Numerical Gaussian Processes for Time-Dependent and Nonlinear Partial Differential Equations
- Computer Science, MathematicsSIAM J. Sci. Comput.
The method circumvents the need for spatial discretization of the differential operators by proper placement of Gaussian process priors and is an attempt to construct structured and data-efficient learning machines, which are explicitly informed by the underlying physics that possibly generated the observed data.
High order linearly implicit methods for evolution equations: How to solve an ODE by inverting only linear systems
- Computer ScienceESAIM: Mathematical Modelling and Numerical Analysis
This paper introduces a new class of numerical methods for the time integration of evolution equations set as Cauchy problems of ODEs or PDEs that are linearly implicit and have high order, and sets suitable definitions of consistency and stability for these methods.
Numerical contributions for the study of sediment transport beneath tidal bores
Une etude de l'impact des mascarets sur le transport des sediments a l'aide de la simulation numerique a ete realisee dans ce travail. En utilisant le logiciel OpenFOAM CFD, nous avons genere 17…
Multi-Fidelity Model Predictive Control of Upstream Energy Production Processes
Multi-Fidelity Model Predictive Control of Upstream Energy Production Processes Ammon Nephi Eaton Department of Chemical Engineering, BYU Doctor of Philosophy Increasing worldwide demand for…
Parameter perturbation extrapolation algorithm for Runge-Kutta methods
- Computer Science
Abstract In this paper, in order to improve the accuracy of extrapolation Runge-Kutta methods, parameter perturbation is introduced on the basis of extrapolation algorithm, i.e., parameter…
Numerical integration of differential-algebraic equations with harmless critical points
Differential-algebraic equations (DAEs) are implicit singular ordinary differential equations, which describe dynamical processes that are restricted by some constraints. In contrast to explicit…
Isomeric trees and the order of Runge-Kutta methods
- Computer Science, MathematicsJ. Comput. Appl. Math.
Learning to Assimilate in Chaotic Dynamical Systems
- Computer ScienceNeurIPS
Amortized assimilation is introduced, a framework for learning to assimilate in dynamical systems from sequences of noisy observations with no need for ground truth data, and is motivated by powerful results from self-supervised denoising to the dynamical system setting through the use of differentiable simulation.
Statistics of Sliding on Periodic and Atomically Flat Surfaces
- PhysicsFrontiers in Mechanical Engineering
Among the so-called analytical models of friction, the most popular and widely used one, the Prandtl-Tomlinson model in one and two dimensions is considered here to numerically describe the sliding…
Dynamics of Glyphosate and Aminomethylphosphonic Acid in Soil Under Conventional and Conservation Tillage
- International Journal of Environmental Research
This study investigates the adsorption and dissipation of glyphosate and the formation/dissipation of AMPA in non-tilled (NT) and conventionally tilled (CT) soil at 0–5 and 5–20 cm depth. Glyphosate…