Efficiently embedding and/or integrating mechanistic information with data-driven models is
essential if it is desired to simultaneously take advantage of both engineering principles and …

With the availability of data and computational technologies in the modern world, machine
learning (ML) has emerged as a preferred methodology for data analysis and prediction …

Physics-informed neural networks (PINNs) have recently emerged as an alternative way of
numerically solving partial differential equations (PDEs) without the need of building …

We developed a new class of physics-informed generative adversarial networks (PI-GANs)
to solve forward, inverse, and mixed stochastic problems in a unified manner based on a …

This work leverages recent advances in probabilistic machine learning to discover
governing equations expressed by parametric linear operators. Such equations involve, but …

Now in its second edition, this accessible text presents a unified Bayesian treatment of state-
of-the-art filtering, smoothing, and parameter estimation algorithms for non-linear state …

For more than two centuries, solutions of differential equations have been obtained either
analytically or numerically based on typically well-behaved forcing and boundary conditions …

We introduce a sampling-based machine learning approach, Monte Carlo fractional physics-
informed neural networks (MC-fPINNs), for solving forward and inverse fractional partial …

Gaussian process regression is a popular Bayesian framework for surrogate modeling of
expensive data sources. As part of a broader effort in scientific machine learning, many …

Electrochemical impedance spectroscopy (EIS) is one of the most important techniques in
electrochemistry. However, analyzing the EIS data is not a simple task. The distribution of …