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Model error estimation remains one of the key challenges in uncertainty quantification and predictive science. For computational models of complex physical systems, model error, also known as structural error or model inadequacy, is often…
This paper presents a novel framework for characterizing dissipativity of uncertain systems whose dynamics evolve according to differential-algebraic equations. Sufficient conditions for dissipativity (specializing to, e.g., stability or…
We use a semantic interpretation to investigate the problem of defining an expressive but decidable type system with bounded quantification. Typechecking in the widely studied System Fsub is undecidable thanks to an undecidable subtyping…
Neural networks (NNs) lack measures of "reliability" estimation that would enable reasoning over their predictions. Despite the vital importance, especially in areas of human well-being and health, state-of-the-art uncertainty estimation…
We study aleatoric and epistemic uncertainty estimation in a learned regressive system dynamics model. Disentangling aleatoric uncertainty (the inherent randomness of the system) from epistemic uncertainty (the lack of data) is crucial for…
The uncertainty principle limits quantum states such that when one observable takes predictable values there must be some other mutually unbiased observables which take uniformly random values. We show that this restrictive condition plays…
Here, we investigate the uncertainty of dynamical observables in classical systems manipulated by repeated measurements and feedback control; the precision should be enhanced in the presence of an external controller but limited by the…
The uncertainty principle brings out intrinsic quantum bounds on the precision of measuring non-commuting observables. Statistical outcomes in the measurement of incompatible observables reveal a trade-off on the sum of corresponding…
Deep unrolling is an emerging deep learning-based image reconstruction methodology that bridges the gap between model-based and purely deep learning-based image reconstruction methods. Although deep unrolling methods achieve…
Robust stabilization conditions for uncertain switched affine systems subject to a unitary input delay are presented. They are obtained through the Lyapunov framework and a min-switching state-feedback predictive control law. The result…
We consider bounded extremum seeking controls for time-varying linear systems with uncertain coefficient matrices and measurement uncertainty. Using a new change of variables, Lyapunov functions, and a comparison principle, we provide…
This paper develops a unified analytical framework for determinant identities under finite-rank perturbations of square matrices that remains valid without invertibility assumptions. In contrast to classical inverse-based formulations, the…
Different aspects of the predictability problem in dynamical systems are reviewed. The deep relation among Lyapunov exponents, Kolmogorov-Sinai entropy, Shannon entropy and algorithmic complexity is discussed. In particular, we emphasize…
In this paper, we present a new explainability formalism designed to shed light on how each input variable of a test set impacts the predictions of machine learning models. Hence, we propose a group explainability formalism for trained…
Much of uncertainty quantification to date has focused on determining the effect of variables modeled probabilistically, and with a known distribution, on some physical or engineering system. We develop methods to obtain information on the…
We study the robustness of system estimation to parametric perturbations in system dynamics and initial conditions. We define the problem of sensitivity-based parametric uncertainty quantification in dynamical system estimation. The main…
Uncertainty relations in quantum mechanics express bounds on our ability to simultaneously obtain knowledge about expectation values of non-commuting observables of a quantum system. They quantify trade-offs in accuracy between…
Thermodynamic entropy, as defined by Clausius, characterizes macroscopic observations of a system based on phenomenological quantities such as temperature and heat. In contrast, information-theoretic entropy, introduced by Shannon, is a…
This report addresses state inference for hidden Markov models. These models rely on unobserved states, which often have a meaningful interpretation. This makes it necessary to develop diagnostic tools for quantification of state…
Epistemic uncertainty in neural networks is commonly modeled using two second-order paradigms: distribution-based representations, which rely on posterior parameter distributions, and set-based representations based on credal sets (convex…