Search Results for "numerical"
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Showing 20 open source projects for "numerical"
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ProbNumDiffEq.jl
Probabilistic Numerical Differential Equation solvers via Bayesian fil
ProbNumDiffEq.jl provides probabilistic numerical ODE solvers to the DifferentialEquations.jl ecosystem. The implemented ODE filters solve differential equations via Bayesian filtering and smoothing. The filters compute not just a single point estimate of the true solution, but a posterior distribution that contains an estimate of its numerical approximation error. -
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Calculus.jl
Calculus functions in Julia
...You can use the Calculus package to produce approximate derivatives by several forms of finite differencing or to produce exact derivatives using symbolic differentiation. You can also compute definite integrals by different numerical methods. -
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SymbolicNumericIntegration.jl
SymbolicNumericIntegration.jl: Symbolic-Numerics for Solving Integrals
SymbolicNumericIntegration.jl is a hybrid symbolic/numerical integration package that works on the Julia Symbolics expressions. -
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QuadGK.jl
adaptive 1d numerical Gauss–Kronrod integration in Julia
This package provides support for one-dimensional numerical integration in Julia using adaptive Gauss-Kronrod quadrature. The code was originally part of Base Julia. It supports the integration of arbitrary numeric types, including arbitrary-precision (BigFloat), and even the integration of arbitrary normed vector spaces. The package provides three basic functions: quadgk, gauss, and kronrod. quadgk performs the integration, gauss computes Gaussian quadrature points and weights for integrating over the interval [a, b], and kronrod computes Kronrod points, weights, and embedded Gaussian quadrature weights for integrating over [-1, 1]. -
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DFTK.jl
Density-functional toolkit
The density-functional toolkit, DFTK for short, is a collection of Julia routines for experimentation with plane-wave density-functional theory (DFT). The unique feature of this code is its emphasis on simplicity and flexibility with the goal of facilitating algorithmic and numerical developments as well as interdisciplinary collaboration in solid-state research. -
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PowerSimulations.jl
Julia for optimization simulation and modeling of PowerSystems
...The modularity of PowerSimulations results from the structure of the simulations enabled by the package. Simulations define a set of problems that can be solved using numerical techniques. -
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SciML Style Guide for Julia
A style guide for stylish Julia developers
The SciML Style Guide is a style guide for the Julia programming language. It is used by the SciML Open Source Scientific Machine Learning Organization. As such, it is open to discussion with the community. If the standard for code contributions is that every PR needs to support every possible input type that anyone can think of, the barrier would be too high for newcomers. Instead, the principle is to be as correct as possible to begin with, and grow the generic support over time. All... -
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PolyChaos.jl
Julia package to construct orthogonal polynomials
PolyChaos is a collection of numerical routines for orthogonal polynomials written in the Julia programming language. Starting from some non-negative weight (aka an absolutely continuous nonnegative measure). -
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Reduce.jl
Symbolic parser for Julia language term rewriting using REDUCE algebra
REDUCE is a portable general-purpose computer algebra system. It is a system for doing scalar, vector and matrix algebra by computer, which also supports arbitrary precision numerical approximation and interfaces to gnuplot to provide graphics. It can be used interactively for simple calculations (as illustrated in the screenshot below) but also provides a full programming language, with a syntax similar to other modern programming languages. REDUCE supports alternative user interfaces including Run-REDUCE, TeXmacs and GNU Emacs. ... -
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Surrogates.jl
Surrogate modeling and optimization for scientific machine learning
...In more mathematical terms: suppose we are attempting to optimize a function f(p), but each calculation of f is very expensive. It may be the case we need to solve a PDE for each point or use advanced numerical linear algebra machinery, which is usually costly. The idea is then to develop a surrogate model g which approximates f by training on previous data collected from evaluations of f. -
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SciMLBase.jl
The Base interface of the SciML ecosystem
