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A well-established approach for inferring full displacement and stress fields from possibly sparse data is to calibrate the parameter of a given constitutive model using a Bayesian update. After calibration, a (stochastic) forward…
We consider the problem of evaluating risk for a system that is modeled by a complex stochastic simulation with many possible input parameter values. Two sources of computational burden can be identified: the effort associated with…
In this paper, we propose a stochastic dynamic model for earthquake rupture and suggest that the Langevin equation of frictions may be used for interpreting the slip distributions of rupture processes in earthquakes. The steady-state…
A stochastic approach based on generalized Polynomial Chaos (gPC) is used to quantify the error in Large-Eddy Simulation (LES) of a spatially-evolving mixing layer flow and its sensitivity to different simulation parameters, viz. the grid…
The Polynomial Chaos Expansion (PCE) technique recovers a finite second order random variable exploiting suitable linear combinations of orthogonal polynomials which are functions of a given stochas- tic quantity {\xi}, hence acting as a…
We propose a new method to test the effectiveness of a spatial point process forecast based on a log-likelihood score for predicted point density and the information gain for events that actually occurred in the test period. The method…
Stochastic simulators exhibit intrinsic stochasticity due to unobservable, uncontrollable, or unmodeled input variables, resulting in random outputs even at fixed input conditions. Such simulators are common across various scientific…
Stochastic partial differential equations (SPDEs) are ubiquitous in engineering and computational sciences. The stochasticity arises as a consequence of uncertainty in input parameters, constitutive relations, initial/boundary conditions,…
Epileptic seizure activity shows complicated dynamics in both space and time. To understand the evolution and propagation of seizures spatially extended sets of data need to be analysed. We have previously described an efficient filtering…
The application of polynomial chaos expansions (PCEs) to the propagation of uncertainties in stochastic dynamical models is well-known to face challenging issues. The accuracy of PCEs degenerates quickly in time. Thus maintaining a…
In modern engineering, physical processes are modelled and analysed using advanced computer simulations, such as finite element models. Furthermore, concepts of reliability analysis and robust design are becoming popular, hence, making…
Global pandemics, such as the recent COVID-19 crisis, highlight the need for stochastic epidemic models that can capture the randomness inherent in the spread of disease. Such models must be accompanied by methods for estimating parameters…
In this work we provide a simple estimation procedure for a general frailty model for analysis of prospective correlated failure times. Rigorous large-sample theory for the proposed estimators of both the regression coefficient vector and…
The spatio-temporal properties of seismicity give us incisive insight into the stress state evolution and fault structures of the crust. Empirical models based on self-exciting point-processes continue to provide an important tool for…
Data driven approaches have the potential to make modeling complex, nonlinear physical phenomena significantly more computationally tractable. For example, computational modeling of fracture is a core challenge where machine learning…
In this work, we consider systems that are subjected to intermittent instabilities due to external stochastic excitation. These intermittent instabilities, though rare, have a large impact on the probabilistic response of the system and…
Modeling the time-varying covariance structures of high-dimensional variables is critical across diverse scientific and industrial applications; however, existing approaches exhibit notable limitations in either modeling flexibility or…
Stochastic simulators are ubiquitous in many fields of applied sciences and engineering. In the context of uncertainty quantification and optimization, a large number of simulations is usually necessary, which becomes intractable for…
This paper tackles the challenge of parameter calibration in stochastic models, particularly in scenarios where the likelihood function is unavailable in an analytical form. We introduce a gradient-based simulated parameter estimation…
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…