634, 2025.
• An Imbalanced Learning-Based Sampling Method for Physics-Informed Neural Networks.
Jiaqi Luo, Yahong Yang, Yuan Yuan, Shixin Xu*, and Wenrui Hao. Journal of Computational Physics, 534, 114010, 2025.
• CLEP-GAN: An Innovative Approach to Subject-Independent ECG Reconstruction from PPG Signals.
Xiaoyan Li, Shixin Xu, Faisal Habib, Neda Aminnejad, Arvind Gupta, and Huaxiong Huang. BMC Bioinformatics, 26, 306, 2025.
• NCART: Neural Classification and Regression Tree for Tabular Data.
Jiaqi Luo and Shixin Xu*. Pattern Recognition, 110578, 2024.
• VSG-GAN: A High-Fidelity Image Synthesis Method with Semantic Manipulation in Retinal Fundus Images.
Junjie Liu, Ping He, Sirong Wu, Xi Luo, Yuhui Deng, Shixin Xu, and Huaxiong Huang. Biophysical Journal, 123(17), 2815–2829, 2024.
• Assessing the Nonlinear Association of Environmental Factors with Antibiotic-Resistance Genes in the Yangtze River Estuary, China.
Jiazheng Miao, Yikai Ling, Xiaoyuan Chen, Siyuan Wu, Sajid Umar, Benjamin D. Anderson, and Shixin Xu. Scientific Reports, 13, 20367, 2023.
• TRBoost: A Generic Gradient-Boosting Machine Based on the Trust-Region Method.
Jiaqi Luo, Zihao Wei, Junkai Man, and Shixin Xu*. Applied Intelligence, 2023.
• Multi-Objective Learning and Explanation for Stroke-Risk Assessment in Shanxi Province.
Jing Ma, Yiyang Sun, Junjie Liu, Huaxiong Huang, Xiaoshuang Zhou, and Shixin Xu*. Scientific Reports, 12, 22337, 2022.
• Analysis of Clinical Predictors of Kidney Disease in Patients with Type 2 Diabetes Based on Machine Learning.
Dongna Hui, Yiyang Sun, Shixin Xu, and collaborators. International Urology and Nephrology, 2022.
• Neural-PDE: A Recurrent-Neural-Network-Based Method for Solving Time-Dependent Partial Differential Equations.
Yihao Hu, Tong Zhao, Lizhen Lin, Zhiliang Xu, and Shixin Xu. Communications in Information and Systems, 22(2), 223–245, 2022.
• Analysis of the Main Risk Factors for Stroke in Shanxi Province Based on Machine-Learning Models.
Junjie Liu, Yiyang Sun, Jing Ma, Jiachen Tu, Yuhui Deng, Ping He, Rongshan Li, Fengyun Hu, Huaxiong Huang, Xiaoshuang Zhou, and Shixin Xu*. Informatics in Medicine Unlocked, 26, 100712, 2021.
• Numerical Method for Parameter Inference of Nonlinear Ordinary Differential Equations with Partial Observation.
Yu Chen, Jin Cheng, Arvind Gupta, Huaxiong Huang, and Shixin Xu*. Royal Society Open Science, 8, 210171, 2021.
• Predicting the Risk of Rupture for Vertebral Aneurysms Based on Geometric Features of Blood Vessels.
Shixuan Li, Ruiqi Pan, Arvind Gupta, Yibin Fang, Huaxiong Huang, and Shixin Xu*. Royal Society Open Science, 8, 210392, 2021.
• Vertebral-Artery Fusiform-Aneurysm Geometry in Predicting Rupture Risk.
Xiukun Zhao, Nathan Gold, Yibin Fang, Yongxin Zhang, Jianmin Liu, Arvind Gupta, Huaxiong Huang, and Shixin Xu*. Royal Society Open Science, 5, 180780, 2018.
• Characterization of Phospholipid–Cholesterol Bilayers as Self-Assembled Amphiphile Block Polymers Containing Headgroups.
Xiaoyuan Wang, Fred S. Cohen, Shixin Xu*, and Yongqiang Cai. Physica A, 688, 131430.
