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In this paper, we consider the problem of state estimation through observations possibly corrupted with both bad data and additive observation noises. A mixed $\ell_1$ and $\ell_2$ convex programming is used to separate both sparse bad data…

Deterministic hydrological models with uncertain, but inferred-to-be-time-invariant parameters typically show time-dependent model structural errors. Such errors can occur if a hydrological process is active in certain time periods in…

Sparse Identification of Nonlinear Dynamics (SINDy) has been shown to successfully recover governing equations from data; however, this approach assumes the initial condition to be exactly known in advance and is sensitive to noise. In this…

In the era of Model-as-a-Service, organizations increasingly rely on third-party AI models for rapid deployment. However, the dynamic nature of emerging AI applications, the continual introduction of new datasets, and the growing number of…

This review paper describes the basic concept and technical details of sparse modeling and its applications to quantum many-body problems. Sparse modeling refers to methodologies for finding a small number of relevant parameters that well…

Assessing data informativity, determining whether the measured data contains sufficient information for a specific control objective, is a fundamental challenge in data-driven control. In noisy scenarios, existing studies deal with system…

Fitting nonlinear dynamical models to sparse and noisy observations is fundamentally challenging. Identifying dynamics requires data assimilation (DA) to estimate system states, but DA requires an accurate dynamical model. To break this…

Predictive dynamical models for marine ecosystems are used for a variety of needs. Due to sparse measurements and limited understanding of the myriad of ocean processes, there is however significant uncertainty. There is model uncertainty…

Modern data analyses frequently encounter settings where samples of variables are contaminated by measurement error. Ignoring measurement noise can substantially degrade statistical inference, while existing correction techniques are often…

Confirmation bias, the tendency to interpret information in a way that aligns with one's preconceptions, can profoundly impact scientific research, leading to conclusions that reflect the researcher's hypotheses even when the observational…

Long-range geophysical forecasts are fundamentally limited by chaotic dynamics and numerical errors. While data assimilation can mitigate these issues, classical variational smoothers require computationally expensive tangent-linear and…

In the problem of learning mixtures of linear regressions, the goal is to learn a collection of signal vectors from a sequence of (possibly noisy) linear measurements, where each measurement is evaluated on an unknown signal drawn uniformly…

The success of the ensemble Kalman filter has triggered a strong interest in expanding its scope beyond classical state estimation problems. In this paper, we focus on continuous-time data assimilation where the model and measurement errors…

A challenge arising from the local Bayesian assimilation of data in an atmospheric flow simulation is the imbalances it may introduce. Acoustic fast-mode imbalances of the order of the slower dynamics can be negated by employing a blended…

Compressive sensing is a powerful technique for recovering sparse solutions of underdetermined linear systems, which is often encountered in uncertainty quantification analysis of expensive and high-dimensional physical models. We perform…

The use of data assimilation for the merging of observed data with dynamical models is becoming standard in modern physics. If a parametric model is known, methods such as Kalman filtering have been developed for this purpose. If no model…

This paper proposes a robust disturbance observer framework for maritime autonomous surface vessels considering model and measurement uncertainties. The core contribution lies in a nonlinear disturbance observer, reconstructing the forces…

Fault diagnosis of mechanical equipment involves data collection, feature extraction, and pattern recognition but is often hindered by the imbalanced nature of industrial data, introducing significant uncertainty and reducing diagnostic…

Wide-area data and algorithms in large power systems are creating new opportunities for implementation of measurement-based dynamic load modeling techniques. These techniques improve the accuracy of dynamic load models, which are an…

The Sparse Identification of Nonlinear Dynamics (SINDy) is a method for discovering nonlinear dynamical system models from data. Quantifying uncertainty in SINDy models is essential for assessing their reliability, particularly in…