曾昱豪教授(國立高雄大學 應用數學系)

演講時間：112年11月14日下午1點30分
演講地點：A813

講題： A machine learning method for solving Stokes interface problems

摘要：  In this talk, we present a physics-informed neural network called the
Discontinuity-Cusps Capturing Physics-Informed Neural Network for
solving piecewise-constant viscosity Stokes interface problems. The
network consists of two fully connected sub-networks that handle the
pressure and velocity vectors separately. These sub-networks share the
same primary input arguments but have different augmented features: the
Discontinuity-Capturing Shallow Neural Network (DCSNN) uses an indicator
function to capture the discontinuities, while the Cusp-Capturing Neural
Network (CuspNN) employs a cusp-enforced level set function to capture
cusp-like velocity profiles caused by jumps in viscous stresses. The
main objective of this study is to explore the use of the stress balance
formulation directly in the training process for obtaining accurate
predictions, as opposed to the force formulation used in the Immersed
Interface Method (IIM). We perform a series of numerical experiments to
solve two- and three-dimensional Stokes interface problems and
demonstrate the effectiveness and accuracy of the proposed network
model. Our results indicate that even a shallow network with a moderate
number of neurons and sufficient training data points can achieve
prediction accuracy comparable to that of immersed interface methods.