Search Results for "nonlinear"
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Showing 20 open source projects for "nonlinear"
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VoronoiFVM.jl
Solution of nonlinear multiphysics partial differential equations
Solver for coupled nonlinear partial differential equations (elliptic-parabolic conservation laws) based on the Voronoi finite volume method. It uses automatic differentiation via ForwardDiff.jl and DiffResults.jl to evaluate user functions along with their jacobians and calculate derivatives of solutions with respect to their parameters. -
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ImageFiltering.jl
Julia implementations of multidimensional array convolution
Julia implementations of multidimensional array convolution and nonlinear stencil operations. ImageFiltering implements blurring, sharpening, gradient computation, and other linear filtering operations, as well nonlinear filters like min/max. -
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ChaosTools.jl
Tools for the exploration of chaos and nonlinear dynamics
A Julia module that offers various tools for analyzing nonlinear dynamics and chaotic behavior. It can be used as a standalone package, or as part of DynamicalSystems.jl. All further information is provided in the documentation, which you can either find online or build locally by running the docs/make.jl file. ChaosTools.jl is the jack-of-all-trades package of the DynamicalSystems.jl library: methods that are not extensive enough to be a standalone package are added here. -
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The NLopt module for Julia
Package to call the NLopt nonlinear-optimization library from Julia
This module provides a Julia-language interface to the free/open-source NLopt library for nonlinear optimization. NLopt provides a common interface for many different optimization algorithms. -
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DynamicalSystems.jl
Award winning software library for nonlinear dynamics timeseries
DynamicalSystems.jl is an award-winning Julia software library for nonlinear dynamics and nonlinear time series analysis. To install DynamicalSystems.jl, run import Pkg; Pkg.add("DynamicalSystems"). To learn how to use it and see its contents visit the documentation, which you can either find online or build locally by running the docs/make.jl file. DynamicalSystems.jl is part of JuliaDynamics, an organization dedicated to creating high-quality scientific software. -
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NonlinearSolve.jl
High-performance and differentiation-enabled nonlinear solvers
...Use the in-development documentation for the version of the documentation that contains the unreleased features. NonlinearSolve.jl is a unified interface for the nonlinear solving packages of Julia. The package includes its own high-performance nonlinear solvers which include the ability to swap out to fast direct and iterative linear solvers, along with the ability to use sparse automatic differentiation for Jacobian construction and Jacobian-vector products. NonlinearSolve.jl interfaces with other packages of the Julia ecosystem to make it easy to test alternative solver packages and pass small types to control algorithm swapping. ... -
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JuMP
Modeling language for Mathematical Optimization
...JuMP makes it easy to formulate and solve a range of problem classes, including linear programs, integer programs, conic programs, semidefinite programs, and constrained nonlinear programs. JuMP is used to solve large-scale inventory routing problems at Renault, schedule trains at Thales Inc., plan power grid expansion at PSR, and route school buses. -
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PETSc.jl
Julia wrappers for the PETSc library
This package provides a low level interface for PETSc and allows combining julia features (such as automatic differentiation) with the PETSc infrastructure and nonlinear solvers. -
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Sundials.jl
Julia interface to Sundials, including a nonlinear solver
This is a suite for numerically solving differential equations written in Julia and available for use in Julia, Python, and R. The purpose of this package is to supply efficient Julia implementations of solvers for various differential equations. -
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NeuralPDE.jl
Physics-Informed Neural Networks (PINN) Solvers
NeuralPDE.jl is a Julia library for solving partial differential equations (PDEs) using physics-informed neural networks and scientific machine learning. Built on top of the SciML ecosystem, it provides a flexible and composable interface for defining PDEs and training neural networks to approximate their solutions. NeuralPDE.jl enables hybrid modeling, data-driven discovery, and fast PDE solvers in high dimensions, making it suitable for scientific research and engineering applications. -
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MethodOfLines.jl
Automatic Finite Difference PDE solving with Julia SciML
