1,710 research outputs found
Towards Large-Scale Learned Solvers for Parametric PDEs with Model-Parallel Fourier Neural Operators
Fourier neural operators (FNOs) are a recently introduced neural network
architecture for learning solution operators of partial differential equations
(PDEs), which have been shown to perform significantly better than comparable
approaches based on convolutional networks. Once trained, FNOs can achieve
speed-ups of multiple orders of magnitude over conventional numerical PDE
solvers. However, due to the high dimensionality of their input data and
network weights, FNOs have so far only been applied to two-dimensional or small
three-dimensional problems. To remove this limited problem-size barrier, we
propose a model-parallel version of FNOs based on domain-decomposition of both
the input data and network weights. We demonstrate that our model-parallel FNO
is able to predict time-varying PDE solutions of over 3.2 billions variables on
Summit using up to 768 GPUs and show an example of training a distributed FNO
on the Azure cloud for simulating multiphase CO dynamics in the Earth's
subsurface
Massively Parallel Continuous Local Search for Hybrid SAT Solving on GPUs
Although state-of-the-art (SOTA) SAT solvers based on conflict-driven clause
learning (CDCL) have achieved remarkable engineering success, their sequential
nature limits the parallelism that may be extracted for acceleration on
platforms such as the graphics processing unit (GPU). In this work, we propose
FastFourierSAT, a highly parallel hybrid SAT solver based on gradient-driven
continuous local search (CLS). This is realized by a novel parallel algorithm
inspired by the Fast Fourier Transform (FFT)-based convolution for computing
the elementary symmetric polynomials (ESPs), which is the major computational
task in previous CLS methods. The complexity of our algorithm matches the best
previous result. Furthermore, the substantial parallelism inherent in our
algorithm can leverage the GPU for acceleration, demonstrating significant
improvement over the previous CLS approaches. We also propose to incorporate
the restart heuristics in CLS to improve search efficiency. We compare our
approach with the SOTA parallel SAT solvers on several benchmarks. Our results
show that FastFourierSAT computes the gradient 100+ times faster than previous
prototypes implemented on CPU. Moreover, FastFourierSAT solves most instances
and demonstrates promising performance on larger-size instances
GASPACHO : a generic automatic solver using proximal algorithms for convex Huge optimization problems
Many inverse problems (e.g., demosaicking, deblurring, denoising, image fusion, HDR synthesis) share various similarities: degradation operators are often modeled by a specific data fitting function while image prior knowledge (e.g., sparsity) is incorporated by additional regularization terms. In this paper, we investigate automatic algorithmic techniques for evaluating proximal operators. These algorithmic techniques also enable efficient calculation of adjoints from linear operators in a general matrix-free setting. In particular, we study the simultaneous-direction method of multipliers (SDMM) and the parallel proximal algorithm (PPXA) solvers and show that the automatically derived implementations are well suited for both single-GPU and multi-GPU processing. We demonstrate this approach for an Electron Microscopy (EM) deconvolution problem
The prospect of using LES and DES in engineering design, and the research required to get there
In this paper we try to look into the future to divine how large eddy and
detached eddy simulations (LES and DES, respectively) will be used in the
engineering design process about 20-30 years from now. Some key challenges
specific to the engineering design process are identified, and some of the
critical outstanding problems and promising research directions are discussed.Comment: accepted for publication in the Royal Society Philosophical
Transactions
Learned multiphysics inversion with differentiable programming and machine learning
We present the Seismic Laboratory for Imaging and Modeling/Monitoring (SLIM)
open-source software framework for computational geophysics and, more
generally, inverse problems involving the wave-equation (e.g., seismic and
medical ultrasound), regularization with learned priors, and learned neural
surrogates for multiphase flow simulations. By integrating multiple layers of
abstraction, our software is designed to be both readable and scalable. This
allows researchers to easily formulate their problems in an abstract fashion
while exploiting the latest developments in high-performance computing. We
illustrate and demonstrate our design principles and their benefits by means of
building a scalable prototype for permeability inversion from time-lapse
crosswell seismic data, which aside from coupling of wave physics and
multiphase flow, involves machine learning
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