相关论文: On structural and practical identifiability
Experience in the physical sciences suggests that the only realistic means of understanding complex systems is through the use of mathematical models. Typically, this has come to mean the identification of quantitative models expressed as…
The focus of this thesis is on the applications of nonlinear dynamical systems in bioengineering which are mainly used in large-scale and generally categorised into two groups: (1) dynamical systems from biology (2) dynamical systems for…
This paper explores the identification and estimation of nonseparable panel data models. We show that the structural function is nonparametrically identified when it is strictly increasing in a scalar unobservable variable, the conditional…
This paper studies the problems of identifiability and estimation in high-dimensional nonparametric latent structure models. We introduce an identifiability theorem that generalizes existing conditions, establishing a unified framework…
The main features of the statistical approach to inverse problems are described on the example of a linear model with additive noise. The approach does not use any Bayesian hypothesis regarding an unknown object; instead, the standard…
In this paper, a pointwise weighted identity for some stochastic partial differential operators (with complex principal parts) is established. This identity presents a unified approach in studying the controllability, observability and…
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…
We consider structure discovery of undirected graphical models from observational data. Inferring likely structures from few examples is a complex task often requiring the formulation of priors and sophisticated inference procedures.…
Many practical problems can be understood as the search for a state of affairs that extends a fixed partial state of affairs, the \emph{environment}, while satisfying certain conditions that are formally specified. Such problems are found…
Modeling biological processes is a highly demanding task because not all processes are fully understood. Mathematical models allow us to test hypotheses about possible mechanisms of biological processes. The mathematical mechanisms…
Physics-informed neural networks have emerged as an alternative method for solving partial differential equations. However, for complex problems, the training of such networks can still require high-fidelity data which can be expensive to…
Proximal causal inference is a recently proposed framework for evaluating causal effects in the presence of unmeasured confounding. For point identification of causal effects, it leverages a pair of so-called treatment and outcome…
This review article provides an overview of structurally oriented experimental datasets that can be used to benchmark protein force fields, focusing on data generated by nuclear magnetic resonance (NMR) spectroscopy and room temperature…
Understanding output variance is critical in modeling nonlinear dynamic systems, as it reflects the system's sensitivity to input variations and feature interactions. This work presents a methodology for dynamically determining relevance…
The Fisher information matrix (FIM) is a key quantity in statistics as it is required for example for evaluating asymptotic precisions of parameter estimates, for computing test statistics or asymptotic distributions in statistical testing,…
The feasibility of uniquely estimating parameters of dynamical systems from observations is a widely discussed aspect of mathematical modelling. Several approaches have been published for analyzing identifiability. However, they are…
Estimating the governing equation parameter values is essential for integrating experimental data with scientific theory to understand, validate, and predict the dynamics of complex systems. In this work, we propose a new method for…
Dynamical systems with quadratic or polynomial drift exhibit complex dynamics, yet compared to nonlinear systems in general form, are often easier to analyze, simulate, control, and learn. Results going back over a century have shown that…
Despite many advances in computational modeling of protein structures, these methods have not been widely utilized by experimental structural biologists. Two major obstacles are preventing the transition from a purely-experimental to a…
Identifiability of parameters is a fundamental prerequisite for model identification. It concerns uniqueness of the model parameters determined from experimental or simulated observations. This dissertation specifically deals with…