There is a growing consensus that solutions to complex science and engineering problems
require novel methodologies that are able to integrate traditional physics-based modeling …

Kernel methods are among the most popular techniques in machine learning. From a
regularization perspective they play a central role in regularization theory as they provide a …

In the context of science, the well-known adage" a picture is worth a thousand words" might
well be" a model is worth a thousand datasets." In this manuscript we introduce the SciML …

There is a growing consensus that solutions to complex science and engineering problems
require novel methodologies that are able to integrate traditional physics-based modeling …

Stochastic differential equations are differential equations whose solutions are stochastic
processes. They exhibit appealing mathematical properties that are useful in modeling …

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

Scientific computing is increasingly incorporating the advancements in machine learning
and the ability to work with large amounts of data. At the same time, machine learning …

In this paper, we offer a gentle introduction to Gaussian processes for time-series data
analysis. The conceptual framework of Bayesian modelling for time-series data is discussed …

Recently there has been an increasing interest in regression methods that deal with multiple
outputs. This has been motivated partly by frameworks like multitask learning, multisensor …

The coronavirus pandemic has rapidly evolved into an unprecedented crisis. The
susceptible-infectious-removed (SIR) model and its variants have been used for modeling …