Related papers: A Tracking Approach to Parameter Estimation in Lin…

In this set of papers we formulate a stand alone method to derive maximal number of linearizing transformations for nonlinear ordinary differential equations (ODEs) of any order including coupled ones from a knowledge of fewer number of…

This paper presents a new and efficient method for the construction of optimal designs for regression models with dependent error processes. In contrast to most of the work in this field, which starts with a model for a finite number of…

Dynamic systems are ubiquitous in nature and are used to model many processes in biology, chemistry, physics, medicine, and engineering. In particular, systems of ordinary differential equations are commonly used for the mathematical…

This paper discusses the problem of adaptive estimation of a univariate object like the value of a regression function at a given point or a linear functional in a linear inverse problem. We consider an adaptive procedure originated from…

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…

Combinations of neural ODEs with recurrent neural networks (RNN), like GRU-ODE-Bayes or ODE-RNN are well suited to model irregularly observed time series. While those models outperform existing discrete-time approaches, no theoretical…

We consider the problem of making nonparametric inference in a class of multi-dimensional diffusions in divergence form, from low-frequency data. Statistical analysis in this setting is notoriously challenging due to the intractability of…

We present results on parameter estimation and non-parameter estimation of the linear partially observed Gaussian system of stochastic differential equations. We propose new one-step estimators which have the same asymptotic properties as…

We consider the problem of parameter estimation for the partially observed linear stochastic differential equation. We assume that the unobserved Ornstein-Uhlenbeck process depends on some unknown parameter and estimate the unobserved…

Ordinary differential equations (ODEs) provide a powerful framework for modeling dynamic systems arising in a wide range of scientific domains. However, most existing ODE methods focus on a single system, and do not adequately address the…

We propose a reduced-order modeling approach for nonlinear, parameter-dependent ordinary differential equations (ODE). Dimensionality reduction is achieved using nonlinear maps represented by autoencoders. The resulting low-dimensional ODE…

Neural ordinary differential equations are an attractive option for modelling temporal dynamics. However, a fundamental issue is that the solution to an ordinary differential equation is determined by its initial condition, and there is no…

Machines of all kinds from vehicles to industrial equipment are increasingly instrumented with hundreds of sensors. Using such data to detect anomalous behaviour is critical for safety and efficient maintenance. However, anomalies occur…

The neural ordinary differential equation (ODE) framework has emerged as a powerful tool for developing accelerated surrogate models of complex physical systems governed by partial differential equations (PDEs). A popular approach for PDE…

A general, variational approach to derive low-order reduced systems is presented. The approach is based on the concept of optimal parameterizing manifold (OPM) that substitutes the more classical notions of invariant or slow manifold when…

Uncovering the underlying ordinary differential equations (ODEs) that govern dynamic systems is crucial for advancing our understanding of complex phenomena. Traditional symbolic regression methods often struggle to capture the temporal…

Opportunistic detection rules (ODRs) are variants of fixed-sample-size detection rules in which the statistician is allowed to make an early decision on the alternative hypothesis opportunistically based on the sequentially observed…

Estimation of parameters is a crucial part of model development. When models are deterministic, one can minimise the fitting error; for stochastic systems one must be more careful. Broadly parameterisation methods for stochastic dynamical…

Uncertainty estimation aims to evaluate the confidence of a trained deep neural network. However, existing uncertainty estimation approaches rely on low-dimensional distributional assumptions and thus suffer from the high dimensionality of…

We propose a general approach to construct weighted likelihood estimating equations with the aim of obtaining robust parameter estimates. We modify the standard likelihood equations by incorporating a weight that reflects the statistical…