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We investigate a lossy source compression problem in which both the encoder and decoder are equipped with a pre-trained sequence predictor. We propose an online lossy compression scheme that, under a 0-1 loss distortion function, ensures a…
We present a combined numerical and data-driven workflow for efficient prediction of nonlinear, instationary convection-diffusion-reaction dynamics on a two-dimensional phenotypic domain, motivated by macroscopic modeling of cancer cell…
The Classic Howard's algorithm, a technique of resolution for discrete Hamilton-Jacobi equations, is of large use in applications for its high efficiency and good performances. A special beneficial characteristic of the method is the…
We present and analyze a preconditioned conjugate gradient method (PCG) for solving spatial network problems. Primarily, we consider diffusion and structural mechanics simulations for fiber based materials, but the methodology can be…
In this work, we consider the numerical recovery of a spatially dependent diffusion coefficient in a subdiffusion model from distributed observations. The subdiffusion model involves a Caputo fractional derivative of order $\alpha\in(0,1)$…
In this paper we propose local approximation spaces for localized model order reduction procedures such as domain decomposition and multiscale methods. Those spaces are constructed from local solutions of the partial differential equation…
Online conformal prediction has demonstrated its capability to construct a prediction set for each incoming data point that covers the true label with a predetermined probability. To cope with potential distribution shift, multi-model…
Achieving global optimality in nonlinear model predictive control (NMPC) is challenging due to the non-convex nature of the underlying optimization problem. Since commonly employed local optimization techniques depend on carefully chosen…
Conventional offline training of reduced-order bases in a predetermined region of a parameter space leads to parametric reduced-order models that are vulnerable to extrapolation. This vulnerability manifests itself whenever a queried…
One way to analyze Cyber-Physical Systems is by modeling them as hybrid automata. Since reachability analysis for hybrid nonlinear automata is a very challenging and computationally expensive problem, in practice, engineers try to solve the…
We present a simple discretization scheme for the hypersingular integral representation of the fractional Laplace operator and solver for the corresponding fractional Laplacian problem. Through singularity subtraction, we obtain a…
We present an abstract framework for a posteriori error estimation for approximations of scalar parabolic evolution equations, based on elliptic reconstruction techniques [10, 9, 3, 5]. In addition to its original application (to derive…
We revisit the problem of estimating the parameters of a partially observed diffusion process, consisting of a hidden state process and an observed process, with a continuous time parameter. The estimation is to be done online, i.e. the…
We develop a new spatial semidiscrete multiscale method based upon the edge multiscale methods to solve semilinear parabolic problems with heterogeneous coefficients and smooth initial data. This method allows for a cheap spatial…
Finite element methods typically require a high resolution to satisfactorily approximate micro and even macro patterns of an underlying physical model. This issue can be circumvented by appropriate multiscale strategies that are able to…
In this work we combine the framework of the Reduced Basis method (RB) with the framework of the Localized Orthogonal Decomposition (LOD) in order to solve parametrized elliptic multiscale problems. The idea of the LOD is to split a high…
This paper studies a distributed multi-agent convex optimization problem. The system comprises multiple agents in this problem, each with a set of local data points and an associated local cost function. The agents are connected to a…
Large-scale eigenvalue problems arise in various fields of science and engineering and demand computationally efficient solutions. In this study, we investigate the subspace approximation for parametric linear eigenvalue problems, aiming to…
Mixed-dimensional partial differential equations (PDEs) are characterized by coupled operators defined on domains of varying dimensions and pose significant computational challenges due to their inherent ill-conditioning. Moreover, the…
The Helmholtz equation poses significant computational challenges due to its oscillatory solutions, particularly for large wavenumbers. Inspired by the Schur complement system for elliptic problems, this paper presents a novel…