USACM Technical Thrust Areas

Committee: Novel Methods in Computational Engineering and Sciences

Chair: John Foster, University of Texas at Austin
Vice-Chair: Pania Newell, University of Utah
Members-at-Large: Michael Hillman, Karagozian and Case, Inc.
Steve WaiChing Sun, Columbia University

Past Seminars

2024 USACM Novel Methods Fall Seminar

October 18, 2024; 10:00 - 11:30 AM ET

Title: Nonlocal Attention Operator: Towards a Foundation Model for Material Responses

Speaker: Prof. Yue Yu, Lehigh University

Abstract: While foundation models have gained considerable attention in core AI fields such as natural language processing (NLP) and computer vision (CV), their application to learning complex responses of physical systems from experimental measurements remains underexplored. In physical systems, learning problems are often characterized as discovering operators that map between function spaces, using only a few samples of corresponding function pairs. For instance, in the automated discovery of heterogeneous material models, the foundation model must be capable of identifying the mapping between applied loading fields and the resulting displacement fields, while also inferring the underlying microstructure that governs this mapping. While the former task can be seen as a PDE forward problem, the later task frequently constitutes a severely ill-posed PDE inverse problem.

In this talk, we will consider the learning of heterogeneous material responses as an exemplar problem to explore the development of a foundation model for physical systems. Specifically, we show that the attention mechanism is mathematically equivalent to a double integral operator, enabling nonlocal interactions among spatial tokens through a data-dependent kernel that characterizes the inverse mapping from data to the hidden microstructure/parameter field of the underlying operator. Consequently, the attention mechanism captures global prior information from training data generated by multiple systems (i.e., specimens with different microstructures) and suggests an exploratory space in the form of a nonlinear kernel map. Based on this theoretical analysis, we introduce a novel neural operator architecture, the Nonlocal Attention Operator (NAO). By leveraging the attention mechanism, NAO can address ill-posedness and rank deficiency in inverse PDE problems by encoding regularization and enhancing generalizability. To demonstrate the applicability of NAO to material modeling problems, we apply it to the development of a foundation constitutive law across multiple materials, showcasing its generalizability to unseen data resolutions and system states. Furthermore, we investigate the potentials of NAO in microstructure discovery and multiscale crack propagation problems. Our work not only suggests a novel neural operator architecture for learning an interpretable foundation model of physical systems, but also offers a new perspective towards understanding the attention mechanism.

Title: Unlocking the Challenge of Simulating Corrosion Through a New Phase Field Revolution

Speaker: Emilio Martinez-Pañeda, University of Oxford

Abstract: Corrosion has long been considered too complex to be predicted with computer models. However, increasing computer power and new multi-physics, phase field-based corrosion models enable the development of electro-chemo-mechanical phase field models that explicitly resolve the meso-scale phenomena involved and can therefore deliver predictions based on physical parameters and with minimal assumptions. Phase field modelling has revolutionised the modelling of many interfacial problems, from solidification to fracture mechanics, and this paradigm can also be used to predict the evolution of the corrosion front (electrolyte-metal interface). Recent developments in this emerging field of phase field corrosion have shown that this new class of models can capture key phenomena such as film rupture and repassivation, the transition from activation- to diffusion-controlled corrosion, interactions with mechanical fields, microstructural and electrochemical effects, intergranular corrosion, material biodegradation, and the interplay with other environmentally-assisted damage phenomena such as hydrogen embrittlement. Examples of potential future directions will also be provided to showcase the potential of this new, exciting field.

2024 USACM Novel Methods Spring Seminar

April 19, 2024

Title: Multiscale optimization of (meta-)materials by computational mechanics vs. machine learning

Speaker: Professor, Dennis Kochmann, ETH Zurich

Abstract: The optimization of materials and architected materials across scales is a crucial challenge towards the design of novel materials systems with as-designed, extreme, or peculiar mechanical properties. Especially the advent of architected materials has led to the emergence of a large array of new computational methods, which include both (more traditional) computational methods and data-driven approaches based on machine learning. We will survey some of these recent approaches for the inverse design of (meta-)materials: from multiscale topology optimization of cellular solids and ray tracing in spatially graded metamaterials to the use of machine learning. We will show how the latter can efficiently solve the inverse homogenization problem (a classically ill-posed problem) through generative modeling of novel material architectures with as-designed properties – beyond what classical methods can achieve.

Biography: Dennis M. Kochmann received his education at Ruhr-University Bochum in Germany and at the University of Wisconsin-Madison. After postdoc positions at Wisconsin and Caltech, he became Assistant Professor of Aerospace at the California Institute of Technology in 2011, and Professor of Aerospace in 2016, a position he held through 2019. Since April 2017 he has been Professor of Mechanics and Materials at ETH Zürich, where he served as Head of the Institute of Mechanical Systems and as Deputy Head of Department. His research focuses on the link between microstructure and properties of natural and architected materials, which includes the development of theoretical, computational, and experimental methods to bridge across scales from nano to macro. His research has been recognized by, among others, IUTAM’s Bureau Prize in Solid Mechanics, GAMM’s Richard von Mises Prize, an NSF CAREER Award, ASME’s T.J.R. Hughes Young Investigator Award, an ERC Consolidator Grant, and IACM’s John Argyris Award. He is Associate Editor of Archive of Applied Mechanics and Applied Mechanics Reviews.

Title: Data driven modeling of mechanical systems

Speaker: Assistant Professor, Emma Lejeune, Boston University

Abstract: Over the past decade, there has been a growing interest in leveraging machine learning techniques to model complex mechanical systems. Compellingly, these techniques have become invaluable tools for applications ranging from topology optimization, to uncertainty quantification, to real-time prediction, to multi-scale modeling and beyond. Typically, researchers take either a “problem-centric” or “model-centric” approach to this work. Namely, they focus on either an overarching engineering challenge, or they focus on developing machine learning methods and model architectures. In this talk, we will present a “data-centric” approach to data driven modeling of mechanical systems. Specifically, we will discuss work where we focus on defining and curating datasets as our top priority. First, we will share our work in developing and disseminating benchmark datasets for engineering mechanics problems. Then, we will share our work in defining an open science based methodological foundation for data driven modeling of (bio)mechanical systems. In brief, we envision a methodological framework with three essential components: (1) open access datasets, (2) open source software to extract interpretable quantities of interest from these data, and (3) combined mechanistic and statistical models of (bio)mechanical behavior informed by these data. As an illustrative example, we will discuss our recent collaborative work in cardiac tissue engineering. Overall, the goal of this talk is to spark discussion and inspire future work on “data-centric” approaches to mechanical modeling.

Biography: Emma Lejeune is an Assistant Professor in the Mechanical Engineering Department at Boston University. She received her PhD from Stanford University in September 2018, and was a Peter O’Donnell, Jr. postdoctoral research fellow at the Oden Institute at the University of Texas at Austin until 2020 when she joined the faculty at BU. Current areas of research involve integrating data-driven and physics based computational models, and characterizing and predicting the mechanical behavior of heterogeneous materials and biological systems.