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The focus in this paper is Bayesian system identification based on noisy incomplete modal data where we can impose spatially-sparse stiffness changes when updating a structural model. To this end, based on a similar hierarchical sparse…

A novel strategy is proposed to improve the accuracy of state estimation and reconstruction from low-fidelity models and sparse data from sensors. This strategy combines ensemble Data Assimilation (DA) and Machine Learning (ML) tools,…

Discovering the partial differential equations underlying spatio-temporal datasets from very limited and highly noisy observations is of paramount interest in many scientific fields. However, it remains an open question to know when model…

To account for measurement error (ME) in explanatory variables, Bayesian approaches provide a flexible framework, as expert knowledge about unobserved covariates can be incorporated in the prior distributions. However, given the analytic…

This paper describes methods for comparative evaluation of the interpretability of models of high dimensional time series data inferred by unsupervised machine learning algorithms. The time series data used in this investigation were logs…

In atmospheric and turbulent flow modeling, Large Eddy Simulation (LES) is often used to reduce computational cost, while observational data typically originates from the underlying physical system. Motivated by this setting, we study a…

Multimodal emotion recognition (MER) in practical scenarios is significantly challenged by the presence of missing or incomplete data across different modalities. To overcome these challenges, researchers have aimed to simulate incomplete…

Ideally, a meta-analysis will summarize data from several unbiased studies. Here we consider the less than ideal situation in which contributing studies may be compromised by measurement error. Measurement error affects every study design,…

System inference for nonlinear dynamic models, represented by ordinary differential equations (ODEs), remains a significant challenge in many fields, particularly when the data are noisy, sparse, or partially observable. In this paper, we…

This paper proposes a hierarchical, multi-resolution framework for the identification of model parameters and their spatially variability from noisy measurements of the response or output. Such parameters are frequently encountered in…

There has been a recent surge in development of accurate machine learning (ML) weather prediction models, but evaluation of these models has mainly been focused on medium-range forecasts, not their performance in cycling data assimilation…

Reduced-order models based on level-set methods are widely used tools to qualitatively capture and track the nonlinear dynamics of an interface. The aim of this paper is to develop a physics-informed, data-driven, statistically rigorous…

Compressive Sensing (CS) stipulates that a sparse signal can be recovered from a small number of linear measurements, and that this recovery can be performed efficiently in polynomial time. The framework of model-based compressive sensing…

This article presents a general framework for recovering missing dynamical systems using available data and machine learning techniques. The proposed framework reformulates the prediction problem as a supervised learning problem to…

Chaos is ubiquitous in physical systems. The associated sensitivity to initial conditions is a significant obstacle in forecasting the weather and other geophysical fluid flows. Data assimilation is the process whereby the uncertainty in…

Data assimilation (DA) aims to optimally combine model forecasts and observations that are both partial and noisy. Multi-model DA generalizes the variational or Bayesian formulation of the Kalman filter, and we prove that it is also the…

Precise control in modern robotic applications is always an open issue due to unknown time-varying disturbances. Existing meta-learning-based approaches require a shared representation of environmental structures, which lack flexibility for…

Recovering dynamical equations from observed noisy data is the central challenge of system identification. We develop a statistical mechanics approach to analyze sparse equation discovery algorithms, which typically balance data fit and…

Anomaly detection (AD) plays a pivotal role in multimedia applications for detecting defective products and automating quality inspection. Deep learning (DL) models typically require large-scale annotated data, which are often highly…

Measurement error occurs when a covariate influencing a response variable is corrupted by noise. This can lead to misleading inference outcomes, particularly in problems where accurately estimating the relationship between covariates and…