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In several applications such as databases, planning, and sensor networks, parameters such as selectivity, load, or sensed values are known only with some associated uncertainty. The performance of such a system (as captured by some…
In this paper, we give an overview of the differential algebra approach to identifiability, and then note a very simple observation about input-output equivalence and identifiability, that describes the identifiability equivalence between…
A novel data-driven method for formal verification is proposed to study complex systems operating in safety-critical domains. The proposed approach is able to formally verify discrete-time stochastic dynamical systems against temporal logic…
Balancing the model complexity and the representation capability towards the process to be captured remains one of the main challenges in nonlinear system identification. One possibility to reduce model complexity is to impose structure on…
Reduced order modeling (ROM) techniques are numerical methods that approximate the solution of parametric partial differential equation (PDE) by properly combining the high-fidelity solutions of the problem obtained for several…
Motivated by certain applications from physics, biochemistry, economics, and computer science, in which the objects under investigation are not accessible because of various limitations, we propose a trial-and-error model to examine…
Mechanistic dynamic models of biochemical networks such as Ordinary Differential Equations (ODEs) contain unknown parameters like the reaction rate constants and the initial concentrations of the compounds. The large number of parameters as…
We developed a novel approach to identification and model testing in linear structural equation models (SEMs) based on auxiliary variables (AVs), which generalizes a widely-used family of methods known as instrumental variables. The…
Causal models communicate our assumptions about causes and effects in real-world phe- nomena. Often the interest lies in the identification of the effect of an action which means deriving an expression from the observed probability…
The identifiability problem for interventions aims at assessing whether the total effect of some given interventions can be written with a do-free formula, and thus be computed from observational data only. We study this problem,…
It has been recognized that using time-varying initialization functions to solve the initial value problem of fractional-order systems (FOS) is both complex and essential in defining the dynamical behavior of the states of FOSs. In this…
This paper presents a kernel-based framework for physics-informed nonlinear system identification. The key contribution is a structured methodology that extends kernel-based techniques to seamlessly embed partially known physics-based…
Using mathematical models to assist in the interpretation of experiments is becoming increasingly important in research across applied mathematics, and in particular in biology and ecology. In this context, accurate parameter estimation is…
Mathematical modelling is a widely used approach to understand and interpret clinical trial data. This modelling typically involves fitting mechanistic mathematical models to data from individual trial participants. Despite the widespread…
We revisit identification based on timing and information set assumptions in structural models, which have been used in the context of production functions, demand equations, and hedonic pricing models (e.g. Olley and Pakes (1996), Blundell…
Partial differential equation (PDE) models are widely used in engineering and natural sciences to describe spatio-temporal processes. The parameters of the considered processes are often unknown and have to be estimated from experimental…
In safety-critical applications, language models should be able to characterize their uncertainty with meaningful probabilities. Many uncertainty quantification approaches require supervised data; however, finding suitable unseen…
The goal of this article is to study fundamental mechanisms behind so-called indirect and direct data-driven control for unknown systems. Specifically, we consider policy iteration applied to the linear quadratic regulator problem. Two…
Solution of Ordinary Differential Equation (ODE) model of dynamical system may not agree with its observed values. Often this discrepancy can be attributed to unmodeled forcings in the evolution rule of the dynamical system. In this…