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Bayesian optimization is a popular and versatile approach that is well suited to solve challenging optimization problems. Their popularity comes from their effective minimization of expensive function evaluations, their capability to…

Gaussian processes allow for flexible specification of prior assumptions of unknown dynamics in state space models. We present a procedure for efficient Bayesian learning in Gaussian process state space models, where the representation is…

Bayesian learning is a powerful learning framework which combines the external information of the data (background information) with the internal information (training data) in a logically consistent way in inference and prediction. By…

In this paper we present a practical Bayesian self-supervised learning method with Cyclical Stochastic Gradient Hamiltonian Monte Carlo (cSGHMC). Within this framework, we place a prior over the parameters of a self-supervised learning…

Hamiltonian neural networks (HNNs) are state-of-the-art models that regress the vector field of a dynamical system under the learning bias of Hamilton's equations. A recent observation is that embedding a bias regarding the additive…

Robust physics discovery is of great interest for many scientific and engineering fields. Inspired by the principle that a representative model is the one simplest possible, a new model selection criteria considering both model's Parsimony…

Sparse signal recovery algorithms like sparse Bayesian learning work well but the complexity quickly grows when tackling higher dimensional parametric dictionaries. In this work we propose a novel Bayesian strategy to address the two…

Bayesian optimization has proven to be a highly effective methodology for the global optimization of unknown, expensive and multimodal functions. The ability to accurately model distributions over functions is critical to the effectiveness…

The performance of deep (reinforcement) learning systems crucially depends on the choice of hyperparameters. Their tuning is notoriously expensive, typically requiring an iterative training process to run for numerous steps to convergence.…

Learning and predicting the dynamics of physical systems requires a profound understanding of the underlying physical laws. Recent works on learning physical laws involve generalizing the equation discovery frameworks to the discovery of…

In this article a novel approach for training deep neural networks using Bayesian techniques is presented. The Bayesian methodology allows for an easy evaluation of model uncertainty and additionally is robust to overfitting. These are…

A quality-Bayesian approach, combining the direct sampling method and the Bayesian inversion, is proposed to reconstruct the locations and intensities of the unknown acoustic sources using partial data. First, we extend the direct sampling…

Detecting symmetry from data is a fundamental problem in signal analysis, providing insight into underlying structure and constraints. When data emerge as trajectories of dynamical systems, symmetries encode structural properties of the…

In this work, we propose a novel variational Bayesian adaptive learning approach for cross-domain knowledge transfer to address acoustic mismatches between training and testing conditions, such as recording devices and environmental noise.…

We study the problem of estimating the mode and maximum of an unknown regression function in the presence of noise. We adopt the Bayesian approach by using tensor-product B-splines and endowing the coefficients with Gaussian priors. In the…

This paper presents an efficient Bayesian framework for solving nonlinear, high-dimensional model calibration problems. It is based on a Variational Bayesian formulation that aims at approximating the exact posterior by means of solving an…

We study system design problems stated as parameterized stochastic programs with a chance-constraint set. We adopt a Bayesian approach that requires the computation of a posterior predictive integral which is usually intractable. In…

We introduce a scalable Bayesian preference learning method for identifying convincing arguments in the absence of gold-standard rat- ings or rankings. In contrast to previous work, we avoid the need for separate methods to perform quality…

The quantitative formulation of evolution equations is the backbone for prediction, control, and understanding of dynamical systems across diverse scientific fields. Besides deriving differential equations for dynamical systems based on…

Hamiltonian neural networks (HNNs) represent a promising class of physics-informed deep learning methods that utilize Hamiltonian theory as foundational knowledge within neural networks. However, their direct application to engineering…