Announcement Detail
Friday, October 18, 2024
10:00 - 11:30 AM ET
Join via Zoom: https://utah.zoom.us/j/
Novel Method Virtual Seminar
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.
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.