Related papers: Algebraic identifiability of partial differential …
Many real-world processes and phenomena are modeled using systems of ordinary differential equations with parameters. Given such a system, we say that a parameter is globally identifiable if it can be uniquely recovered from input and…
Structural global parameter identifiability indicates whether one can determine a parameter's value in an ODE model from given inputs and outputs. If a given model has parameters for which there is exactly one value, such parameters are…
Data-driven modeling of dynamical systems often faces numerous data-related challenges. A fundamental requirement is the existence of a unique set of parameters for a chosen model structure, an issue commonly referred to as identifiability.…
Structural global parameter identifiability indicates whether one can determine a parameter's value from given inputs and outputs in the absence of noise. If a given model has parameters for which there may be infinitely many values, such…
Interpreting data with mathematical models is an important aspect of real-world industrial and applied mathematical modeling. Often we are interested to understand the extent to which a particular set of data informs and constrains model…
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…
Structural identifiability concerns the question of which unknown parameters of a model can be recovered from (perfect) input-output data. If all of the parameters of a model can be recovered from data, the model is said to be identifiable.…
Solving partial differential equations (PDEs) can be prohibitively expensive using traditional numerical methods. Deep learning-based surrogate models typically specialize in a single PDE with fixed parameters. We present a framework for…
Elimination of unknowns in a system of differential equations is often required when analysing (possibly nonlinear) dynamical systems models, where only a subset of variables are observable. One such analysis, identifiability, often relies…
We introduce and analyze a method of learning-informed parameter identification for partial differential equations (PDEs) in an all-at-once framework. The underlying PDE model is formulated in a rather general setting with three unknowns:…
Structural identifiability is an important property of parametric ODE models. When conducting an experiment and inferring the parameter value from the time-series data, we want to know if the value is globally, locally, or non-identifiable.…
Linear compartmental models are a widely used tool for analyzing systems arising in biology, medicine, and more. In such settings, it is essential to know whether model parameters can be recovered from experimental data. This is the…
Learning the unknown causal parameters of a linear structural causal model is a fundamental task in causal analysis. The task, known as the problem of identification, asks to estimate the parameters of the model from a combination of…
Many statistical models are algebraic in that they are defined by polynomial constraints or by parameterizations that are polynomial or rational maps. This opens the door for tools from computational algebraic geometry. These tools can be…
A key step in mechanistic modelling of dynamical systems is to conduct a structural identifiability analysis. This entails deducing which parameter combinations can be estimated from a given set of observed outputs. The standard…
Parameter identifiability is a structural property of an ODE model for recovering the values of parameters from the data (i.e., from the input and output variables). This property is a prerequisite for meaningful parameter identification in…
We present a Bayesian methodology for infinite as well as finite dimensional parameter identification for partial differential equation models. The Bayesian framework provides a rigorous mathematical framework for incorporating prior…
Parameter identifiability describes whether, for a given differential model, one can determine parameter values from model equations. Knowing global or local identifiability properties allows construction of better practical experiments to…
This paper presents a method for investigating, through an automatic procedure, the (lack of) identifiability of parametrized dynamical models. This method takes into account constraints on parameters and returns parameters whose…
Structural identifiability is a property of an ODE model with parameters that allows for the parameters to be determined from continuous noise-free data. This is a natural prerequisite for practical identifiability. Conducting multiple…