During Oct. 2-4 2017, Professor Leslie Greengard, an eminent mathematician, physicist and computer scientist, visited CCMA and gave three lectures as the CCMA Distinguished Lecture Series. He brought to multiple audiences at Penn State University a new appreciation of the power of fast algorithms and their applications in interdisciplinary researches.
Professor Greengard is best known as co-inventor of the fast multipole method (FMM) in 1987, recognized as one of the top-ten algorithms of the 20th century. He is a member of the National Academy of Sciences and the National Academy of Engineering, and currently the (founding) director of the Center for Computational Biology. Prior to that, Professor Greengard served as director of the Courant Institute of Mathematical Sciences at New York University, where he has been a member of the faculty since 1989. Greengard holds an M.D. and Ph.D. in computer science from Yale University.
During his visit to CCMA, Professor Greengard discussed the applications of fast algorithms to a variety of physical problems in his three lectures. The first lecture provided an overview of recent progress on fast integral equation approaches to electromagnetics, acoustics, gravitation, elasticity, and fluid dynamics. The second lecture gave new representations for electromagnetic fields that leads to well-conditioned integral equations for the problem of scattering from perfect conductors or dielectrics. The third lecture focused on the application of recursive linearization combined with suitable fast solver on acoustic scattering and cryo-electron microscopy.
On Oct. 3, a mini-workshop was held to interact with Professor Greengard. During the workshop, Penn State professors and researchers presented some of the latest results from their researches. Professor Xiantao Li gave a talk titled From DtN map to data-driven stochastic parameterization. His talk presented reduction techniques for high-dimensional problems. The main tool is a Dirichlet-to-Neumann map that enables domain reduction, temporal reduction as well as a statistical reduction for highly correlated noise.
Professor Wenrui Hao presented his work on Mathematical modeling for cardiovascular disease. In this talk, he introduced a mathematical model of the formation of a plaque inside the arteries, which causes atherosclerosis.The model was given by a system of partial differential equations with in evolving plaque. Simulations of the model showed how the combination of the concentrations of LDL and HDL in the blood determine whether a plaque would grow or disappear.
Dr. Shuonan Wu’s talk was On the stability and accuracy of partially and fully implicit schemes for multiphase modeling. In the talk, he demonstrated that, for robust and accurate simulations using phase-field models, it is necessary to use fully implicit schemes with energy minimization. He theoretically showed that for the Allen-Cahn model the standard convex splitting scheme (CSS) is exactly the same as the standard fully implicit scheme (FIS) but with a much smaller time step size. As a result, it would provide an approximation to the original solution of the Allen-Cahn model at a delayed time (although the magnitude of the delay is reduced when the time step size is reduced).
Dr. Arthur Bousquet presented his research on Stochastic Descent Algorithms. His talk presented various stochastic refinements to optimization algorithms, such as simulated annealing, and their application to computing Allen-Cahn dynamics and solving neural nets in deep learning.
Dr. Qingguo Hong presented A unified framework for the continuous and discontinuous Galerkin Methods. A unified study is presented in the talk for the design andanalysis of different finite element methods (FEMs). Both hybrid discontinuous Galerkni and weak Galerkin are
shown to admit inf-sup conditions that hold uniformly with respect to both mesh and penalization parameters. In addition, by taking the limit of the stabilization parameters, a weak Galerkin method is shown to converge to a mixed method whereas an hybrid discontinuous Galerkin method is shown to converge to a primal method.
Dr. Hongxuan Zhang presented his work with Professor Xu’s group on Predicting Alzheimer’s Disease from an MRI scan using Deep Learning. A model was presented consisting of a 3D convolutional neural network (CNN) to extract features from 3D MRI images, and a fully-connected neural network to classify whether the MRI scans belong to Alzheimer’s disease, mild cognitive impairment (MCI) or normal. To improve the training efficiency, a convolutional autoencoder (CAE) was used to pre-train the kernels in each convolutional layer. The model achieved satisfactory predictions for both binary classification (AD vs normal) and trinary classification (AD vs MCI vs normal).
Undergraduates, graduates, and other professors were involved in these activities.
The CCMA Distinguished Lecture Series are aimed at broadening the educational and research experiences of Penn State students and research community by bringing distinguished researchers to campus to give a sequence of lectures on forefront research topics in theoretical computational and applied mathematics.