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High-dimensional and complex discrete distributions often exhibit multimodal behavior due to inherent discontinuities, posing significant challenges for sampling. Gradient-based discrete samplers, while effective, frequently become trapped…
The spectral transformation Lanczos method for the sparse symmetric definite generalized eigenvalue problem for matrices $A$ and $B$ is an iterative method that addresses the case of semidefinite or ill conditioned $B$ using a shifted and…
Superintegrable systems are classical and quantum Hamiltonian systems which enjoy much symmetry and structure that permit their solubility via analytic and even, algebraic means. They include such well-known and important models as the…
This paper presents an improved implicit sampling method for hierarchical Bayesian inverse problems. A widely used approach for sampling posterior distribution is based on Markov chain Monte Carlo (MCMC). However, the samples generated by…
This paper concerns models and convergence principles for dealing with stochasticity in a wide range of algorithms arising in nonlinear analysis and optimization in Hilbert spaces. It proposes a flexible geometric framework within which…
Entropic optimal transport problems are regularized versions of optimal transport problems. These models play an increasingly important role in machine learning and generative modelling. For finite spaces, these problems are commonly solved…
This paper reviews recent results on hybrid inverse problems, which are also called coupled-physics inverse problems of multi-wave inverse problems. Inverse problems tend to be most useful in, e.g., medical and geophysical imaging, when…
Global and block Krylov subspace methods are efficient iterative solvers for large sparse linear systems with multiple right-hand sides. However, global or block Lanczos-type solvers often exhibit large oscillations in the residual norms…
We consider iterative methods for solving linear ill-posed problems with compact operator and right-hand side only available via noise-polluted measurements. Conjugate gradients (CG) applied to the normal equations with an appropriate…
We introduce an efficient and scalable method for density-based multi-material topology optimization, integrating classical mirror descent techniques with point-wise polytopal design constraints. Such constraints arise naturally in this…
Sampling from high-dimensional Gibbs measures poses a challenge when the energy landscape consists of multiple metastable states. Enhanced-sampling methods mitigate this difficulty by introducing adaptive biasing potentials to facilitate…
We develop primal and mixed variational formulations of transport phenomena on cell complexes with simple polytope connectivity. This framework addresses materials with internal structures comprising components of different topological…
The goal of this work is to construct and study hybrid and multiplicative two-level overlapping Schwarz algorithms with standard coarse spaces for the almost incompressible linear elasticity and Stokes systems, discretized by mixed finite…
We consider a bilevel optimatisation method for inverse linear atmospheric dispersion problems where both linear and non-linear model parameters are to be determined. We propose that a smooth weighted Mahalanobis distance function is used…
High-throughput characterization often requires estimating parameters and model dimension from experimental data of limited quantity and quality. Such data may result in an ill-posed inverse problem, where multiple sets of parameters and…
The Variational Theory of Complex Rays (VTCR) is an indirect Trefftz method designed to study systems governed by Helmholtz-like equations. It uses wave functions to represent the solution inside elements, which reduces the dispersion error…
This paper presents a modified general viscosity iterative process designed to solve variational inclusion and fixed point problems involving multi-valued quasi-nonexpansive and demi-contractive operators. The modified iterative process…
In this paper, we introduce and study a new extragradient iterative process for finding a common element of the set of fixed points of an infinite family of nonexpansive mappings and the set of solutions of a variational inequality for an…
We introduce a revised derivation of the bitwise Markov Chain Monte Carlo (MCMC) multiple-input multiple-output (MIMO) detector. The new approach resolves the previously reported high SNR stalling problem of MCMC without the need for…
Inverse problems defined on the sphere arise in many fields, including seismology and cosmology where problems are defined on the globe and the cosmic sphere. These are generally high-dimensional and computationally very complex and, as a…