Related papers: Bayesian deep learning for error estimation in the…

Recent work has focused on data-driven learning of the evolution of unknown systems via deep neural networks (DNNs), with the goal of conducting long time prediction of the evolution of the unknown system. Training a DNN with low…

We propose a framework to perform Bayesian inference using conditional score-based diffusion models to solve a class of inverse problems in mechanics involving the inference of a specimen's spatially varying material properties from noisy…

Diffusion models recently proved to be remarkable priors for Bayesian inverse problems. However, training these models typically requires access to large amounts of clean data, which could prove difficult in some settings. In this work, we…

Deep Gaussian processes (DGPs) are multi-layer hierarchical generalisations of Gaussian processes (GPs) and are formally equivalent to neural networks with multiple, infinitely wide hidden layers. DGPs are probabilistic and non-parametric…

Nonlinear system identification is important with a wide range of applications. The typical approaches for nonlinear system identification include Volterra series models, nonlinear autoregressive with exogenous inputs models,…

In order to characterize the mechanisms governing the diffusion of particles in biological scenarios, it is essential to accurately determine their diffusive properties. To do so, we propose a machine learning method to characterize…

Dynamical system state estimation and parameter calibration problems are ubiquitous across science and engineering. Bayesian approaches to the problem are the gold standard as they allow for the quantification of uncertainties and enable…

In this paper Gaussian models of retarded and accelerated anomalous diffusion are considered. Stochastic differential equations of fractional order driven by single or multiple fractional Gaussian noise terms are introduced to describe…

We study aleatoric and epistemic uncertainty estimation in a learned regressive system dynamics model. Disentangling aleatoric uncertainty (the inherent randomness of the system) from epistemic uncertainty (the lack of data) is crucial for…

Denoising diffusion models have emerged as a dominant approach for image generation, however they still suffer from slow convergence in training and color shift issues in sampling. In this paper, we identify that these obstacles can be…

State estimation remains a fundamental challenge across numerous domains, from autonomous driving, aircraft tracking to quantum system control. Although Bayesian filtering has been the cornerstone solution, its classical model-based…

Deep learning provides a powerful tool for machine perception when the observations resemble the training data. However, real-world robotic systems must react intelligently to their observations even in unexpected circumstances. This…

The topic of deep learning has seen a surge of interest in recent years both within and outside of the field of Statistics. Deep models leverage both nonlinearity and interaction effects to provide superior predictions in many cases when…

We focus on using the predictive uncertainty signal calculated by Bayesian neural networks to guide learning in the self-same task the model is being trained on. Not opting for costly Monte Carlo sampling of weights, we propagate the…

Despite the dominant role of deep models in machine learning, limitations persist, including overconfident predictions, susceptibility to adversarial attacks, and underestimation of variability in predictions. The Bayesian paradigm provides…

Diffusion processes are important in several physical, chemical, biological and human phenomena. Examples include molecular encounters in reactions, cellular signalling, the foraging of animals, the spread of diseases, as well as trends in…

Large scale datasets created from user labels or openly available data have become crucial to provide training data for large scale learning algorithms. While these datasets are easier to acquire, the data are frequently noisy and…

In computational inverse problems, it is common that a detailed and accurate forward model is approximated by a computationally less challenging substitute. The model reduction may be necessary to meet constraints in computing time when…

This paper addresses the problem of fault diagnosis in multistation assembly systems. Fault diagnosis is to identify process faults that cause the excessive dimensional variation of the product using dimensional measurements. For such…

The passive and active motion of micron-sized tracer particles in crowded liquids and inside living biological cells is ubiquitously characterised by "viscoelastic" anomalous diffusion, in which the increments of the motion feature…