| Publication | Date of Publication | Type |
|---|
| HomPINNs: homotopy physics-informed neural networks for solving the inverse problems of nonlinear differential equations with multiple solutions | 2024-02-29 | Paper |
| A numerical method for solving elliptic equations on real closed algebraic curves and surfaces | 2023-11-16 | Paper |
| Companion-Based Multi-Level Finite Element Method for Computing Multiple Solutions of Nonlinear Differential Equations | 2023-05-06 | Paper |
| Greedy training algorithms for neural networks and applications to PDEs | 2023-04-26 | Paper |
| Deep Learning via Neural Energy Descent | 2023-02-20 | Paper |
| Bifurcation analysis of a free boundary model of vascular tumor growth with a necrotic core and chemotaxis | 2023-01-23 | Paper |
| Two neural-network-based methods for solving elliptic obstacle problems | 2023-01-12 | Paper |
| A cancer model with nonlocal free boundary dynamics | 2022-10-21 | Paper |
| Bifurcation Analysis Reveals Solution Structures of Phase Field Models | 2022-10-12 | Paper |
| HomPINNs: Homotopy physics-informed neural networks for learning multiple solutions of nonlinear elliptic differential equations | 2022-09-16 | Paper |
| Randomized Newton's method for solving differential equations based on the neural network discretization | 2022-08-04 | Paper |
| Predict Blood Pressure by Photoplethysmogram with the Fluid-Structure Interaction Modeling | 2022-05-19 | Paper |
| A Continuous Finite Element Method with Homotopy Vanishing Viscosity for Solving the Static Eikonal Equation | 2022-05-19 | Paper |
| Nonlinear simulation of vascular tumor growth with chemotaxis and the control of necrosis | 2022-05-11 | Paper |
| Multiscale and monolithic arbitrary Lagrangian-Eulerian finite element method for a hemodynamic fluid-structure interaction problem involving aneurysms | 2022-04-01 | Paper |
| An adaptive homotopy tracking algorithm for solving nonlinear parametric systems with applications in nonlinear ODEs | 2021-12-13 | Paper |
| A weight initialization based on the linear product structure for neural networks | 2021-11-16 | Paper |
| Two neural-network-based methods for solving obstacle problems | 2021-11-02 | Paper |
| A homotopy training algorithm for fully connected neural networks | 2021-10-29 | Paper |
| Mathematical model of atherosclerotic aneurysm | 2021-09-09 | Paper |
| A Weight Initialization Based on the Linear Product Structure for Neural Networks | 2021-08-31 | Paper |
| Nonlinear simulation of vascular tumor growth with chemotaxis and the control of necrosis | 2021-07-24 | Paper |
| Greedy Training Algorithms for Neural Networks and Applications to PDEs | 2021-07-09 | Paper |
| A stochastic homotopy tracking algorithm for parametric systems of nonlinear equations | 2021-06-15 | Paper |
| Convergence analysis of neural networks for solving a free boundary problem | 2021-05-27 | Paper |
| Ecological and evolutionary dynamics in advective environments: critical domain size and boundary conditions | 2021-05-20 | Paper |
| Power Series Expansion Neural Network | 2021-02-25 | Paper |
| Projection based model reduction for the immersed boundary method | 2021-01-28 | Paper |
| Bifurcation analysis of a free boundary model of the atherosclerotic plaque formation associated with the cholesterol ratio | 2020-12-10 | Paper |
| A gradient descent method for solving a system of nonlinear equations | 2020-12-03 | Paper |
| Convergence analysis of neural networks for solving a free boundary system | 2020-10-31 | Paper |
| Singular solutions, repeated roots and completeness for higher-spin chains | 2020-08-11 | Paper |
| An adaptive homotopy method for computing bifurcations of nonlinear parametric systems | 2020-02-26 | Paper |
| Spatial pattern formation in reaction-diffusion models: a computational approach | 2020-02-18 | Paper |
