400 research outputs found
Improving Pseudo-Time Stepping Convergence for CFD Simulations With Neural Networks
Computational fluid dynamics (CFD) simulations of viscous fluids described by
the Navier-Stokes equations are considered. Depending on the Reynolds number of
the flow, the Navier-Stokes equations may exhibit a highly nonlinear behavior.
The system of nonlinear equations resulting from the discretization of the
Navier-Stokes equations can be solved using nonlinear iteration methods, such
as Newton's method. However, fast quadratic convergence is typically only
obtained in a local neighborhood of the solution, and for many configurations,
the classical Newton iteration does not converge at all. In such cases,
so-called globalization techniques may help to improve convergence.
In this paper, pseudo-transient continuation is employed in order to improve
nonlinear convergence. The classical algorithm is enhanced by a neural network
model that is trained to predict a local pseudo-time step. Generalization of
the novel approach is facilitated by predicting the local pseudo-time step
separately on each element using only local information on a patch of adjacent
elements as input. Numerical results for standard benchmark problems, including
flow through a backward facing step geometry and Couette flow, show the
performance of the machine learning-enhanced globalization approach; as the
software for the simulations, the CFD module of COMSOL Multiphysics is
employed
An extensive study on iterative solver resilience : characterization, detection and prediction
Soft errors caused by transient bit flips have the potential to significantly impactan applicalion's behavior. This has motivated the design of an array of techniques to detect, isolate, and correct soft errors using microarchitectural, architectural, compilationbased, or application-level techniques to minimize their impact on the executing application. The first step toward the design of good error detection/correction techniques involves an understanding of an application's vulnerability to soft errors. This work focuses on silent data e orruption's effects on iterative solvers and efforts to mitigate those effects.
In this thesis, we first present the first comprehensive characterizalion of !he impact of soft errors on !he convergen ce characteris tics of six iterative methods using application-level fault injection. We analyze the impact of soft errors In terms of the type of error (single-vs multi-bit), the distribution and location of bits affected, the data structure and statement impacted, and varialion with time. We create a public access database with more than 1.5 million fault injection results. We then analyze the performance of soft error detection mechanisms and present the comparalive results. Molivated by our observations, we evaluate a machine-learning based detector that takes as features that are the runtime features observed by the individual detectors to arrive al their conclusions. Our evalualion demonstrates improved results over individual detectors. We then propase amachine learning based method to predict a program's error behavior to make fault injection studies more efficient. We demonstrate this method on asse ssing the performance of soft error detectors. We show that our method maintains 84% accuracy on average with up to 53% less cost. We also show, once a model is trained further fault injection tests would cost 10% of the expected full fault injection runs.“Soft errors” causados por cambios de estado transitorios en bits, tienen el potencial de impactar significativamente el comportamiento de una aplicación. Esto, ha motivado el diseño de una variedad de técnicas para detectar, aislar y corregir soft errors aplicadas a micro-arquitecturas, arquitecturas, tiempo de compilación y a nivel de aplicación para minimizar su impacto en la ejecución de una aplicación. El primer paso para diseñar una buna técnica de detección/corrección de errores, implica el conocimiento de las vulnerabilidades de la aplicación ante posibles soft errors. Este trabajo se centra en los efectos de la corrupción silenciosa de datos en soluciones iterativas, así como en los esfuerzos para mitigar esos efectos. En esta tesis, primeramente, presentamos la primera caracterización extensiva del impacto de soft errors sobre las características convergentes de seis métodos iterativos usando inyección de fallos a nivel de aplicación. Analizamos el impacto de los soft errors en términos del tipo de error (único vs múltiples-bits), de la distribución y posición de los bits afectados, las estructuras de datos, instrucciones afectadas y de las variaciones en el tiempo. Creamos una base de datos pública con más de 1.5 millones de resultados de inyección de fallos. Después, analizamos el desempeño de mecanismos de detección de soft errors actuales y presentamos los resultados de su comparación. Motivados por las observaciones de los resultados presentados, evaluamos un detector de soft errors basado en técnicas de machine learning que toma como entrada las características observadas en el tiempo de ejecución individual de los detectores anteriores al llegar a su conclusión. La evaluación de los resultados obtenidos muestra una mejora por sobre los detectores individualmente. Basados en estos resultados propusimos un método basado en machine learning para predecir el comportamiento de los errores en un programa con el fin de hacer el estudio de inyección de errores mas eficiente. Presentamos este método para evaluar el rendimiento de los detectores de soft errors. Demostramos que nuestro método mantiene una precisión del 84% en promedio con hasta un 53% de mejora en el tiempo de ejecución. También mostramos que una vez que un modelo ha sido entrenado, las pruebas de inyección de errores siguientes costarían 10% del tiempo esperado de ejecución.Postprint (published version
Towards a Machine-Learned Poisson Solver for Low-Temperature Plasma Simulations in Complex Geometries
Poisson's equation plays an important role in modeling many physical systems.