...It is a low-dependency library made to be depended on by the downstream libraries to supply the common interface and allow for the interexchange of mathematical problems. The SciML common interface ties together the numerical solvers of the Julia package ecosystem into a single unified interface. It is designed for maximal efficiency and parallelism, while incorporating essential features for large-scale scientific machine learning such as differentiability, composability, and sparsity. -
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Parameters.jl
Types w/ default field values, keyword constructors, (un-)pack macros
This is a package I use to handle numerical-model parameters, thus the name. However, it should be useful otherwise too. -
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ReachabilityAnalysis.jl
Compute reachable states of dynamical systems
Reachability analysis is concerned with computing rigorous approximations of the set of states reachable by a dynamical system. In the scope of this package are systems modeled by continuous or hybrid dynamical systems, where the dynamics change with discrete events. Systems are modeled by ordinary differential equations (ODEs) or semi-discrete partial differential equations (PDEs), with uncertain initial states, uncertain parameters or non-deterministic inputs. -
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FiniteDifferences.jl
High accuracy derivatives, estimated via numerical finite differences
FiniteDifferences.jl estimates derivatives with finite differences. See also the Python package FDM. FiniteDiff.jl and FiniteDifferences.jl are similar libraries: both calculate approximate derivatives numerically. You should definitely use one or the other, rather than the legacy Calculus.jl finite differencing, or reimplementing it yourself. At some point in the future, they might merge, or one might depend on the other. -
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HomotopyContinuation.jl
A Julia package for solving systems of polynomials
HomotopyContinuation.jl is a Julia package for solving systems of polynomial equations by numerical homotopy continuation. Many models in the sciences and engineering are expressed as sets of real solutions to systems of polynomial equations. We can optimize any objective whose gradient is an algebraic function using homotopy methods by computing all critical points of the objective function. An important special case is when the objective function is the euclidean distance to a given point. ... -
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HCubature.jl
Pure-Julia multidimensional h-adaptive integration
...You can integrate real, complex, and matrix-valued integrands, for example. Note that HCubature assumes that your function f(x) can be computed at arbitrary points in the integration domain. (This is the ideal way to do numerical integration.) If you instead have f(x) precomputed at a fixed set of points, such as a Cartesian grid, you will need to use some other method (e.g. Trapz.jl for a multidimensional trapezoidal rule). -
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Measurements.jl
Error propagation calculator and library for physical measurements
Error propagation calculator and library for physical measurements. It supports real and complex numbers with uncertainty, arbitrary precision calculations, operations with arrays, and numerical integration. Physical measures are typically reported with an error, a quantification of the uncertainty of the accuracy of the measurement. Whenever you perform mathematical operations involving these quantities you have also to propagate the uncertainty, so that the resulting number will also have an attached error to quantify the confidence about its accuracy. ... -
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Kinetic.jl
Universal modeling and simulation of fluid mechanics upon ML
...It aims to furnish efficient modeling and simulation methodologies for fluid dynamics, augmented by the power of machine learning. Based on differentiable programming, mechanical and neural network models are fused and solved in a unified framework. Simultaneous 1-3 dimensional numerical simulations can be performed on CPUs and GPUs. -
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JuliaCall for Seamless Integration of R
Embed Julia in R
Package JuliaCall is an R interface to Julia, which is a high-level, high-performance dynamic programming language for numerical computing. Below is an image for Mandelbrot set. JuliaCall brings more than 100 times speedup of the calculation. -
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ClimateMachine.jl
Earth System Model that automatically learns from data
The ClimateMachine is a software package that models the evolution of the Earth system over weeks to centuries. The ClimateMachine solves three-dimensional partial differential equations for the distributions of water, momentum, energy, and tracers such as carbon in the atmosphere, oceans, and on land. The ClimateMachine will harness a wide range of Earth observations and data generated computationally to predict the evolution of Earth’s climate and features such as droughts, rainfall...
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