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The Frequency Response Functions (FRFs) are the most widely used functions to characterise the dynamic behaviour of structures. The natural frequencies and damping behaviour can be easily and quickly detected from a Bode diagram. The modal…
We propose a dynamic factor model (DFM) where the latent factors are linked to observed variables with unknown and potentially nonlinear functions. The key novelty and source of flexibility of our approach is a nonparametric observation…
Continuous-time random disturbances (also called stochastic excitations) due to increasing renewable generation have an increasing impact on power system dynamics; However, except from the Monte Carlo simulation, most existing methods for…
Parameter identification and comparison of dynamical systems is a challenging task in many fields. Bayesian approaches based on Gaussian process regression over time-series data have been successfully applied to infer the parameters of a…
We focus on variational inference in dynamical systems where the discrete time transition function (or evolution rule) is modelled by a Gaussian process. The dominant approach so far has been to use a factorised posterior distribution,…
Accurate prediction of structural dynamics is imperative for preserving digital twin fidelity throughout operational lifetimes. Parametric models with fixed nominal parameters often omit critical physical effects due to simplifications in…
We propose a stochastic process for stock movements that, with just one source of Brownian noise, has an instantaneous volatility that rises from a type of statistical feedback across many time scales. This results in a stationary…
Heterogeneous diffusion processes are prevalent in various fields, including the motion of proteins in living cells, the migratory movement of birds and mammals, and finance. These processes are often characterized by time-varying dynamics,…
Differential equations based on physical principals are used to represent complex dynamic systems in all fields of science and engineering. Through repeated use in both academics and industry, these equations have been shown to represent…
In complex physical systems, conventional differential equations often fall short in capturing non-local and memory effects, as they are limited to local dynamics and integer-order interactions. This study introduces a stepwise data-driven…
Complex systems are sometimes subject to non Gaussian alpha stable Levy fluctuations. A new method is devised to estimate this uncertain parameter and other system parameters, using observations on either mean exit time or escape…
We introduce a flexible, scalable Bayesian inference framework for nonlinear dynamical systems characterised by distinct and hierarchical variability at the individual, group, and population levels. Our model class is a generalisation of…
Knowledge of the force time history of a structure is essential to assess its behaviour, ensure safety and maintain reliability. However, direct measurement of external forces is often challenging due to sensor limitations, unknown force…
The Gaussian phase-space representation can be used to implement quantum dynamics for fermionic particles numerically. To improve numerical results, we explore the use of dynamical diffusion gauges in such implementations. This is achieved…
This study is motivated by the need to develop an efficient numerical model to simulate non-uniform interfacial degradation of reinforcing steel in concrete in an accelerated corrosion setup. In this study, a multi physics finite element…
Quantum molecular dynamics requires an accurate representation of the molecular potential energy surface from a minimal number of electronic structure calculations, particularly for nonadiabatic dynamics where excited states are required.…
A Gaussian operator basis provides a means to formulate phase-space simulations of the real- and imaginary-time evolution of quantum systems. Such simulations are guaranteed to be exact while the underlying distribution remains…
Discrete-time fractional-order dynamical systems (DT-FODS) have found innumerable applications in the context of modeling spatiotemporal behaviors associated with long-term memory. Applications include neurophysiological signals such as…
Friction modeling has always been a challenging problem due to the complexity of real physical systems. Although a few state-of-the-art structured data-driven methods show their efficiency in nonlinear system modeling, deterministic…
In applied sciences, we often deal with deterministic simulation models that are too slow for simulation-intensive tasks such as calibration or real-time control. In this paper, an emulator for a generic dynamic model, given by a system of…