MethodOfLines.jl is a Julia package for automated finite difference discretization of symbolically defined PDEs in N dimensions. It uses symbolic expressions for systems of partial differential equations as defined with ModelingToolkit.jl, and Interval from DomainSets.jl to define the space(time) over which the simulation runs. This project is under active development, therefore the interface is subject to change. The docs will be updated to reflect any changes, please check back for current... -
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EAGO.jl
A development environment for robust and global optimization
EAGO is an open-source development environment for robust and global optimization in Julia. EAGO is a deterministic global optimizer designed to address a wide variety of optimization problems, emphasizing nonlinear programs (NLPs), by propagating McCormick relaxations along the factorable structure of each expression in the NLP. Most operators supported by modern automatic differentiation (AD) packages (e.g., +, sin, cosh) are supported by EAGO and a number of utilities for sanitizing native Julia code and generating relaxations on a wide variety of user-defined functions have been included. ... -
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Gridap.jl
Grid-based approximation of partial differential equations in Julia
Gridap provides a set of tools for the grid-based approximation of partial differential equations (PDEs) written in the Julia programming language. The library currently supports linear and nonlinear PDE systems for scalar and vector fields, single and multi-field problems, conforming and nonconforming finite element (FE) discretizations, on structured and unstructured meshes of simplices and n-cubes. It also provides methods for time integration. Gridap is extensible and modular. One can implement new FE spaces, new reference elements, use external mesh generators, linear solvers, post-processing tools, etc. ... -
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ModelingToolkit.jl
Modeling framework for automatically parallelized scientific ML
ModelingToolkit.jl is a modeling language for high-performance symbolic-numeric computation in scientific computing and scientific machine learning. It then mixes ideas from symbolic computational algebra systems with causal and acausal equation-based modeling frameworks to give an extendable and parallel modeling system. It allows for users to give a high-level description of a model for symbolic preprocessing to analyze and enhance the model. Automatic symbolic transformations, such as... -
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Convex.jl
A Julia package for disciplined convex programming
...Convex.jl makes it easy to describe optimization problems in a natural, mathematical syntax, and to solve those problems using a variety of different (commercial and open-source) solvers. Convex.jl works by transforming the problem—which possibly has nonsmooth, nonlinear constructions like the nuclear norm, the log determinant, and so forth—into a linear optimization problem subject to conic constraints. This reformulation often involves adding auxiliary variables and is called an "extended formulation", since the original problem has been extended with additional variables. These formulations rely on the problem being modeled by combining Convex.jl's "atoms" or primitives according to certain rules which ensure convexity, called the disciplined convex programming (DCP) ruleset. ... -
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Nonlinear Dynamics
A concise introduction interlaced with code
This repository holds material related with the textbook Nonlinear Dynamics: A Concise Introduction Interlaced with code, co-authored by George Datseris and Ulrich Parlitz. The textbook will be published by Springer-Nature, in the series Undergraduate Lecture Notes in Physics. -
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ManifoldLearning
Package for manifold learning and nonlinear dimensionality reduction
A Julia package for manifold learning and nonlinear dimensionality reduction. Most of the methods use k-nearest neighbors method for constructing local subspace representation. By default, neighbors are computed from a distance matrix of a dataset. This is not an efficient method, especially, for large datasets. -
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TimeseriesPrediction.jl
Prediction of timeseries using methods of nonlinear dynamics
Repository for predicting time series using methods from nonlinear dynamics and time series analysis. It uses DelayEmbeddings. -
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NLOptControl.jl
nonlinear control optimization tool
This software solves nonlinear control problems at a high level very quickly. -
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JuliaFEM.jl
The JuliaFEM software library is a framework
...It is designed to scale up from single servers to thousands of machines, each offering local computation and storage. The basic design principle is: that everything is nonlinear. All physics models are nonlinear from which the linearization are made as special cases.
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