• Micro-Macro Modeling of Polymeric Fluids and Shear-Induced Microscopic Behaviors with Bond-Breaking.
Xuelian Bao, Huaxiong Huang, Zilong Song, and Shixin Xu*. Physical Review Fluids, 9, 103301, 2024.
• Study of Impacts of Two Types of Cellular Aging on Yeast Bud Morphogenesis.
Kevin Tsai, Zhen Zhou, Jiadong Yang, Zhiliang Xu, Roya Zandi, Nan Hao, Weitao Chen, Mark Alber, and Shixin Xu. PLOS Computational Biology, 20(9), e1012491, 2024.
• Mimicking the Effects of Cholesterol in Lipid-Bilayer Membranes Using Self-Assembled Amphiphilic Block Copolymers.
Xiaoyuan Wang, Fredric S. Cohen, Jiwei Zhang, Yongqiang Cai, and Shixin Xu. Soft Matter, 2023.
• Diffuse Interface Model for Cell Interaction and Aggregation with Lennard-Jones-Type Potential.
Lingyue Shen, Ping Lin, Zhiliang Xu, and Shixin Xu*. Computer Methods in Applied Mechanics and Engineering, 415, 116257, 2023.
• Three-Phase Model of Viscoelastic Incompressible Fluid Flow and Its Computational Implementation.
Shixin Xu†, Mark Alber, and Zhiliang Xu. Communications in Computational Physics, 25(2), 586–624, 2019.
• Deformation, Embolization, and Permeability of Partially Obstructive Blood Clots under Shear Flow.
Shixin Xu†, Zhiliang Xu, Oleg Kim, Rustem I. Litvinov, John W. Weisel, and Mark Alber. Journal of the Royal Society Interface, 14, 20170441, 2017.
• Strong Binding of Platelet Integrin αIIbβ3 to Fibrin Clots: A Potential Target for Destabilizing Thrombi.
Peter Hook, Rustem I. Litvinov, Oleg Kim, Zhiliang Xu, Joel S. Bennett, Mark Alber, John W. Weisel, and Shixin Xu. Scientific Reports, 7, 2017.
• Homogenization Theory of Ion Transport in Multicellular Tissue.
Chun Xiao, Huaxiong Huang, Tao Yu, Xingye Yue, and Shixin Xu*. Discrete and Continuous Dynamical Systems–B, 28(11), 5701–5728, 2023.
• Homogenization of a Discrete-Network Model for the Chemical-Vapor-Infiltration Process.
Chun Xiao, Xingye Yue, Changjuan Zhang, Changrong Zhang, and Shixin Xu. Communications in Mathematical Sciences, 19(7), 1809–1826, 2021.
• Numerical Method for the Multi-Allele Genetic-Drift Problem.
Shixin Xu†, Xinfu Chen, Chun Liu, and Xingye Yue. SIAM Journal on Numerical Analysis, 57(4), 1770–1788, 2019.
• Behavior of Different Numerical Schemes for Population Genetic-Drift Problems.
Shixin Xu†, Minxin Chen, Chun Liu, Xingye Yue, and Ran Zhang. BIT Numerical Mathematics, 59(3), 797–821, 2019.
• Homogenization Theory for the Chemical-Vapor-Infiltration Process.
Changjuan Zhang, Yun Bai, Xingye Yue, and Shixin Xu. Communications in Mathematical Sciences, 15(4), 1021–1040, 2017.
• Homogenization: In Mathematics or Physics?
Shixin Xu† and Xingye Yue. Discrete and Continuous Dynamical Systems–S, 9(5), 1575–1590, 2016.
• Homogenization of Thermal–Hydro–Mass Transfer Processes.
Shixin Xu† and Xingye Yue. Discrete and Continuous Dynamical Systems–S, 8(1), 55–76, 2015.
• Multi-Scale Models of Deformation of Blood Clots.
Shixin Xu, Mark Alber, Zhiliang Xu, Oleg Kim, S. Britton, Rustem I. Litvinov, and John W. Weisel. Biophysical Journal, 116(3), 323a, 2019.