Related papers: A Bayesian approach with persistent homology prior…
Posterior distributions arising in ill-posed Bayesian inverse problems are often both analytically intractable and highly sensitive to parameters of the chosen prior family. We aim to understand the sensitivity of intractable posterior…
When related learning tasks are naturally arranged in a hierarchy, an appealing approach for coping with scarcity of instances is that of transfer learning using a hierarchical Bayes framework. As fully Bayesian computations can be…
Bayesian methods have been widely used in the last two decades to infer statistical properties of spatially variable coefficients in partial differential equations from measurements of the solutions of these equations. Yet, in many cases…
This paper presents a mathematically rigorous framework for brain-inspired representation learning founded on the interplay between persistent topological structures and cohomological flows. Neural computation is reformulated as the…
We consider an acoustic obstacle reconstruction problem with Poisson data. Due to the stochastic nature of the data, we tackle this problem in the framework of Bayesian inversion. The unknown obstacle is parameterized in its angular form.…
We use persistent homology to build a quantitative understanding of large complex systems that are driven far-from-equilibrium; in particular, we analyze image time series of flow field patterns from numerical simulations of two important…
This paper develops a methodology for robust Bayesian inference through the use of disparities. Metrics such as Hellinger distance and negative exponential disparity have a long history in robust estimation in frequentist inference. We…
Bayesian nonparametric methods are a popular choice for analysing survival data due to their ability to flexibly model the distribution of survival times. These methods typically employ a nonparametric prior on the survival function that is…
Parabolic equations on evolving domains model a multitude of applications including various industrial processes such as the molding of heated materials. Such equations are numerically challenging as they require large-scale computations…
Port-Hamiltonian theory is an established way to describe nonlinear physical systems widely used in various fields such as robotics, energy management, and mechanical engineering. This has led to considerable research interest in the…
This paper presents a method of performing topology optimisation of transient heat conduction problems using the parallel-in-time method Parareal. To accommodate the adjoint analysis, the Parareal method was modified to store intermediate…
In recent years, persistent homology (PH) has been successfully applied to real-world data in many different settings. Despite significant computational advances, PH algorithms do not yet scale to large datasets preventing interesting…
Quantitative monitoring of subsurface changes is essential for ensuring the safety of geological CO2 sequestration. Full-waveform monitoring (FWM) can resolve these changes at high spatial resolution, but conventional deterministic…
A general shape identification inverse problem is studied in a Bayesian framework. This problem requires the determination of the unknown shape of a domain in the Euclidean space from finite-dimensional observation data with some Gaussian…
Dynamically rescaled Hamiltonian Monte Carlo (DRHMC) is introduced as a computationally fast and easily implemented method for performing full Bayesian analysis in hierarchical statistical models. The method relies on introducing a modified…
We propose to use L\'evy {\alpha}-stable distributions for constructing priors for Bayesian inverse problems. The construction is based on Markov fields with stable-distributed increments. Special cases include the Cauchy and Gaussian…
Persistent Homology (PH) allows tracking homology features like loops, holes and their higher-dimensional analogs, along with a single-parameter family of nested spaces. Currently, computing descriptors for complex data characterized by…
Actin cytoskeleton networks generate local topological signatures due to the natural variations in the number, size, and shape of holes of the networks. Persistent homology is a method that explores these topological properties of data and…
Variable selection methods with nonlocal priors have been widely studied in linear regression models, and their theoretical and empirical performances have been reported. However, the crucial model selection properties for hierarchical…
Persistent homology (PH) is a relatively new field in applied mathematics that studies the components and shapes of discrete data. In this work, we demonstrate that PH can be used as a universal framework to identify phases in spin models,…