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Nonlinear dynamic models are widely used for characterizing functional forms of processes that govern complex biological pathway systems. Over the past decade, validation and further development of these models became possible due to data…

Identifying and calibrating quantitative dynamical models for physical quantum systems is important for a variety of applications. Here we present a closed-loop Bayesian learning algorithm for estimating multiple unknown parameters in a…

To fully understand, analyze, and determine the behavior of dynamical systems, it is crucial to identify their intrinsic modal coordinates. In nonlinear dynamical systems, this task is challenging as the modal transformation based on the…

Data-driven discovery of differential equations has been an emerging research topic. We propose a novel algorithm subsampling-based threshold sparse Bayesian regression (SubTSBR) to tackle high noise and outliers. The subsampling technique…

Sparse Bayesian Learning (SBL) is a powerful framework for attaining sparsity in probabilistic models. Herein, we propose a coordinate ascent algorithm for SBL termed Relevance Matching Pursuit (RMP) and show that, as its noise variance…

Accurate channel estimation is a key requirement in extremely large-scale multiple-input multiple-output (XL-MIMO) systems. Sparse Bayesian learning (SBL) is a well-established framework for exploiting channel sparsity, but its performance…

Recent works have established the utility of sparsity-promoting norms for extracting spatially-localized instability mechanisms in fluid flows, with possible implications for flow control. However, these prior works have focused on linear…

Sparse Bayesian learning (SBL) is a powerful framework for tackling the sparse coding problem. However, the most popular inference algorithms for SBL become too expensive for high-dimensional settings, due to the need to store and compute a…

The ability to discover physical laws and governing equations from data is one of humankind's greatest intellectual achievements. A quantitative understanding of dynamic constraints and balances in nature has facilitated rapid development…

We introduce a flexible, scalable Bayesian inference framework for nonlinear dynamical systems characterised by distinct and hierarchical variability at the individual, group, and population levels. Our model class is a generalisation of…

Scientific machine learning has been successfully applied to inverse problems and PDE discovery in computational physics. One caveat concerning current methods is the need for large amounts of ("clean") data, in order to characterize the…

Often the underlying system of differential equations driving a stochastic dynamical system is assumed to be known, with inference conditioned on this assumption. We present a Bayesian framework for discovering this system of differential…

The performance of sparse signal recovery from noise corrupted, underdetermined measurements can be improved if both sparsity and correlation structure of signals are exploited. One typical correlation structure is the intra-block…

Sparse Bayesian learning (SBL) associates to each weight in the underlying linear model a hyperparameter by assuming that each weight is Gaussian distributed with zero mean and precision (inverse variance) equal to its associated…

The accuracy of the underlying model predictions is crucial for the success of model predictive control (MPC) applications. If the model is unable to accurately analyze the dynamics of the controlled system, the performance and stability…

Reliable optimal control is challenging when the dynamics of a nonlinear system are unknown and only infrequent, noisy output measurements are available. This work addresses this setting of limited sensing by formulating a Bayesian prior…

We address the recovery of sparse vectors in an overcomplete, linear and noisy multiple measurement framework, where the measurement matrix is known upto a permutation of its rows. We derive sparse Bayesian learning (SBL) based updates for…

Limit cycle oscillations are phenomena arising in nonlinear dynamical systems and characterized by periodic, locally-stable, and self-sustained state trajectories. Systems controlled in a closed loop along a periodic trajectory can also be…

This work is a re-examination of the sparse Bayesian learning (SBL) of linear regression models of Tipping (2001) in a high-dimensional setting. We propose a hard-thresholded version of the SBL estimator that achieves, for orthogonal design…

In many problems of data-driven modeling for dynamical systems, the governing equations are not known a priori and must be selected phenomenologically from a large set of candidate interactions and basis functions. In such situations, point…