| A homotopy method with adaptive basis selection for computing multiple solutions of differential equations | 2020-01-31 | Paper |
| Convergence of a homotopy finite element method for computing steady states of Burgers’ equation | 2019-11-22 | Paper |
| Concentration phenomena in an integro-PDE model for evolution of conditional dispersal | 2019-10-18 | Paper |
| Computational causal modeling of the dynamic biomarker cascade in Alzheimer's disease | 2019-05-14 | Paper |
| Mathematical model of chronic pancreatitis | 2019-01-11 | Paper |
| An equation-by-equation method for solving the multidimensional moment constrained maximum entropy problem | 2018-10-10 | Paper |
| Two-Level Spectral Methods for Nonlinear Elliptic Equations with Multiple Solutions | 2018-08-24 | Paper |
| Algorithm 976 | 2018-08-17 | Paper |
| The role of exosomes in pancreatic cancer microenvironment | 2018-07-05 | Paper |
| A homotopy method for parameter estimation of nonlinear differential equations with multiple optima | 2018-04-13 | Paper |
| Convergence of boundary integral method for a free boundary system | 2018-01-12 | Paper |
| Vibrations of thin plates with small clamped patches | 2017-09-29 | Paper |
| Dimorphism by singularity theory in a model for river ecology | 2017-06-27 | Paper |
| Mathematical model of renal interstitial fibrosis | 2017-02-16 | Paper |
| Mathematical model of sarcoidosis | 2017-02-16 | Paper |
| A fictitious domain method with a hybrid cell model for simulating motion of cells in fluid flow | 2016-12-05 | Paper |
| A homotopy method based on WENO schemes for solving steady state problems of hyperbolic conservation laws | 2016-11-15 | Paper |
| Mathematical modeling of liver fibrosis | 2016-11-02 | Paper |
| A mathematical model of pre-diagnostic glioma growth | 2016-08-18 | Paper |
| Counting solutions of the Bethe equations of the quantum group invariant open XXZ chain at roots of unity | 2016-01-15 | Paper |
| A mathematical model of atherosclerosis with reverse cholesterol transport and associated risk factors | 2015-08-03 | Paper |
| A free boundary problem for steady small plaques in the artery and their stability | 2015-05-18 | Paper |
| Efficient sampling methods for global reliability sensitivity analysis | 2014-12-17 | Paper |
| A new interpretation and validation of variance based importance measures for models with correlated inputs | 2014-12-17 | Paper |
| Algorithm 931 | 2014-09-12 | Paper |
| Bertini_real: Software for One- and Two-Dimensional Real Algebraic Sets | 2014-09-08 | Paper |
| A bootstrapping approach for computing multiple solutions of differential equations | 2014-07-16 | Paper |
| Moving least squares based sensitivity analysis for models with dependent variables | 2013-11-12 | Paper |
| Domain decomposition schemes with high-order accuracy and unconditional stability | 2013-10-10 | Paper |
| Cell cycle control and bifurcation for a free boundary problem modeling tissue growth | 2013-09-09 | Paper |
| On the completeness of solutions of Bethe's equations | 2013-08-21 | Paper |
| Continuation along bifurcation branches for a tumor model with a necrotic core | 2013-08-13 | Paper |
| Computing steady-state solutions for a free boundary problem modeling tumor growth by Stokes equation | 2012-10-22 | Paper |
| A three-dimensional steady-state tumor system | 2012-06-08 | Paper |
| Bifurcation for a free boundary problem modeling the growth of a tumor with a necrotic core | 2012-05-20 | Paper |
| Multiple stable steady states of a reaction-diffusion model on zebrafish dorsal-ventral patterning | 2011-06-10 | Paper |
| Parallel iterative methods for parabolic equations | 2009-03-20 | Paper |
| An algorithmic approach to finding factorial designs with generalized minimum aberration | 2009-01-30 | Paper |
