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This study presents a physics-informed machine learning-based control method for nonlinear dynamic systems with highly noisy measurements. Existing data-driven control methods that use machine learning for system identification cannot…

In the study of gas dynamics, theoretical modeling and numerical simulation are mostly set up with deterministic settings. Given the coarse-grained modeling in theories of fluids, considerable uncertainties may exist between flow-field…

Clinical decision requires reasoning in the presence of imperfect data. DTs are a well-known decision support tool, owing to their interpretability, fundamental in safety-critical contexts such as medical diagnosis. However, learning DTs…

Bayesian neural networks with latent variables are scalable and flexible probabilistic models: They account for uncertainty in the estimation of the network weights and, by making use of latent variables, can capture complex noise patterns…

Uncertainty quantification for image data is dominated by complex deep learning methods, yet the field lacks an interpretable, mathematically grounded baseline. We propose Bayesian scattering to fill this gap, serving as a first-step…

In this paper, we consider discrete-time non-linear stochastic dynamical systems with additive process noise in which both the initial state and noise distributions are uncertain. Our goal is to quantify how the uncertainty in these…

Parameter identification and comparison of dynamical systems is a challenging task in many fields. Bayesian approaches based on Gaussian process regression over time-series data have been successfully applied to infer the parameters of a…

Uncertainty in state or model parameters is common in robotics and typically handled by acquiring system measurements that yield information about the uncertain quantities of interest. Inputs to a nonlinear dynamical system yield outcomes…

Real-world data contains aleatoric uncertainty - irreducible noise arising from imperfect measurements or from incomplete knowledge about the data generation process. Mean-variance estimation networks can learn this type of uncertainty but…

Two non-intrusive uncertainty propagation approaches are proposed for the performance analysis of engineering systems described by expensive-to-evaluate deterministic computer models with parameters defined as interval variables. These…

Hyperparameter tuning is a challenging problem especially when the system itself involves uncertainty. Due to noisy function evaluations, optimization under uncertainty can be computationally expensive. In this paper, we present a novel…

Data-driven, model-free analytics are natural choices for discovery and forecasting of complex, nonlinear systems. Methods that operate in the system state-space require either an explicit multidimensional state-space, or, one approximated…

The discovery of governing equations from data has been an active field of research for decades. One widely used methodology for this purpose is sparse regression for nonlinear dynamics, known as SINDy. Despite several attempts, noisy and…

This paper addresses the problem of learning linear dynamical systems from noisy observations. In this setting, existing algorithms either yield biased parameter estimates or have large sample complexities. We resolve these issues by…

Neural Linear Models (NLM) are deep Bayesian models that produce predictive uncertainty by learning features from the data and then performing Bayesian linear regression over these features. Despite their popularity, few works have focused…

This paper introduces a novel system identification and tracking method for PieceWise Smooth (PWS) nonlinear stochastic hybrid systems. We are able to correctly identify and track challenging problems with diverse dynamics and low…

This paper proposes a sparse identification of nonlinear dynamics (SINDy) with control and exogenous inputs for highly accurate and reliable prediction. Although SINDy is recognized as a remarkable approach for identifying nonlinear…

This work proposes a robust data-driven predictive control approach for unknown nonlinear systems in the presence of bounded process and measurement noise. Data-driven reachable sets are employed for the controller design instead of using…

In many applications, smooth processes generate data that is recorded under a variety of observation regimes, such as dense, sparse or fragmented observations that are often contaminated with error. The statistical goal of registering and…

In this paper, we derive a novel procedure for set-membership estimation of dynamical systems affected by stochastic noise with unbounded support. Employing a bound on the sample covariance matrix, we are able to provide a finite- sample…