276 research outputs found
Schroedinger equation on a generic radial grid
In this note, we discuss the choice of radial grid in the numerical
resolution of the Schroedinger equation. We detail the transformation of the
equation resulting from a change of variable and function for a generic radial
grid, using either the explicit or implicit form of the relation describing the
change of variable, and apply it to the log-linear mesh. It is
shown that, in the former case, the first three derivatives of the Lambert
function are required. This complication becomes unnecessary if we adopt the
implicit relation instead.Comment: submitted to High Energy Density Phy
Using AI libraries for Incompressible Computational Fluid Dynamics
Recently, there has been a huge effort focused on developing highly efficient
open source libraries to perform Artificial Intelligence (AI) related
computations on different computer architectures (for example, CPUs, GPUs and
new AI processors). This has not only made the algorithms based on these
libraries highly efficient and portable between different architectures, but
also has substantially simplified the entry barrier to develop methods using
AI. Here, we present a novel methodology to bring the power of both AI software
and hardware into the field of numerical modelling by repurposing AI methods,
such as Convolutional Neural Networks (CNNs), for the standard operations
required in the field of the numerical solution of Partial Differential
Equations (PDEs). The aim of this work is to bring the high performance,
architecture agnosticism and ease of use into the field of the numerical
solution of PDEs. We use the proposed methodology to solve the
advection-diffusion equation, the non-linear Burgers equation and
incompressible flow past a bluff body. For the latter, a convolutional neural
network is used as a multigrid solver in order to enforce the incompressibility
constraint. We show that the presented methodology can solve all these problems
using repurposed AI libraries in an efficient way, and presents a new avenue to
explore in the development of methods to solve PDEs and Computational Fluid
Dynamics problems with implicit methods.Comment: 24 pages, 6 figure
GAN for time series prediction, data assimilation and uncertainty quantification
We propose a new method in which a generative adversarial network (GAN) is
used to quantify the uncertainty of forward simulations in the presence of
observed data. Previously, a method has been developed which enables GANs to
make time series predictions and data assimilation by training a GAN with
unconditional simulations of a high-fidelity numerical model. After training,
the GAN can be used to predict the evolution of the spatial distribution of the
simulation states and observed data is assimilated. In this paper, we describe
the process required in order to quantify uncertainty, during which no
additional simulations of the high-fidelity numerical model are required. These
methods take advantage of the adjoint-like capabilities of generative models
and the ability to simulate forwards and backwards in time. Set within a
reduced-order model framework for efficiency, we apply these methods to a
compartmental model in epidemiology to predict the spread of COVID-19 in an
idealised town. The results show that the proposed method can efficiently
quantify uncertainty in the presence of measurements using only unconditional
simulations of the high-fidelity numerical model.Comment: arXiv admin note: text overlap with arXiv:2105.0772
Towards the Fully-coupled Numerical Modelling of Floating Wind Turbines
AbstractThe aim of this study is to model the interactions between fluids and solids using fully nonlinear models. Non- linearity is important in the context of floating wind turbines, for example, to model breaking waves impacting on the structure and the effect of the solid's elasticity. The fluid- and solid-dynamics equations are solved using two unstructured finite-element models, which are coupled at every time step. Importantly, the coupling ensures that the action-reaction principle is satisfied at a discrete level, independently of the order of representation of the discrete fields. To the authorsâ knowledge, the present algorithm is novel in that it can simultaneously handle: (i) non- matching fluid and solid meshes, (ii) different polynomial orders of the basis functions on each mesh, and (iii) different fluid and solid time steps. First, results are shown for the flow past a fixed actuator-disk immersed in a uniform flow and representing a wind turbine. The present numerical results for the velocity deficit induced by the disk are shown to be in good agreement with the semi-analytical solution, for three values of thrust coefficients. The presence of a non-zero fluid viscosity in the numerical simulation affects wake recovery and fluid entrainment around the disk. Second, the dynamic response of a cylindrical pile is computed when placed at an interface between air and water. The results qualitatively demonstrate that the present models are applicable to the modelling of multiple fluids interacting with a floating solid. This work provides a first-step towards the fully coupled simulation of offshore wind turbines supported by a floating spar
Social communication between virtual characters and children with autism
Children with ASD have difficulty with social communication, particularly joint attention. Interaction in a virtual environment (VE) may be a means for both understanding these difficulties and addressing them. It is first necessary to discover how this population interacts with virtual characters, and whether they can follow joint attention cues in a VE. This paper describes a study in which 32 children with ASD used the ECHOES VE to assist a virtual character in selecting objects by following the characterâs gaze and/or pointing. Both accuracy and reaction time data suggest that children were able to successfully complete the task, and qualitative data further suggests that most children perceived the character as an intentional being with relevant, mutually directed behaviour
Numerical Modelling of Melt Behaviour in the Lower Vessel Head of a Nuclear Reactor
Acknowledgements The authors would like to thank the EPSRC MEMPHIS multi-phase programme grant, the EPSRC Computational modelling for advanced nuclear power plants project and the EU FP7 projects THINS and GoFastR for helping to fund this work.Peer reviewedPublisher PD
An autoencoder-based reduced-order model for eigenvalue problems with application to neutron diffusion
Using an autoencoder for dimensionality reduction, this paper presents a
novel projection-based reduced-order model for eigenvalue problems.
Reduced-order modelling relies on finding suitable basis functions which define
a low-dimensional space in which a high-dimensional system is approximated.
Proper orthogonal decomposition (POD) and singular value decomposition (SVD)
are often used for this purpose and yield an optimal linear subspace.
Autoencoders provide a nonlinear alternative to POD/SVD, that may capture, more
efficiently, features or patterns in the high-fidelity model results.
Reduced-order models based on an autoencoder and a novel hybrid
SVD-autoencoder are developed. These methods are compared with the standard
POD-Galerkin approach and are applied to two test cases taken from the field of
nuclear reactor physics.Comment: 35 pages, 33 figure
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