34,179 research outputs found
Reliable Efficient Difference Methods for Random Heterogeneous Diffusion Reaction Models with a Finite Degree of Randomness
[EN] This paper deals with the search for reliable efficient finite difference methods for the
numerical solution of random heterogeneous diffusion reaction models with a finite degree of
randomness. Efficiency appeals to the computational challenge in the random framework that
requires not only the approximating stochastic process solution but also its expectation and variance.
After studying positivity and conditional random mean square stability, the computation of the
expectation and variance of the approximating stochastic process is not performed directly but
through using a set of sampling finite difference schemes coming out by taking realizations of the
random scheme and using Monte Carlo technique. Thus, the storage accumulation of symbolic
expressions collapsing the approach is avoided keeping reliability. Results are simulated and a
procedure for the numerical computation is given.This work was supported by the Spanish Ministerio de Economia, Industria y Competitividad (MINECO), the Agencia Estatal de Investigacion (AEI) and Fondo Europeo de Desarrollo Regional (FEDER UE) grant MTM2017-89664-PCasabán, M.; Company Rossi, R.; Jódar Sánchez, LA. (2021). Reliable Efficient Difference Methods for Random Heterogeneous Diffusion Reaction Models with a Finite Degree of Randomness. Mathematics. 9(3):1-15. https://doi.org/10.3390/math9030206S1159
Devito: Towards a generic Finite Difference DSL using Symbolic Python
Domain specific languages (DSL) have been used in a variety of fields to
express complex scientific problems in a concise manner and provide automated
performance optimization for a range of computational architectures. As such
DSLs provide a powerful mechanism to speed up scientific Python computation
that goes beyond traditional vectorization and pre-compilation approaches,
while allowing domain scientists to build applications within the comforts of
the Python software ecosystem. In this paper we present Devito, a new finite
difference DSL that provides optimized stencil computation from high-level
problem specifications based on symbolic Python expressions. We demonstrate
Devito's symbolic API and performance advantages over traditional Python
acceleration methods before highlighting its use in the scientific context of
seismic inversion problems.Comment: pyHPC 2016 conference submissio
On the Verification of a WiMax Design Using Symbolic Simulation
In top-down multi-level design methodologies, design descriptions at higher
levels of abstraction are incrementally refined to the final realizations.
Simulation based techniques have traditionally been used to verify that such
model refinements do not change the design functionality. Unfortunately, with
computer simulations it is not possible to completely check that a design
transformation is correct in a reasonable amount of time, as the number of test
patterns required to do so increase exponentially with the number of system
state variables. In this paper, we propose a methodology for the verification
of conformance of models generated at higher levels of abstraction in the
design process to the design specifications. We model the system behavior using
sequence of recurrence equations. We then use symbolic simulation together with
equivalence checking and property checking techniques for design verification.
Using our proposed method, we have verified the equivalence of three WiMax
system models at different levels of design abstraction, and the correctness of
various system properties on those models. Our symbolic modeling and
verification experiments show that the proposed verification methodology
provides performance advantage over its numerical counterpart.Comment: In Proceedings SCSS 2012, arXiv:1307.802
Efficient Instantiation of Parameterised Boolean Equation Systems to Parity Games
Parameterised Boolean Equation Systems (PBESs) are sequences of Boolean fixed point equations with data variables, used for, e.g., verification of modal μ-calculus formulae for process algebraic specifications with data. Solving a PBES is usually done by instantiation to a Parity Game and then solving the game. Practical game solvers exist, but the instantiation step is the bottleneck. We enhance the instantiation in two steps. First, we transform the PBES to a Parameterised Parity Game (PPG), a PBES with each equation either conjunctive or disjunctive. Then we use LTSmin, that offers transition caching, efficient storage of states and both distributed and symbolic state space generation, for generating the game graph. To that end we define a language module for LTSmin, consisting of an encoding of variables with parameters into state vectors, a grouped transition relation and a dependency matrix to indicate the dependencies between parts of the state vector and transition groups. Benchmarks on some large case studies, show that the method speeds up the instantiation significantly and decreases memory usage drastically
Automatic Differentiation of Algorithms for Machine Learning
Automatic differentiation---the mechanical transformation of numeric computer
programs to calculate derivatives efficiently and accurately---dates to the
origin of the computer age. Reverse mode automatic differentiation both
antedates and generalizes the method of backwards propagation of errors used in
machine learning. Despite this, practitioners in a variety of fields, including
machine learning, have been little influenced by automatic differentiation, and
make scant use of available tools. Here we review the technique of automatic
differentiation, describe its two main modes, and explain how it can benefit
machine learning practitioners. To reach the widest possible audience our
treatment assumes only elementary differential calculus, and does not assume
any knowledge of linear algebra.Comment: 7 pages, 1 figur
Theano: new features and speed improvements
Theano is a linear algebra compiler that optimizes a user's
symbolically-specified mathematical computations to produce efficient low-level
implementations. In this paper, we present new features and efficiency
improvements to Theano, and benchmarks demonstrating Theano's performance
relative to Torch7, a recently introduced machine learning library, and to
RNNLM, a C++ library targeted at recurrent neural networks.Comment: Presented at the Deep Learning Workshop, NIPS 201
- …