Related papers: Improved convergence of forward and inverse finite…
The increased availability of observation data from engineering systems in operation poses the question of how to incorporate this data into finite element models. To this end, we propose a novel statistical construction of the finite…
The importance of mission or safety critical software systems in many application domains of embedded systems is continuously growing, and so is the effort and complexity for reliability and safety analysis. Model driven development is…
Fine-tuning pre-trained models for downstream tasks is a widely adopted technique known for its adaptability and reliability across various domains. Despite its conceptual simplicity, fine-tuning entails several troublesome engineering…
Substantial progress has been made recently on developing provably accurate and efficient algorithms for low-rank matrix factorization via nonconvex optimization. While conventional wisdom often takes a dim view of nonconvex optimization…
The oversampling multiscale finite element method (MsFEM) is one of the most popular methods for simulating composite materials and flows in porous media which may have many scales. But the method may be inapplicable or inefficient in some…
In this article we develop convergence theory for a class of goal-oriented adaptive finite element algorithms for second order nonsymmetric linear elliptic equations. In particular, we establish contraction results for a method of this type…
The numerical analysis for the small amplitude motion of an elastic beam with internal damping is investigated in domain with moving ends. An efficient numerical method is constructed to solve this moving boundary problem. The stability and…
The Forward-Forward algorithm is an alternative learning method which consists of two forward passes rather than a forward and backward pass employed by backpropagation. Forward-Forward networks employ layer local loss functions which are…
Deep learning (DL) inverse techniques have increased the speed of artificial electromagnetic material (AEM) design and improved the quality of resulting devices. Many DL inverse techniques have succeeded on a number of AEM design tasks, but…
The need to blend observational data and mathematical models arises in many applications and leads naturally to inverse problems. Parameters appearing in the model, such as constitutive tensors, initial conditions, boundary conditions, and…
This paper presents a new parameter free partially penalized immersed finite element method and convergence analysis for solving second order elliptic interface problems. A lifting operator is introduced on interface edges to ensure the…
Physical modeling of robotic system behavior is the foundation for controlling many robotic mechanisms to a satisfactory degree. Mechanisms are also typically designed in a way that good model accuracy can be achieved with relatively simple…
Forward-backward methods are a very useful tool for the minimization of a functional given by the sum of a differentiable term and a nondifferentiable one and their investigation has experienced several efforts from many researchers in the…
In this paper we survey the most recent advances in supervised machine learning and high-dimensional models for time series forecasting. We consider both linear and nonlinear alternatives. Among the linear methods we pay special attention…
In this book chapter, we discuss recent advances in data-driven approaches for inverse problems. In particular, we focus on the \emph{paired autoencoder} framework, which has proven to be a powerful tool for solving inverse problems in…
This research is concerned with evolution equations and their forward-backward discretizations. Our first contribution is an estimation for the distance between iterates of sequences generated by forward-backward schemes, useful in the…
Statistical learning additions to physically derived mathematical models are gaining traction in the literature. A recent approach has been to augment the underlying physics of the governing equations with data driven Bayesian statistical…
The rigorous convergence analysis of adaptive finite element methods for regularized variational models of quasi-static brittle fracture in strain-limiting elastic solids is presented. This work introduces two novel adaptive mesh refinement…
Modeling environmental ecosystems is essential for effective resource management, sustainable development, and understanding complex ecological processes. However, traditional methods frequently struggle with the inherent complexity,…
The recent advancements in Deep Learning models and techniques have led to significant strides in performance across diverse tasks and modalities. However, while the overall capabilities of models show promising growth, our understanding of…