A survey of uncertainty quantification in machine learning for space weather prediction
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 …
learning (ML) has emerged as a preferred methodology for data analysis and prediction …
Machine learning of linear differential equations using Gaussian processes
M Raissi, P Perdikaris, GE Karniadakis - Journal of Computational Physics, 2017 - Elsevier
This work leverages recent advances in probabilistic machine learning to discover
governing equations expressed by parametric linear operators. Such equations involve, but …
governing equations expressed by parametric linear operators. Such equations involve, but …
State estimation of a physical system with unknown governing equations
State estimation is concerned with reconciling noisy observations of a physical system with
the mathematical model believed to predict its behaviour for the purpose of inferring …
the mathematical model believed to predict its behaviour for the purpose of inferring …
[HTML][HTML] Physics informed machine learning: Seismic wave equation
S Karimpouli, P Tahmasebi - Geoscience Frontiers, 2020 - Elsevier
Similar to many fields of sciences, recent deep learning advances have been applied
extensively in geosciences for both small-and large-scale problems. However, the necessity …
extensively in geosciences for both small-and large-scale problems. However, the necessity …
Gene regulatory network inference: an introductory survey
VA Huynh-Thu, G Sanguinetti - Gene regulatory networks: Methods and …, 2019 - Springer
Gene regulatory networks are powerful abstractions of biological systems. Since the advent
of high-throughput measurement technologies in biology in the late 1990s, reconstructing …
of high-throughput measurement technologies in biology in the late 1990s, reconstructing …
Random feature expansions for deep Gaussian processes
The composition of multiple Gaussian Processes as a Deep Gaussian Process DGP
enables a deep probabilistic nonparametric approach to flexibly tackle complex machine …
enables a deep probabilistic nonparametric approach to flexibly tackle complex machine …
A survey of Bayesian calibration and physics-informed neural networks in scientific modeling
FAC Viana, AK Subramaniyan - Archives of Computational Methods in …, 2021 - Springer
Computer simulations are used to model of complex physical systems. Often, these models
represent the solutions (or at least approximations) to partial differential equations that are …
represent the solutions (or at least approximations) to partial differential equations that are …
Differential equations in data analysis
I Dattner - Wiley Interdisciplinary Reviews: Computational …, 2021 - Wiley Online Library
Differential equations have proven to be a powerful mathematical tool in science and
engineering, leading to better understanding, prediction, and control of dynamic processes …
engineering, leading to better understanding, prediction, and control of dynamic processes …
Probabilistic ODE solvers with Runge-Kutta means
M Schober, DK Duvenaud… - Advances in neural …, 2014 - proceedings.neurips.cc
Runge-Kutta methods are the classic family of solvers for ordinary differential equations
(ODEs), and the basis for the state of the art. Like most numerical methods, they return point …
(ODEs), and the basis for the state of the art. Like most numerical methods, they return point …
Learning unknown ODE models with Gaussian processes
In conventional ODE modelling coefficients of an equation driving the system state forward
in time are estimated. However, for many complex systems it is practically impossible to …
in time are estimated. However, for many complex systems it is practically impossible to …