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Short Courses

Sunday, July 14, 2:00pm-5:00pm, Fee $25 each

Instructor: Jian-Xun Wang, Assistant Professor, University of Notre Dame, US

Course Description: While traditional methods of modeling and simulation using PDEs and numerical discretization have achieved considerable success, they face significant challenges in areas such as inverse problems, uncertainty quantification, and design optimization. These challenges are particularly pronounced in systems where the governing physics are not fully understood, complicating the development of first-principle numerical solvers. Recent advancements in data science and machine learning, coupled with the increasing availability of data, are paving the way for innovative data-enabled computational models. Despite the potential of state-of-the-art machine/deep learning techniques, they confront hurdles like dependency on large datasets, issues with generalizability and extrapolation, and a lack of interpretability. This course aims to address these challenges by introducing scientific machine learning (SciML) techniques that are deeply rooted in physics. These techniques leverage the wealth of existing knowledge about physical systems, including established physical laws and phenomenological principles, to develop transformative machine learning techniques specifically tailored for computational physics and predictive modeling.

Learning Objectives: Participants will learn various aspects of SciML for modeling complex physical systems, including the integration of physics into neural network architectures, the design of hybrid neural solvers via differentiable programming, the use of physics to inform or regularize ML training, and data-driven knowledge/equation discovery with uncertainty quantification (UQ).

30 minutes: Introduction
30 minutes: Physics-informed Neural Network and Neural Operators
60 minutes: Physics-integrated Differentiable Neural Modeling
30 minutes: Generative Models for Chaotic and Stochastic Systems
30 minutes: Scalable Bayesian Learning and Model Form Discovery

Dr. Jian-Xun Wang

Jian-Xun Wang is an Assistant Professor in the Department of Aerospace and Mechanical Engineering at the University of Notre Dame. He earned his Ph.D. in Aerospace Engineering from Virginia Tech in 2017. Dr. Wang has a multidisciplinary research background, crossing over into SciML data assimilation, Bayesian inference, UQ, and computational mechanics. His research particularly focuses on the intersection of data-driven modeling, UQ, and computational fluid dynamics. He has led research projects sponsored by multiple agencies, including NSF, ONR, AFSOR, and DARPA. Dr. Wang is a recipient of the 2021 NSF CAREER Award and the 2023 ONR YIP Award. He is also an elected member-at-large of the US Association of Computational Mechanics (USACM) Technical Thrust Area on Uncertainty Quantification and the Technical Thrust Area on Data-Driven Modeling.


Instructor: Luís Eça, Associate Professor, IST, Portugal

Course Description: Computational simulations have become an Engineering tool that complements model testing. As for physical models, such capability requires the assessment of the quality of the results, which depends on the mathematical model (basin or wind tunnel for physical models in fluid dynamics) and its numerical solution (instrumentation for experiments).

This course teaches Computational Simulations practitioners to distinguish numerical and modelling errors. It presents the definitions of the different contributions to the numerical error of steady and unsteady flow simulations. Techniques to quantify numerical (Verification) and modelling errors (Validation) in Computational Simulations are presented including examples from practical simulations of Computational Fluid Dynamics (CFD). The course provides a framework for the establishment of the credibility of simulations so that they can be safely used for engineering decisions.

You will learn how to demonstrate the quality of your computational simulations and evaluate the accuracy of the mathematical models behind those simulations.

30 minutes: Introduction
30 minutes: Numerical Errors and Uncertainties
30 minutes: Code Verification
30 minutes: Solution Verification
60 minutes: Validation

Luís Eça

Luís Eça is an Associate Professor in the Department of Mechanical Engineering of Instituto Superior Técnico (IST) of the University of Lisbon. He received the M.S, Ph.D. and “Agregação” degrees from Technical University of Lisbon in 1987, 1993 and 2009 respectively. He has been working in Computational Fluid Dynamics (CFD) for the last 35 years in cooperation with the Maritime Research Institute Netherlands (MARIN). The main topics of the research have been the simulation of high Reynolds number flows around complex geometries and Verification and Validation in CFD. He is a member of the ASME Standards Sub-Committee in Verification, Validation and Uncertainty Quantification in Computational Fluid Dynamics and Heat Transfer since June 2015. Member of the ASME Standards Committee of Verification, Validation and Uncertainty Quantification since June 2018.