Search Results for "differential equation"
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Showing 43 open source projects for "differential equation"
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Diffrax
Numerical differential equation solvers in JAX
Diffrax is a numerical differential equation solving library built for the JAX ecosystem, with a strong focus on composability, differentiability, and high-performance scientific computing. The project provides tools for solving ordinary differential equations, stochastic differential equations, controlled differential equations, and related systems in a way that fits naturally into modern machine learning and differentiable programming workflows. ... -
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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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DiffEqBayes.jl
Extension functionality which uses Stan.jl, DynamicHMC.jl
This repository is a set of extension functionality for estimating the parameters of differential equations using Bayesian methods. It allows the choice of using CmdStan.jl, Turing.jl, DynamicHMC.jl and ApproxBayes.jl to perform a Bayesian estimation of a differential equation problem specified via the DifferentialEquations.jl interface. -
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OrdinaryDiffEq.jl
High performance ordinary differential equation (ODE)
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. The well-optimized DifferentialEquations solvers benchmark as some of the fastest implementations, using classic algorithms and ones from recent research that routinely outperform the “standard” C/Fortran methods, and include algorithms optimized... -
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DataDrivenDiffEq.jl
Data driven modeling and automated discovery of dynamical systems
DataDrivenDiffEq.jl is a package for finding systems of equations automatically from a dataset. The methods in this package take in data and return the model which generated the data. A known model is not required as input. These methods can estimate equation-free and equation-based models for discrete, continuous differential equations or direct mappings. -
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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 index reduction of differential-algebraic equations, make it possible to solve equations that are impossible to solve with a purely numeric-based technique. ... -
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FourierFlows.jl
Tools for building fast, hackable, pseudospectral equation solvers
This software provides tools for partial differential equations on periodic domains using Fourier-based pseudospectral methods. A central intent of the software's design is also to provide a framework for writing new, fast solvers for new physical problems. The code is written in Julia. -
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Book-Reviews-In-Mathematica
Partial Differential Equations, Complex Analysis, Mathematica, Farlow
Cliff* Notes, Mathematica Evaluatable "Partial Differential Equations for Scientists and Engineers", Farlow "Physics for Scientists and Engineers", Serway "A First Course in Complex Analysis", Beck "PDE", Asmar "PDE, An Introduction", Colton "Elementary Differential Equations", 7th, Rainville "Ordinary Differential Equations", Tenenbaum "Linear Algebra And It's Applications", Lay "Swokowski Calculus", 5th, Swokowski "Chemistry Concepts & Problems, A Self-Teaching Guide",... -
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Zgoubi is a raytracing code. Since 1972 it pushes charged particles through accelerators and beam lines, by stepwise solution of Lorentz force equation - and their spins via Thomas-BMT differential equation. Zgoubi simulates beam dynamics and polarization in a variety of accelerators (storage ring, synchrotron, cyclotron, betatron, microtron, FFAG, multi-pass ERL, etc) and optical systems (beam lines, magnetic and electrostatic optical components, time-of-flight and mass spectrometers, etc). ...
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basic_numerical_methods
Didactic application to aid students in learning Numerical Methods;
A practical tool (for students and engineers) to foresee the result of calculus exercises. Calculation and visualization numerical methods for nonlinear equation, ODE, integration, linear system, polynomial fitting,..... -
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Math Model
Code, resources, and templates for mathematical modeling
Math_Model is a repository collecting resources, code, and algorithm templates for mathematical modeling and competition (e.g. Chinese modeling contests, US undergraduate modeling competitions). It includes LaTeX templates for writing solutions, records of past contest problems and winning solutions, algorithm implementations in MATLAB / M scripts for optimization, intelligent algorithms, numerical methods, and model frameworks. In effect, it is a curated library of modeling code, papers,... -
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PyTorch Implementation of SDE Solvers
Differentiable SDE solvers with GPU support and efficient sensitivity
This library provides stochastic differential equation (SDE) solvers with GPU support and efficient backpropagation. examples/demo.ipynb gives a short guide on how to solve SDEs, including subtle points such as fixing the randomness in the solver and the choice of noise types. examples/latent_sde.py learns a latent stochastic differential equation, as in Section 5 of [1]. -
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DPM-Solver
Fast ODE Solver for Diffusion Probabilistic Model Sampling
...The project introduces a specialized numerical solver designed to approximate the diffusion process using a small number of high-order integration steps. By reformulating the sampling problem as the solution of a diffusion-related ordinary differential equation, the solver can produce high-quality samples much more efficiently. This approach significantly reduces the computational cost required to generate images while maintaining strong generation quality. -
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IntegralOs
Numerical integration
Build a mathematical model of a differential equation, using building blocks like integrator, addition, functions and output pens. Chose an integration method: Euler, Trapez or Simpson. Specify calculation parameter, like time step, end time etc. Run the model and output the results as chart or as CSV file. For example the Lorenz equations can be calculated in 3 000 000 integration steps in 63 seconds. -
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SciMLBenchmarks.jl
Benchmarks for scientific machine learning (SciML) software
SciMLBenchmarks.jl holds webpages, pdfs, and notebooks showing the benchmarks for the SciML Scientific Machine Learning Software ecosystem. -
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WaveTrain (Python)
Quantum dynamics of chain-like systems using tensor train formats
WaveTrain is an open-source software for numerical simulations of chain-like quantum systems with nearest-neighbor (NN) interactions only (with or without periodic boundary conditions). This Python package is centered around tensor train (TT, or matrix product) representations of quantum-mechanical Hamiltonian operators and (stationary or time-evolving) state vectors. WaveTrain builds on the Python tensor train toolbox scikit_tt, which provides efficient construction methods, storage... -
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HBV interventions model
ODE HBV model and MCMC for fitting HBsAg, HBcAg and HBeAg data.
