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The willingness to trust predictions formulated by automatic algorithms is key in a vast number of domains. However, a vast number of deep architectures are only able to formulate predictions without an associated uncertainty. In this…

Recurrent neural networks (RNNs) are nonlinear dynamical models commonly used in the machine learning and dynamical systems literature to represent complex dynamical or sequential relationships between variables. More recently, as deep…

Bayesian inference promises a framework for principled uncertainty quantification of neural network predictions. Barriers to adoption include the difficulty of fully characterizing posterior distributions on network parameters and the…

Exoplanet detection in the past decade by efforts including NASA's Kepler and TESS missions has discovered many worlds that differ substantially from planets in our own Solar system, including more than 400 exoplanets orbiting binary or…

Deep neural networks offer numerous potential applications across geoscience, for example, one could argue that they are the state-of-the-art method for predicting faults in seismic datasets. In quantitative reservoir characterization…

Deep Neural Networks (DNNs) are powerful tools for various computer vision tasks, yet they often struggle with reliable uncertainty quantification - a critical requirement for real-world applications. Bayesian Neural Networks (BNN) are…

Planet induced sub-structures, like annular gaps, observed in dust emission from protoplanetary disks provide a unique probe to characterize unseen young planets. While deep learning based model has an edge in characterizing the planet's…

Neural networks make accurate predictions but often fail to provide reliable uncertainty estimates, especially under covariate distribution shifts between training and testing. To address this problem, we propose a Bayesian framework for…

Recent advances in reconstruction methods for inverse problems leverage powerful data-driven models, e.g., deep neural networks. These techniques have demonstrated state-of-the-art performances for several imaging tasks, but they often do…

Context: Astronomy and astrophysics demand rigorous handling of uncertainties to ensure the credibility of outcomes. The growing integration of artificial intelligence offers a novel avenue to address this necessity. This convergence…

While deep neural networks have become the go-to approach in computer vision, the vast majority of these models fail to properly capture the uncertainty inherent in their predictions. Estimating this predictive uncertainty can be crucial,…

This paper demonstrates the application of Bayesian Artificial Neural Networks to Ordinary Differential Equation (ODE) inverse problems. We consider the case of estimating an unknown chaotic dynamical system transition model from state…

Third-generation (3G) gravitational-wave detectors will observe thousands of coalescing neutron star binaries with unprecedented fidelity. Extracting the highest precision science from these signals is expected to be challenging owing to…

Nonlinear dynamics are ubiquitous in science and engineering applications, but the physics of most complex systems is far from being fully understood. Discovering interpretable governing equations from measurement data can help us…

We show how to treat systematic uncertainties using Bayesian deep networks for regression. First, we analyze how these networks separately trace statistical and systematic uncertainties on the momenta of boosted top quarks forming fat jets.…

To improve our understanding of orbital instabilities in compact planetary systems, we compare suites of $N$-body simulations against numerical integrations of simplified dynamical models. We show that, surprisingly, dynamical models that…

Machine learning is now used in many areas of astrophysics, from detecting exoplanets in Kepler transit signals to removing telescope systematics. Recent work demonstrated the potential of using machine learning algorithms for atmospheric…

This paper presents a machine learning framework for Bayesian systems identification from noisy, sparse and irregular observations of nonlinear dynamical systems. The proposed method takes advantage of recent developments in differentiable…

A planetary system consists of a host star and one or more planets, arranged into a particular configuration. Here, we consider what information belongs to the configuration, or ordering, of 4286 Kepler planets in their 3277 planetary…

The radio astronomy community is rapidly adopting deep learning techniques to deal with the huge data volumes expected from the next generation of radio observatories. Bayesian neural networks (BNNs) provide a principled way to model…