Special Seminar Department of Applied Mathematics by Guang Lin: Towards Third Wave AI: Interpretable, Robust Trustworthy Machine Learning for Diverse Applications in Science and Engineering

Title:

Towards Third Wave AI: Interpretable, Robust Trustworthy Machine Learning for Diverse Applications in Science and Engineering

Speaker:

Guang Lin, Professor Departments of Mathematics, Statistics and School of Mechanical Engineering, Purdue University

Abstract:

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. We are 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. We will also introduce new NNs that learn functionals and nonlinear operators from functions with simultaneous uncertainty estimates. In particular, we present 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. We demonstrate that the novel probabilistic DeepONet can learn various explicit operators with predictive uncertainties.

Speaker bio:

Guang Lin is a Full Professor in the School of Mechanical Engineering and Department of Mathematics at Purdue University. Prof. Guang Lin is the Director of Data Science Consulting Service that performs cutting-edge research on data science and provides hands-on consulting support for data analysis and business analytics in all areas to overcome data science challenges arising in research, education, and business and organization management. Prof. Lin is currently also Co-Chair of Purdue Engineering Initiative in Data Engineering and Application. His research interests include diverse topics in computational and data science both on algorithms and applications. His main current thrust is machine learning, data-driven modeling, stochastic simulation, and multiscale modeling of interconnected, physical, and biological systems. Prof. Lin has received various awards, such as the NSF CAREER Award, Mid-Career Sigma Xi Award, University Faculty Scholar, Mathematical Biosciences Institute Early Career Award, and Ronald L. Brodzinski Award for Early Career Exception Achievement.

Note: Face coverings will be required. Even if you are fully vaccinated, all students, staff, faculty, and guests must wear a face covering indoors. The university will review and revise the mask protocol as appropriate given changes to state and city public-health guidelines.

 

Computational Mathematics and Statistical Seminar

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