This code implements the MCMC and ordinary differential equation (ODE) model described in [1]. The core MCMC and ODE code is implemented in C/C++, and is wrapped with an R front end. This is not an R-package (although there are plans to extend the code and eventually make it into an R-package). Please read the PDF file supplied for further instructions on how to use this code. [1] HBV vaccination and PMTCT as elimination tools in the presence of HIV: insights from a clinical cohort and dynamic model https://bmcmedicine.biomedcentral.com/articles/10.1186/s12916-019-1269-x -
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Virtual Laboratory Environment
A multi-modeling and simulation environment to study complex systems
...VLE provides a complete set of C++ libraries, called VFL (VLE Foundation Libraries), to develop DEVS models, to gets results of simulations, to launch simulation on cluster. The models can be developed with the DEVS formalism or with the classical mathematical formalism: Ordinary Differential Equation with Euler, Range-Kutta or QSS integrator, Finite state automaton (FDDEVS, UML State chart, Hybrid Petri net). The VLE environment provides an IDE to develop C++ models, DEVS coupled models. VLE have also three ports to use the VFL with Python, Java and R programming languages. -
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...Although novelty is encouraged in regards to the algorithm, proposals could entertain approaches such as: a. Implementing the non-linear mixed effects theory, b. Maximum log-likelihood algorithms (stiff, non-stiff Ordinary Differential Equation solving methods with linearization)
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SODE
Program to solve differential equations using long Taylor series
Program to generate a program to numerically solve either a single ordinary differential equation or a system of them.It is a Ruby program, now called omnisode, which generates either Ruby, C, C++, Maple or Maxima code. Code can be generated for all languages under Linux. Ruby can be generated under Windows. All can be generated under cygwin, but would need work on execution of Maple. Omnisode itself is Ruby, which is needed in all cases to generate the program. -
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WordMat
Math in Word
WordMat is an add-on to Microsoft Word which creates a tab with math functionality. Part of the Math functionality is provided by other open-source applications like Maxima, GeoGebra, Graph and GnuPlot. -
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RAtom
solves nonlinear Kohn-Sham equation for the neutral atom.
RAtom solves nonlinear Kohn-Sham equation for the neutral atom. The adaptive algorithm based on finite element method (FEM) is implemented. Discretization of the differential eigenvalue problem is done by finite element method with Lobatto polynomials as a basis functions. High order Gauss quadratures are applied in order to obtain the total energy of atom with absolut accuracy of 1E-6 hartree. -
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diffeqs
Solving differential equations in Octave and Matlab
A set of scripts which help in solving differential equations by Octave and Matlab. This project currently contains scripts for professional timing, plotting graphs, and generating and displaying animations based on the solutions of equations. In the future there will be also scripts for numerically solving several forms of differential equation while tracking precision and controlling chaos. -
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Programs for Numerical Methods
Didactic program to aid students in learning Numerical Methods.
The program contents and capabilities are the following: 1. Matrices. 1.1 Matrix definition and special types of matrices. 1.2 Determinant of a matrix. 1.3 Inverse of a matrix. 2. Linear equation system. 2.1 Direct methods (Inverse of a Matrix, Cramer's Rule, Gauss Jordan, Montante). 2.2 Iterative methods (Jacobi, Gauss-Seidel). 3. Nonlinear equation systems (Newton 1st order, Newton 2nd order). 4. Roots of equations. 4.1 Bracketing methods (Bisection, Inverse Linear Interpolation, Regula-Falsi). 4.2 Open Methods (Newton-Raphson, Bailey). 5. ... -
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EpidermalERKMAPK
Scripts for Modelling Human Epidermal ERK-MAPK Activation
...Regulation of ERK-MAPK Signalling in Human Epidermis. BMC Systems Biology. doi: 10.1186/s12918-015-0187-6 The model was developed using a set the normalized-Hill differential equation framework, as specified by [Kraeutler, Soltis & Saucerman, (2002). BMC Systems Biology; doi: 10.1186/1752-0509-4-157]. This package includes: - MATLAB code containing the model definition, together with a script to perform non-linear least squares optimisation for a subset of parameters - python scripts which use libSBML to create an SBML representation of the model - SED-ML scripts which execute the SBML model under a range of conditions, produce output plots to recapitulate results shown in Cursons et al. (2015).
