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Mathematical Sciences/CAMS Mini-Workshop on Applied Mathematics

This is a past event.

Thursday, June 29, 2023, 2:30 pm– 5 pm

This is a past event.

Please join us on Thursday June 29th From 2:30 to 5:00 pm as the Department of Mathematical Sciences and the Center for Applied Mathematics and Statistics (CAMS) host a mini-workshop on Applied Mathematics.


Our esteemed guests will be Dr. Guang Lin of Purdue University, Dr. Kui Ren of Columbia University and Dr. Junshan Lin of Auburn Universty.  Each speaker brings their expertice and knowledge about the following topics of interest:


Dr. Guang Lin - "Towards Third Wave AI:  Interpretable, Robust Trustowrthy Machine Learning for Diverse Applications in Science and Engineering".  This talk aims to close the gap by developing new theories and scalable numerical algorithms for complex dynamical systems that can be realistically predicted and validated.  Dr. Lin is creating new technologies that can be translated into more secure and reliable new trustworthy AI systems that can be deployed for real-time complex dynamical system prediction, surveillance, and defense applications to improve the stability and efficiency of complex dynamical systems and national security of the United States. We will present a novel neural homogenization-based physics-informed neural network (NN) for multiscale problems. He will also introduce new NNs that learn functionals and nonlinear operators from functions with simultaneous uncertainty estimates. In particular, he presents a probabilistic neural operator network training procedure for solving partial differential equations with inhomogeneous boundary conditions. Using a light-weight extension of deep operator network (DeepONet) architecture, the trained networks are designed to provide rapid predictions along with simultaneous uncertainty estimates to help identify potential inaccuracies in the network predictions. ), DeepONet consists of a NN for encoding the discrete input function space (branch net) and another NN for encoding the domain of the output functions (trunk net). In particular, the predictive uncertainty of the network is calibrated to anticipate network errors by implementing a loss function that interprets the network prediction as a probability distribution as opposed to a single-point estimate. The proposed technique is also capable of solving problems on irregular, non-rectangular domains, and a series of experiments are presented to evaluate the network accuracy as well as the quality of the predictive uncertainty estimates. This will demonstrate that the novel probabilistic DeepONet can learn various explicit operators with predictive uncertainties.


Dr. Kui Ren - "Inverse Problems to a System of Semilinear Helmholtz Equations".  He and his research group studid an inverse problem for a coupled system of semilinear Helmholtz equations where we are interested in reconstructing multiple coefficients of the system from internal data measured in applications such as thermoacoustic imaging.  He derived results on the uniqueness and stability of the inverse problem in the case of small boundary data, based on the technique of first- and higher-order linearization. Numerical simulations are provided to illustrate the quality of reconstructions that can be expected from noisy data. This is based on a joint work with Nathan Soedjak.


Dr. Junshan Lin - "Several Spectral Problems in Topological Wave Insulators".   In this talk, Dr. Lin will introduce several spectral problems for differential operators arising from topological wave insulators, which were inspired by the success of topological insulators in condensed matter physics and developed for classical waves (including acoustics, photonics,mechanics) in recent years. He will give the theory and computation for these problems based on recent and ongoing work.


Please contact the Department of Mathematical Sciences for more information. 

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  • Vimalesh Raja Karupiah Ramachandran
  • Gregory Jeffers

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