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Automated analysis of complex systems based on multiple readouts remains a challenge. Change point detection algorithms are aimed to locating abrupt changes in the time series behaviour of a process. In this paper, we present a novel change…
Accurately solving partial differential equations (PDEs) is critical to understanding complex scientific and engineering phenomena, yet traditional numerical solvers are computationally expensive. Surrogate models offer a more efficient…
The EM-algorithm is a general procedure to get maximum likelihood estimates if part of the observations on the variables of a network are missing. In this paper a stochastic version of the algorithm is adapted to probabilistic neural…
Partial differential equations (PDEs) play a crucial role in studying a vast number of problems in science and engineering. Numerically solving nonlinear and/or high-dimensional PDEs is often a challenging task. Inspired by the traditional…
We propose machine learning methods for solving fully nonlinear partial differential equations (PDEs) with convex Hamiltonian. Our algorithms are conducted in two steps. First the PDE is rewritten in its dual stochastic control…
Neural network surrogate models have emerged as a promising approach to model solution fields for a wide variety of boundary value problems encountered in physical modeling. Stochastic problems represent an area of particularly high…
Uncertainty quantification appears today as a crucial point in numerous branches of science and engineering. In the past two decades, a growing interest has been devoted to stochastic finite element method (SFEM) for the propagation of…
Numerical models based on physics represent the state-of-the-art in earth system modeling and comprise our best tools for generating insights and predictions. Despite rapid growth in computational power, the perceived need for higher model…
In the context of uncertainty quantification, computational models are required to be repeatedly evaluated. This task is intractable for costly numerical models. Such a problem turns out to be even more severe for stochastic simulators, the…
In recent years, there has been a growing interest in data-driven evolutionary algorithms (DDEAs) employing surrogate models to approximate the objective functions with limited data. However, current DDEAs are primarily designed for…
Multiscale dynamical systems, modeled by high-dimensional stiff ordinary differential equations (ODEs) with wide-ranging characteristic timescales, arise across diverse fields of science and engineering, but their numerical solvers often…
There has been an arising trend of adopting deep learning methods to study partial differential equations (PDEs). In this paper, we introduce a deep recurrent framework for solving time-dependent PDEs without generating large scale data…
We present two effective methods for solving high-dimensional partial differential equations (PDE) based on randomized neural networks. Motivated by the universal approximation property of this type of networks, both methods extend the…
We present a novel approach for solving steady-state stochastic partial differential equations (PDEs) with high-dimensional random parameter space. The proposed approach combines spatial domain decomposition with basis adaptation for each…
In the field of surrogate modeling, polynomial chaos expansion (PCE) allows practitioners to construct inexpensive yet accurate surrogates to be used in place of the expensive forward model simulations. For black-box simulations,…
Generative models and those with computationally intractable likelihoods are widely used to describe complex systems in the natural sciences, social sciences, and engineering. Fitting these models to data requires likelihood-free inference…
Motivated by the need to identify erroneous disparity assignments, various approaches for uncertainty and confidence estimation of dense stereo matching have been presented in recent years. As in many other fields, especially deep learning…
Physics-informed deep learning approaches have been developed to solve forward and inverse stochastic differential equation (SDE) problems with high-dimensional stochastic space. However, the existing deep learning models have difficulties…
Time dependent reliability analysis and uncertainty quantification of structural system subjected to stochastic forcing function is a challenging endeavour as it necessitates considerable computational time. We investigate the efficacy of…
Recent developments in mechanical, aerospace, and structural engineering have driven a growing need for efficient ways to model and analyse structures at much larger and more complex scales than before. While established numerical methods…