In electrostatic self-consistent low-temperature plasma (LTP) simulations,
Poisson's equation is solved at each simulation time step, which can amount to
a significant computational cost for the entire simulation. In this paper, we
describe the development of a generic machine-learned Poisson solver
specifically designed for the requirements of LTP simulations in complex 2D
reactor geometries on structured Cartesian grids. Here, the reactor geometries
can consist of inner electrodes and dielectric materials as often found in LTP
simulations. The approach leverages a hybrid CNN-transformer network
architecture in combination with a weighted multiterm loss function. We train
the network using highly-randomized synthetic data to ensure the
generalizability of the learned solver to unseen reactor geometries. The
results demonstrate that the learned solver is able to produce quantitatively
and qualitatively accurate solutions. Furthermore, it generalizes well on new
reactor geometries such as reference geometries found in the literature. To
increase the numerical accuracy of the solutions required in LTP simulations,
we employ a conventional iterative solver to refine the raw predictions,
especially to recover the high-frequency features not resolved by the initial
prediction. With this, the proposed learned Poisson solver provides the
required accuracy and is potentially faster than a pure GPU-based conventional
iterative solver. This opens up new possibilities for developing a generic and
high-performing learned Poisson solver for LTP systems in complex geometries
A Survey on Intelligent Iterative Methods for Solving Sparse Linear Algebraic Equations
Efficiently solving sparse linear algebraic equations is an important
research topic of numerical simulation. Commonly used approaches include direct
methods and iterative methods. Compared with the direct methods, the iterative
methods have lower computational complexity and memory consumption, and are
thus often used to solve large-scale sparse linear equations. However, there
are numerous iterative methods, parameters and components needed to be
carefully chosen, and an inappropriate combination may eventually lead to an
inefficient solution process in practice. With the development of deep
learning, intelligent iterative methods become popular in these years, which
can intelligently make a sufficiently good combination, optimize the parameters
and components in accordance with the properties of the input matrix. This
survey then reviews these intelligent iterative methods. To be clearer, we
shall divide our discussion into three aspects: a method aspect, a component
aspect and a parameter aspect. Moreover, we summarize the existing work and
propose potential research directions that may deserve a deep investigation
A Preconditioned Interior Point Method for Support Vector Machines Using an ANOVA-Decomposition and NFFT-Based Matrix-Vector Products
In this paper we consider the numerical solution to the soft-margin support
vector machine optimization problem. This problem is typically solved using the
SMO algorithm, given the high computational complexity of traditional
optimization algorithms when dealing with large-scale kernel matrices. In this
work, we propose employing an NFFT-accelerated matrix-vector product using an
ANOVA decomposition for the feature space that is used within an interior point
method for the overall optimization problem. As this method requires the
solution of a linear system of saddle point form we suggest a preconditioning
approach that is based on low-rank approximations of the kernel matrix together
with a Krylov subspace solver. We compare the accuracy of the ANOVA-based
kernel with the default LIBSVM implementation. We investigate the performance
of the different preconditioners as well as the accuracy of the ANOVA kernel on
several large-scale datasets.Comment: Official Code https://github.com/wagnertheresa/NFFTSVMip
Structural dynamics branch research and accomplishments to FY 1992
This publication contains a collection of fiscal year 1992 research highlights from the Structural Dynamics Branch at NASA LeRC. Highlights from the branch's major work areas--Aeroelasticity, Vibration Control, Dynamic Systems, and Computational Structural Methods are included in the report as well as a listing of the fiscal year 1992 branch publications
Combining Machine Learning and Domain Decomposition Methods – A Review
Scientific machine learning, an area of research where techniques from machine learning and scientific computing are combined, has become of increasing importance and receives growing attention. Here, our focus is on a very specific area within scientific machine learning given by the combination of domain decomposition methods with machine learning techniques. The aim of the present work is to make an attempt of providing a review of existing and also new approaches within this field as well as to present some known results in a unified framework; no claim of completeness is made. As a concrete example of machine learning enhanced domain decomposition methods, an approach is presented which uses neural networks to reduce the computational effort in adaptive domain decomposition methods while retaining their robustness. More precisely, deep neural networks are used to predict the geometric location of constraints which are needed to define a robust coarse space. Additionally, two recently published deep domain decomposition approaches are presented in a unified framework. Both approaches use physics-constrained neural networks to replace the discretization and solution of the subdomain problems of a given decomposition of the computational domain. Finally, a brief overview is given of several further approaches which combine machine learning with ideas from domain decomposition methods to either increase the performance of already existing algorithms or to create completely new methods
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