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Stochastic simulation is widely used to study complex systems composed of various interconnected subprocesses, such as input processes, routing and control logic, optimization routines, and data-driven decision modules. In practice, these…

Feature-importance methods show promise in transforming machine learning models from predictive engines into tools for scientific discovery. However, due to data sampling and algorithmic stochasticity, expressive models can be unstable,…

First principles modeling of physical systems has led to significant technological advances across all branches of science. For nonlinear systems, however, small modeling errors can lead to significant deviations from the true, measured…

Inferring information from a set of acquired data is the main objective of any signal processing (SP) method. In particular, the common problem of estimating the value of a vector of parameters from a set of noisy measurements is at the…

We consider estimation under model misspecification where there is a model mismatch between the underlying system, which generates the data, and the model used during estimation. We propose a model misspecification framework which enables a…

It is known that statistical model selection as well as identification of dynamical equations from available data are both very challenging tasks. Physical systems behave according to their underlying dynamical equations which, in turn, can…

Methods for model parameter estimation, uncertainty quantification and experimental design are summarized in this paper. They are based on the generalized least squares estimator and different approximations of its covariance matrix using…

The concept of random dynamical system is a comparatively recent development combining ideas and methods from the well developed areas of probability theory and dynamical systems. Due to our inaccurate knowledge of the particular physical…

The past century has seen a steady increase in the need of estimating and predicting complex systems and making (possibly critical) decisions with limited information. Although computers have made possible the numerical evaluation of…

Data driven models of dynamical systems help planners and controllers to provide more precise and accurate motions. Most model learning algorithms will try to minimize a loss function between the observed data and the model's predictions.…

Most existing evaluations of explainable machine learning (ML) methods rely on simplifying assumptions or proxies that do not reflect real-world use cases; the handful of more robust evaluations on real-world settings have shortcomings in…

Data-driven discovery of model equations is a powerful approach for understanding the behavior of dynamical systems in many scientific fields. In particular, the ability to learn mathematical models from data would benefit systems biology,…

The ability to construct, use, and revise models is a crucial experimental physics skill. Many existing frameworks describe modeling in science education at introductory levels. However, most have limited applicability to the context of…

Fitting model parameters to experimental data is a common yet often challenging task, especially if the model contains many parameters. Typically, algorithms get lost in regions of parameter space in which the model is unresponsive to…

Model selection methods are used in different scientific contexts to represent a characteristic data set in terms of a reduced number of parameters. Apparently, these methods have not found their way into the literature on multibody systems…

Design-based frameworks of uncertainty are frequently used in settings where the treatment is (conditionally) randomly assigned. This paper develops a design-based framework suitable for analyzing quasi-experimental settings in the social…

Robust inference for stochastic dynamical systems is often hampered by sparse sampling and the absence of closed-form likelihoods. We introduce a Monte Carlo path-inference framework that leverages full-path statistics and bridge processes…

The modeling of complex systems such as ecological or socio-economic systems can be very challenging. Although various modeling approaches exist, they are generally not compatible and mutually consistent, and empirical data often do not…

Mechanistic growth models play a major role in bioprocess engineering, design, and control. Their reasonable predictive power and their high level of interpretability make them an essential tool for computer aided engineering methods.…

Computer models are commonly used to represent a wide range of real systems, but they often involve some unknown parameters. Estimating the parameters by collecting physical data becomes essential in many scientific fields, ranging from…