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We consider the convergence of iterative solvers for problems of nonlinear magnetostatics. Using the equivalence to an underlying minimization problem, we can establish global linear convergence of a large class of methods, including the…
A novel semi-supervised learning technique is introduced based on a simple iterative learning cycle together with learned thresholding techniques and an ensemble decision support system. State-of-the-art model performance and increased…
In this paper we approach the problem of unique and stable identifiability of generic deep artificial neural networks with pyramidal shape and smooth activation functions from a finite number of input-output samples. More specifically we…
We propose a custom learning algorithm for shallow over-parameterized neural networks, i.e., networks with single hidden layer having infinite width. The infinite width of the hidden layer serves as an abstraction for the…
The finite element simulation of dynamic wetting phenomena, requiring the computation of flow in a domain confined by intersecting a liquid-fluid free surface and a liquid-solid interface, with the three-phase contact line moving across the…
Polynomial inequalities lie at the heart of many mathematical disciplines. In this paper, we consider the fundamental computational task of automatically searching for proofs of polynomial inequalities. We adopt the framework of…
This research introduces an extended application of neural networks for solving nonlinear partial differential equations (PDEs). A neural network, combined with a pseudo-arclength continuation, is proposed to construct bifurcation diagrams…
Transport and mixing properties of aperiodic flows are crucial to a dynamical analysis of the flow, and often have to be carried out with limited information. Finite-time coherent sets are regions of the flow that minimally mix with the…
We develop a framework for quantitative convergence analysis of Picard iterations of expansive set-valued fixed point mappings. There are two key components of the analysis. The first is a natural generalization of single-valued averaged…
We introduce a pattern mining framework that operates on semi-structured datasets and exploits the dichotomy between outcomes. Our approach takes advantage of constraint reasoning to find sequential patterns that occur frequently and…
A robust finite volume method for viscoelastic flow analysis on general unstructured meshes is developed. It is built upon a general-purpose stabilization framework for high Weissenberg number flows. The numerical framework provides full…
The Kleene theorem establishes a fundamental link between automata and expressions over the free monoid. Numerous generalisations of this result exist in the literature. Lifting this result to a weighted setting has been widely studied.…
Recent work demonstrated that flow-based invertible neural networks are promising tools for solving ambiguous inverse problems. Following up on this, we investigate how ten invertible architectures and related models fare on two intuitive,…
Obtaining predictive low-order models is a central challenge in fluid dynamics. Data-driven frameworks have been widely used to obtain low-order models of aerodynamic systems; yet, resulting models tend to yield predictions that grow…
We consider scalar semilinear elliptic PDEs where the nonlinearity is strongly monotone, but only locally Lipschitz continuous. We formulate an adaptive iterative linearized finite element method (AILFEM) which steers the local mesh…
Given a family of systems, identifying stabilizing switching signals in terms of infinite walks constructed by concatenating cycles on the underlying directed graph of a switched system that satisfy certain conditions, is a well-known…
To optimize efficiently over discrete data and with only few available target observations is a challenge in Bayesian optimization. We propose a continuous relaxation of the objective function and show that inference and optimization can be…
This paper studies the Craig variant of the Golub-Kahan bidiagonalization algorithm as an iterative solver for linear systems with saddle point structure. Such symmetric indefinite systems in 2x2 block form arise in many applications, but…
Clustering ensemble, or consensus clustering, has emerged as a powerful tool for improving both the robustness and the stability of results from individual clustering methods. Weighted clustering ensemble arises naturally from clustering…
First, we consider the problem of hedging in complete binomial models. Using the discrete-time F\"ollmer-Schweizer decomposition, we demonstrate the equivalence of the backward induction and sequential regression approaches. Second, in…