3,521 research outputs found
On Markovian solutions to Markov Chain BSDEs
We study (backward) stochastic differential equations with noise coming from
a finite state Markov chain. We show that, for the solutions of these equations
to be `Markovian', in the sense that they are deterministic functions of the
state of the underlying chain, the integrand must be of a specific form. This
allows us to connect these equations to coupled systems of ODEs, and hence to
give fast numerical methods for the evaluation of Markov-Chain BSDEs
MeshfreeFlowNet: A Physics-Constrained Deep Continuous Space-Time Super-Resolution Framework
We propose MeshfreeFlowNet, a novel deep learning-based super-resolution
framework to generate continuous (grid-free) spatio-temporal solutions from the
low-resolution inputs. While being computationally efficient, MeshfreeFlowNet
accurately recovers the fine-scale quantities of interest. MeshfreeFlowNet
allows for: (i) the output to be sampled at all spatio-temporal resolutions,
(ii) a set of Partial Differential Equation (PDE) constraints to be imposed,
and (iii) training on fixed-size inputs on arbitrarily sized spatio-temporal
domains owing to its fully convolutional encoder. We empirically study the
performance of MeshfreeFlowNet on the task of super-resolution of turbulent
flows in the Rayleigh-Benard convection problem. Across a diverse set of
evaluation metrics, we show that MeshfreeFlowNet significantly outperforms
existing baselines. Furthermore, we provide a large scale implementation of
MeshfreeFlowNet and show that it efficiently scales across large clusters,
achieving 96.80% scaling efficiency on up to 128 GPUs and a training time of
less than 4 minutes.Comment: Supplementary Video: https://youtu.be/mjqwPch9gDo. Accepted to SC2
Theoretical and numerical comparison of hyperelastic and hypoelastic formulations for Eulerian non-linear elastoplasticity
The aim of this paper is to compare a hyperelastic with a hypoelastic model
describing the Eulerian dynamics of solids in the context of non-linear
elastoplastic deformations. Specifically, we consider the well-known
hypoelastic Wilkins model, which is compared against a hyperelastic model based
on the work of Godunov and Romenski. First, we discuss some general conceptual
differences between the two approaches. Second, a detailed study of both models
is proposed, where differences are made evident at the aid of deriving a
hypoelastic-type model corresponding to the hyperelastic model and a particular
equation of state used in this paper. Third, using the same high order ADER
Finite Volume and Discontinuous Galerkin methods on fixed and moving
unstructured meshes for both models, a wide range of numerical benchmark test
problems has been solved. The numerical solutions obtained for the two
different models are directly compared with each other. For small elastic
deformations, the two models produce very similar solutions that are close to
each other. However, if large elastic or elastoplastic deformations occur, the
solutions present larger differences.Comment: 14 figure
Diffusion-based inpainting for coding remote-sensing data
Inpainting techniques based on partial differential equations (PDEs) such as diffusion processes are gaining growing importance as a novel family of image compression methods. Nevertheless, the application of inpainting in the field of hyperspectral imagery has been mainly focused on filling in missing information or dead pixels due to sensor failures. In this paper we propose a novel PDE-based inpainting algorithm to compress hyperspectral images. The method inpaints separately the known data in the spatial and in the spectral dimensions. Then it applies a prediction model to the final inpainting solution to obtain a representation much closer to the original image. Experimental results over a set of hyperspectral images indicate that the proposed algorithm can perform better than a recent proposed extension to prediction-based standard CCSDS-123.0 at low bitrate, better than JPEG 2000 Part 2 with the DWT 9/7 as a spectral transform at all bit-rates, and competitive to JPEG 2000 with principal component analysis (PCA), the optimal spectral decorrelation transform for Gaussian sources
Improving Performance of Iterative Methods by Lossy Checkponting
Iterative methods are commonly used approaches to solve large, sparse linear
systems, which are fundamental operations for many modern scientific
simulations. When the large-scale iterative methods are running with a large
number of ranks in parallel, they have to checkpoint the dynamic variables
periodically in case of unavoidable fail-stop errors, requiring fast I/O
systems and large storage space. To this end, significantly reducing the
checkpointing overhead is critical to improving the overall performance of
iterative methods. Our contribution is fourfold. (1) We propose a novel lossy
checkpointing scheme that can significantly improve the checkpointing
performance of iterative methods by leveraging lossy compressors. (2) We
formulate a lossy checkpointing performance model and derive theoretically an
upper bound for the extra number of iterations caused by the distortion of data
in lossy checkpoints, in order to guarantee the performance improvement under
the lossy checkpointing scheme. (3) We analyze the impact of lossy
checkpointing (i.e., extra number of iterations caused by lossy checkpointing
files) for multiple types of iterative methods. (4)We evaluate the lossy
checkpointing scheme with optimal checkpointing intervals on a high-performance
computing environment with 2,048 cores, using a well-known scientific
computation package PETSc and a state-of-the-art checkpoint/restart toolkit.
Experiments show that our optimized lossy checkpointing scheme can
significantly reduce the fault tolerance overhead for iterative methods by
23%~70% compared with traditional checkpointing and 20%~58% compared with
lossless-compressed checkpointing, in the presence of system failures.Comment: 14 pages, 10 figures, HPDC'1
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