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Multi-sensor state space models underpin fusion applications in networks of sensors. Estimation of latent parameters in these models has the potential to provide highly desirable capabilities such as network self-calibration. Conventional…
Identifiability is a structural property of any ODE model characterized by a set of unknown parameters. It describes the possibility of determining the values of these parameters from fusing the observations of the system inputs and…
Parameter identifiability is often requisite to the effective application of mathematical models in the interpretation of biological data, however theory applicable to the study of partial differential equations remains limited. We present…
Complex numerical weather prediction models incorporate a variety of physical processes, each described by multiple alternative physical schemes with specific parameters. The selection of the physical schemes and the choice of the…
Likelihood profiling is an efficient and powerful frequentist approach for parameter estimation, uncertainty quantification and practical identifiablity analysis. Unfortunately, these methods cannot be easily applied for stochastic models…
We may attempt to encapsulate what we know about a physical system by a model structure, $S$. This collection of related models is defined by parametric relationships between system features; say observables (outputs), unobservable…
Ordinary differential equation models have become a standard tool for the mechanistic description of biochemical processes. If parameters are inferred from experimental data, such mechanistic models can provide accurate predictions about…
SHAP is a popular method for measuring variable importance in machine learning models. In this paper, we study the algorithm used to estimate SHAP scores and outline its connection to the functional ANOVA decomposition. We use this…
We propose a technique for the design and analysis of adaptation algorithms in dynamical systems. The technique applies both to systems with conventional Lyapunov-stable target dynamics and to ones of which the desired dynamics around the…
Background: Many mathematical models have now been employed across every area of systems biology. These models increasingly involve large numbers of unknown parameters, have complex structure which can result in substantial evaluation time…
Rigorous statistical methods, including parameter estimation with accompanying uncertainties, underpin the validity of scientific discovery, especially in the natural sciences. With increasingly complex data models such as deep learning…
Localization of unknown faults in industrial systems is a difficult task for data-driven diagnosis methods. The classification performance of many machine learning methods relies on the quality of training data. Unknown faults, for example…
Every organism in an environment, whether biological, robotic or virtual, must be able to predict certain aspects of its environment in order to survive or perform whatever task is intended. It needs a model that is capable of estimating…
We propose a novel iterative algorithm for estimating a deterministic but unknown parameter vector in the presence of model uncertainties. This iterative algorithm is based on a system model where an overall noise term describes both, the…
In Hezaveh et al. 2017 we showed that deep learning can be used for model parameter estimation and trained convolutional neural networks to determine the parameters of strong gravitational lensing systems. Here we demonstrate a method for…
Prediction of events is the challenge in many different disciplines, from meteorology to finance; the more this task is difficult, the more a system is {\it complex}. Nevertheless, even according to this restricted definition, a general…
A special aspect of parameter identification in finite-strain elasto-plasticity is considered. Namely, we analyze the impact of the measurement errors on the resulting set of material parameters. In order to define the sensitivity of…
Multivariable parametric models are critical for designing, controlling, and optimizing the performance of engineered systems. The main aim of this paper is to develop a parametric identification strategy that delivers accurate and…
Non-stationary systems are found throughout the world, from climate patterns under the influence of variation in carbon dioxide concentration, to brain dynamics driven by ascending neuromodulation. Accordingly, there is a need for methods…
This paper deals with the problem of formulating an adaptive Model Predictive Control strategy for constrained uncertain systems. We consider a linear system, in presence of bounded time varying additive uncertainty. The uncertainty is…