Related papers: Improved convergence of forward and inverse finite…

Analysis of the convergence rates of modern convex optimization algorithms can be achived through binary means: analysis of emperical convergence, or analysis of theoretical convergence. These two pathways of capturing information diverge…

The conformal formulation of the Einstein constraint equations is first reviewed, and we then consider the design, analysis, and implementation of adaptive multilevel finite element-type numerical methods for the resulting coupled nonlinear…

In this work, we describe a new data-driven approach for inverse problems that exploits technologies from machine learning, in particular autoencoder network structures. We consider a paired autoencoder framework, where two autoencoders are…

It is important to accurately model materials' properties at lower length scales (micro-level) while translating the effects to the components and/or system level (macro-level) can significantly reduce the amount of experimentation required…

We consider the task of solving generic inverse problems, where one wishes to determine the hidden parameters of a natural system that will give rise to a particular set of measurements. Recently many new approaches based upon deep learning…

This paper presents a learning-based approach for impromptu trajectory tracking for non-minimum phase systems, i.e., systems with unstable inverse dynamics. Inversion-based feedforward approaches are commonly used for improving tracking…

Parameter sharing has proven to be a parameter-efficient approach. Previous work on Transformers has focused on sharing parameters in different layers, which can improve the performance of models with limited parameters by increasing model…

Multimodal foundation models offer promising advancements for enhancing driving perception systems, but their high computational and financial costs pose challenges. We develop a method that leverages foundation models to refine predictions…

In the first part of this study, a convex-constrained penalized formulation was studied for a class of constant modulus (CM) problems. In particular, the error bound techniques were shown to play a vital role in providing exact penalization…

Adaptive Finite Element Method (adaptivity) is known to be an effective numerical tool for some ill-posed problems. The key advantage of the adaptivity is the image improvement with local mesh refinements. A rigorous proof of this property…

This work proposes an automatic methodology for modeling complex systems. Our methodology is based on the combination of Grammatical Evolution and classical regression to obtain an optimal set of features that take part of a linear and…

The main contribution of this thesis is to investigate the incorporating skin and proximity effects in magnetic induction tomography (MIT) coils and present an improved model for the two-dimensional (2D) forward problem. To evaluate the…

We present a coupling of the Finite Element and the Boundary Element Method in an isogeometric framework to approximate either two-dimensional Laplace interface problems or boundary value problems consisting in two disjoint domains. We…

Modeling complex physical systems such as they arise in civil engineering applications requires finding a trade-off between physical fidelity and practicality. Consequently, deviations of simulation from measurements are ubiquitous even…

Inverse problems describe the task of recovering an underlying signal of interest given observables. Typically, the observables are related via some non-linear forward model applied to the underlying unknown signal. Inverting the non-linear…

Foundation models (FMs) have emerged as a promising approach for time series forecasting. While effective, FMs typically remain fixed during deployment due to the high computational costs of learning them online. Consequently, deployed FMs…

While approaches to model the progression of fracture have received significant attention, methods to find the solution to the associated nonlinear equations have not. In general, nonlinear solution methods and optimization methods have a…

Ensembling is a simple and popular technique for boosting evaluation performance by training multiple models (e.g., with different initializations) and aggregating their predictions. This approach is commonly reserved for the largest…

This paper proposes the response surface method for finite element model updating. The response surface method is implemented by approximating the finite element model surface response equation by a multi-layer perceptron. The updated…

High-dimensional recordings of dynamical processes are often characterized by a much smaller set of effective variables, evolving on low-dimensional manifolds. Identifying these latent dynamics requires solving two intertwined problems:…