144,665 research outputs found
Path-tracing Monte Carlo Library for 3D Radiative Transfer in Highly Resolved Cloudy Atmospheres
Interactions between clouds and radiation are at the root of many
difficulties in numerically predicting future weather and climate and in
retrieving the state of the atmosphere from remote sensing observations. The
large range of issues related to these interactions, and in particular to
three-dimensional interactions, motivated the development of accurate radiative
tools able to compute all types of radiative metrics, from monochromatic, local
and directional observables, to integrated energetic quantities. In the
continuity of this community effort, we propose here an open-source library for
general use in Monte Carlo algorithms. This library is devoted to the
acceleration of path-tracing in complex data, typically high-resolution
large-domain grounds and clouds. The main algorithmic advances embedded in the
library are those related to the construction and traversal of hierarchical
grids accelerating the tracing of paths through heterogeneous fields in
null-collision (maximum cross-section) algorithms. We show that with these
hierarchical grids, the computing time is only weakly sensitivive to the
refinement of the volumetric data. The library is tested with a rendering
algorithm that produces synthetic images of cloud radiances. Two other examples
are given as illustrations, that are respectively used to analyse the
transmission of solar radiation under a cloud together with its sensitivity to
an optical parameter, and to assess a parametrization of 3D radiative effects
of clouds.Comment: Submitted to JAMES, revised and submitted again (this is v2
EuclidNet: Deep Visual Reasoning for Constructible Problems in Geometry
In this paper, we present a deep learning-based framework for solving
geometric construction problems through visual reasoning, which is useful for
automated geometry theorem proving. Constructible problems in geometry often
ask for the sequence of straightedge-and-compass constructions to construct a
given goal given some initial setup. Our EuclidNet framework leverages the
neural network architecture Mask R-CNN to extract the visual features from the
initial setup and goal configuration with extra points of intersection, and
then generate possible construction steps as intermediary data models that are
used as feedback in the training process for further refinement of the
construction step sequence. This process is repeated recursively until either a
solution is found, in which case we backtrack the path for a step-by-step
construction guide, or the problem is identified as unsolvable. Our EuclidNet
framework is validated on complex Japanese Sangaku geometry problems,
demonstrating its capacity to leverage backtracking for deep visual reasoning
of challenging problems.Comment: Accepted by 2nd MATH-AI Workshop at NeurIPS'2
Scalable macromodelling of microwave system responses using sequential sampling with path-simplexes
A scattered sequential sampling algorithm for the automatic construction of stable and passive scalable macromodels of parameterised system responses with a well-conditioned refinement strategy using path-simplexes is proposed. The method is tailored towards the local scalable macromodelling schemes on scattered grids. A pertinent numerical example validates the proposed approach
The DUNE-ALUGrid Module
In this paper we present the new DUNE-ALUGrid module. This module contains a
major overhaul of the sources from the ALUgrid library and the binding to the
DUNE software framework. The main changes include user defined load balancing,
parallel grid construction, and an redesign of the 2d grid which can now also
be used for parallel computations. In addition many improvements have been
introduced into the code to increase the parallel efficiency and to decrease
the memory footprint.
The original ALUGrid library is widely used within the DUNE community due to
its good parallel performance for problems requiring local adaptivity and
dynamic load balancing. Therefore, this new model will benefit a number of DUNE
users. In addition we have added features to increase the range of problems for
which the grid manager can be used, for example, introducing a 3d tetrahedral
grid using a parallel newest vertex bisection algorithm for conforming grid
refinement. In this paper we will discuss the new features, extensions to the
DUNE interface, and explain for various examples how the code is used in
parallel environments.Comment: 25 pages, 11 figure
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