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German Capuano
(Advisor: Julian J. Rimoli)
will propose a doctoral thesis entitled,
Smart finite elements: An application of machine learning to reduced-order modeling of multi-scale problems
On
Monday, April 30 at 12:00 p.m.
Weber Building 200A
Abstract
Surrogate modelling is a technique that uses machine learning to approximate a model using extracted data, with the goal of reducing computational costs. This technique is frequently used in structural optimization and is often applied to finite element models. However, the computational cost of machine learning algorithms considerably increases with the dimension of the model, a problem known as the curse of dimensionality, which severely limits the range of applications. Other data-driven attempts to reduce the computational cost of finite elements have also struggled because they require custom solvers or intrusive techniques that are incompatible with legacy software.
To address these shortcomings in the field, we propose to create surrogate models of individual elements—in contrast to the whole model— with the objective of reducing the computational cost in challenging scenarios such as non-linear multi-scale finite elements. Since individual elements usually have a small dimension, they avoid the curse of dimensionality and make effective use of current machine learning algorithms. We also address some inefficiencies of applying these algorithms directly to finite element data by using corotational coordinates and enforcing physical constraints on the internal forces. Using these techniques, we found we can considerably increase the performance of the method, simultaneously reducing the computational cost and the resulting error. Unlike all other data-driven techniques applied on individual elements, our method is flexible in the sense that it can be used in conjunction with any machine learning algorithm and within any traditional or black box solver.
Committee
