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 …
Deep learning for physical processes: Incorporating prior scientific knowledge
We consider the use of deep learning methods for modeling complex phenomena like those
occurring in natural physical processes. With the large amount of data gathered on these …
occurring in natural physical processes. With the large amount of data gathered on these …
[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 …
Hilbert space methods for reduced-rank Gaussian process regression
This paper proposes a novel scheme for reduced-rank Gaussian process regression. The
method is based on an approximate series expansion of the covariance function in terms of …
method is based on an approximate series expansion of the covariance function in terms of …
Estimation of time-varying reproduction numbers underlying epidemiological processes: A new statistical tool for the COVID-19 pandemic
The coronavirus pandemic has rapidly evolved into an unprecedented crisis. The
susceptible-infectious-removed (SIR) model and its variants have been used for modeling …
susceptible-infectious-removed (SIR) model and its variants have been used for modeling …
Macroscopic traffic flow modeling with physics regularized Gaussian process: A new insight into machine learning applications in transportation
Despite the wide implementation of machine learning (ML) technique in traffic flow modeling
recently, those data-driven approaches often fall short of accuracy in the cases with a small …
recently, those data-driven approaches often fall short of accuracy in the cases with a small …
Transition state clustering: Unsupervised surgical trajectory segmentation for robot learning
Demonstration trajectories collected from a supervisor in teleoperation are widely used for
robot learning, and temporally segmenting the trajectories into shorter, less-variable …
robot learning, and temporally segmenting the trajectories into shorter, less-variable …
A Gaussian process latent force model for joint input-state estimation in linear structural systems
The problem of combined state and input estimation of linear structural systems based on
measured responses and a priori knowledge of structural model is considered. A novel …
measured responses and a priori knowledge of structural model is considered. A novel …
Modeling and interpolation of the ambient magnetic field by Gaussian processes
Anomalies in the ambient magnetic field can be used as features in indoor positioning and
navigation. By using Maxwell's equations, we derive and present a Bayesian nonparametric …
navigation. By using Maxwell's equations, we derive and present a Bayesian nonparametric …
Learning dynamical systems from partial observations
We consider the problem of forecasting complex, nonlinear space-time processes when
observations provide only partial information of on the system's state. We propose a natural …
observations provide only partial information of on the system's state. We propose a natural …