78 citations · 381 across the 20 of their papers we have counts for
20 papers
A Unified Weighted-Loss Physics-Informed Neural Network for Boundary Layer Problems in Singularly Perturbed PDEs
Wei-Fan Hu, Shi-Xiang Zhong, Po-Wen Hsieh +2
Singularly perturbed partial differential equations arise in many applications, including magnetohydrodynamic duct flows, chemical reaction transport systems, and Poisson Boltzmann…
Stabilizing Physics-Informed Consistency Models via Structure-Preserving Training
Che-Chia Chang, Chen-Yang Dai, Te-Sheng Lin +2
We propose a physics-informed consistency modeling framework for solving partial differential equations (PDEs) via fast, few-step generative inference. We identify a key stability…
TINNs: Time-Induced Neural Networks for Solving Time-Dependent PDEs
Chen-Yang Dai, Che-Chia Chang, Te-Sheng Lin +2
Physics-informed neural networks (PINNs) solve time-dependent partial differential equations (PDEs) by learning a mesh-free, differentiable solution that can be evaluated anywhere…
Physics-Informed Machine Learning for Two-Phase Moving-Interface and Stefan Problems
Che-Chia Chang, Te-Sheng Lin, Ming-Chih Lai
The Stefan problem is a classical free-boundary problem that models phase-change processes and poses computational challenges due to its moving interface and nonlinear temperature-…
A categorical embedding discontinuity-capturing shallow neural network for anisotropic elliptic interface problems
Wei-Fan Hu, Te-Sheng Lin, Yu-Hau Tseng +1
In this paper, we propose a categorical embedding discontinuity-capturing shallow neural network for anisotropic elliptic interface problems. The architecture comprises three hidde…
Consistency Training with Physical Constraints
Che-Chia Chang, Chen-Yang Dai, Te-Sheng Lin +2
We propose a physics-aware Consistency Training (CT) method that accelerates sampling in Diffusion Models with physical constraints. Our approach leverages a two-stage strategy: (1…
A hybrid neural-network and MAC scheme for Stokes interface problems
Che-Chia Chang, Chen-Yang Dai, Wei-Fan Hu +2
In this paper, we present a hybrid neural-network and MAC (Marker-And-Cell) scheme for solving Stokes equations with singular forces on an embedded interface in regular domains. As…
A cusp-capturing PINN for elliptic interface problems
Yu-Hau Tseng, Te-Sheng Lin, Wei-Fan Hu +1
In this paper, we propose a cusp-capturing physics-informed neural network (PINN) to solve discontinuous-coefficient elliptic interface problems whose solution is continuous but ha…
An efficient neural-network and finite-difference hybrid method for elliptic interface problems with applications
Wei-Fan Hu, Te-Sheng Lin, Yu-Hau Tseng +1
A new and efficient neural-network and finite-difference hybrid method is developed for solving Poisson equation in a regular domain with jump discontinuities on embedded irregular…
A shallow physics-informed neural network for solving partial differential equations on surfaces
Wei-Fan Hu, Yi-Jun Shih, Te-Sheng Lin +1
In this paper, we introduce a shallow (one-hidden-layer) physics-informed neural network for solving partial differential equations on static and evolving surfaces. For the static…
Motility and Swimming: Universal Description and Generic Trajectories
A. Farutin, M. S. Rizvi, W. F. Hu +3
Autonomous locomotion is a ubiquitous phenomenon in biology and in physics of active systems at microscopic scale. This includes prokaryotic, eukaryotic cells (crawling and swimmin…
A Shallow Ritz Method for Elliptic Problems with Singular Sources
Ming-Chih Lai, Che-Chia Chang, Wei-Syuan Lin +2
In this paper, a shallow Ritz-type neural network for solving elliptic equations with delta function singular sources on an interface is developed. There are three novel features i…
A Discontinuity Capturing Shallow Neural Network for Elliptic Interface Problems
Wei-Fan Hu, Te-Sheng Lin, Ming-Chih Lai
In this paper, a new Discontinuity Capturing Shallow Neural Network (DCSNN) for approximating -dimensional piecewise continuous functions and for solving elliptic interface prob…
Effect of driving on coarsening dynamics in phase-separating systems
D. Tseluiko, M. Alesemi, T. -S. Lin +1
We consider the Cahn-Hilliard (CH) equation with a Burgers-type convective term that is used as a model of coarsening dynamics in laterally driven phase-separating systems. In the…
Two-dimensional pulse dynamics and the formation of bound states on electrified falling films
M. G. Blyth, D. Tseluiko, T. -S. Lin +1
The flow of an electrified liquid film down an inclined plane wall is investigated with the focus on coherent structures in the form of travelling waves on the film surface, in par…
Bifurcation analysis of the behavior of partially wetting liquids on a rotating cylinder
Te-Sheng Lin, Steven Rogers, Dmitri Tseluiko +1
We discuss the behavior of partially wetting liquids on a rotating cylinder using a model that takes into account the effects of gravity, viscosity, rotation, surface tension and w…
Instabilities of layers of deposited molecules on chemically stripe patterned substrates: Ridges vs. drops
Christoph Honisch, Te-Sheng Lin, Andreas Heuer +2
A mesoscopic continuum model is employed to analyse the transport mechanisms and structure formation during the redistribution stage of deposition experiments where organic molecul…
Modelling spreading dynamics of liquid crystals in three spatial dimensions
Te-Sheng Lin, Lou Kondic, Uwe Thiele +1
We study spreading dynamics of nematic liquid crystal droplets within the framework of the long-wave approximation. A fourth order nonlinear parabolic partial differential equation…
Note on the hydrodynamic description of thin nematic films: strong anchoring model
Te-Sheng Lin, Linda J. Cummings, Andrew J. Archer +2
We discuss the long-wave hydrodynamic model for a thin film of nematic liquid crystal in the limit of strong anchoring at the free surface and at the substrate. We rigorously clari…
Thin films flowing down inverted substrates: two dimensional flow
Te-sheng Lin, Lou Kondic
We consider free surface instabilities of films flowing on inverted substrates within the framework of lubrication approximation. We allow for the presence of fronts and related co…