Related papers: Physics-informed Gaussian process model for Euler-…

Reliable prediction of turbulent flows is an important necessity across different fields of science and engineering. In Computational Fluid Dynamics (CFD) simulations, the most common type of models are eddy viscosity models that are…

Neural Networks (NN) has been used in many areas with great success. When a NN's structure (Model) is given, during the training steps, the parameters of the model are determined using an appropriate criterion and an optimization algorithm…

Engineering design and scientific analysis rely upon computer simulations of turbulent fluid flows using turbulence models. These turbulence models are empirical and approximate, leading to large uncertainties in their predictions that…

We introduce a methodology for nonlinear inverse problems using a variational Bayesian approach where the unknown quantity is a spatial field. A structured Bayesian Gaussian process latent variable model is used both to construct a…

Multi-output regression problems are commonly encountered in science and engineering. In particular, multi-output Gaussian processes have been emerged as a promising tool for modeling these complex systems since they can exploit the…

Direct numerical simulation of hierarchical materials via homogenization-based concurrent multiscale models poses critical challenges for 3D large scale engineering applications, as the computation of highly nonlinear and path-dependent…

We introduce a Bayesian Gaussian process latent variable model that explicitly captures spatial correlations in data using a parameterized spatial kernel and leveraging structure-exploiting algebra on the model covariance matrices for…

Accurate characterization of subsurface heterogeneity is challenging but essential for applications such as reservoir pressure management, geothermal energy extraction and CO$_2$, H$_2$, and wastewater injection operations. This challenge…

This study introduces a physics-based machine learning framework for modeling both brittle and ductile fractures. Unlike physics-informed neural networks, which solve partial differential equations by embedding physical laws as soft…

The intersection of physics and machine learning has given rise to the physics-enhanced machine learning (PEML) paradigm, aiming to improve the capabilities and reduce the individual shortcomings of data- or physics-only methods. In this…

In this work, we present a new class of models, called uncertain-input models, that allows us to treat system-identification problems in which a linear system is subject to a partially unknown input signal. To encode prior information about…

As a nonlocal extension of continuum mechanics, peridynamics has been widely and effectively applied in different fields where discontinuities in the field variables arise from an initially continuous body. An important component of the…

We introduce a new, rigorously-formulated Bayesian meta-learning algorithm that learns a probability distribution of model parameter prior for few-shot learning. The proposed algorithm employs a gradient-based variational inference to infer…

Data-driven machine learning models often require extensive datasets, which can be costly or inaccessible, and their predictions may fail to comply with established physical laws. Current approaches for incorporating physical priors…

Data-driven methods have become increasingly more prominent for musculoskeletal modelling due to their conceptually intuitive simple and fast implementation. However, the performance of a pre-trained data-driven model using the data from…

Gaussian process regression is a powerful method for predicting states based on given data. It has been successfully applied for probabilistic predictions of structural systems to quantify, for example, the crack growth in mechanical…

The accurate modelling of structural dynamics is crucial across numerous engineering applications, such as Structural Health Monitoring (SHM), seismic analysis, and vibration control. Often, these models originate from physics-based…

Physics-based simulations are often used to model and understand complex physical systems and processes in domains like fluid dynamics. Such simulations, although used frequently, have many limitations which could arise either due to the…

Passivity-based control ensures system stability by leveraging dissipative properties and is widely applied in electrical and mechanical systems. Port-Hamiltonian systems (PHS), in particular, are well-suited for interconnection and damping…

This paper presents the potential of applying physics-informed neural networks for solving nonlinear multiphysics problems, which are essential to many fields such as biomedical engineering, earthquake prediction, and underground energy…