Search Results for "equation"
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Showing 184 open source projects for "equation"
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Diffrax
Numerical differential equation solvers in JAX
...Because it is written to work closely with JAX, it supports just-in-time compilation, automatic differentiation, vectorization, and accelerator-backed execution on hardware such as GPUs and TPUs. This makes it especially appealing for researchers who need equation solvers that can be embedded inside trainable models or simulation-heavy learning systems. -
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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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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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Symbolics.jl
Symbolic programming for the next generation of numerical software
Symbolics.jl is a high-performance symbolic computation library for the Julia programming language. It enables users to define, manipulate, and analyze mathematical expressions symbolically, with strong support for symbolic differentiation, simplification, equation solving, and code generation. Designed for use in scientific computing, machine learning, and engineering, Symbolics.jl integrates smoothly with Julia’s numerical ecosystem, allowing symbolic expressions to be compiled and optimized for high-speed evaluation. -
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ModelingToolkit.jl
Modeling framework for automatically parallelized scientific ML
...ModelingToolkit.jl is a symbolic-numeric modeling package. Thus it combines some of the features from symbolic computing packages like SymPy or Mathematica with the ideas of equation-based modeling systems like the causal Simulink and the acausal Modelica. -
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StructuralEquationModels.jl
A fast and flexible Structural Equation Modelling Framework
This is a package for Structural Equation Modeling in development. It is written for extensibility, that is, you can easily define your own objective functions and other parts of the model. At the same time, it is (very) fast. We provide fast objective functions, gradients, and for some cases hessians as well as approximations thereof. As a user, you can easily define custom loss functions. -
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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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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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IntervalRootFinding.jl
Find all roots of a function in a guaranteed way with Julia
This package provides guaranteed methods for finding roots of functions, i.e. solutions to the equation f(x) == 0 for a function f. To do so, it uses methods from interval analysis, using interval arithmetic from the IntervalArithmetic.jl package by the same authors. The basic function is roots. A standard Julia function and an interval is provided and the roots function return a list of intervals containing all roots of the function located in the starting interval. -
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LaTeXStrings.jl
convenient input and display of LaTeX equation strings for Julia
This is a small package to make it easier to type LaTeX equations in string literals in the Julia language, written by Steven G. Johnson. With ordinary strings in Julia, to enter a string literal with embedded LaTeX equations you need to manually escape all backslashes and dollar signs: for example, $\alpha^2$ is written \$\\alpha^2\$. Also, even though IJulia is capable of displaying formatted LaTeX equations (via MathJax), an ordinary string will not exploit this. -
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JUDI.jl
Julia Devito inversion
...JUDI's modeling operators can also be used as layers in (convolutional) neural networks to implement physics-augmented deep learning algorithms thanks to its implementation of ChainRules's rrule for the linear operators representing the discre wave equation. -
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MathJax
Beautiful and accessible math in all browsers
A JavaScript display engine for mathematics that works in all browsers. No more setup for readers. It just works. MathJax provides tools to transform your content from traditional print sources into modern, accessible web content and ePubs. The MathJax team is available to train your staff in using our resources for preparing online teaching material and creating accessible STEM content. MathJax is highly flexible and can be tailored to the needs of your institution by creating customized... -
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Jupyter Notebook Tools for Sphinx
Sphinx source parser for Jupyter notebooks
nbsphinx is a Sphinx extension that provides a source parser for *.ipynb files. Custom Sphinx directives are used to show Jupyter Notebook code cells (and of course their results) in both HTML and LaTeX output. Un-evaluated notebooks – i.e. notebooks without stored output cells – will be automatically executed during the Sphinx build process. -
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blavaan
An R package for Bayesian structural equation modeling
blavaan is a free, open-source R package for Bayesian latent variable analysis. It relies on JAGS and Stan to estimate models via MCMC. The blavaan functions and syntax are similar to lavaan. The development version of blavaan (containing updates not yet on CRAN) can be installed via the command provided in the documentation. Compilation is required; this may be a problem for users who currently rely on a binary version of blavaan from CRAN. The blavaan package depends on the lavaan package... -
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PySR
High-Performance Symbolic Regression in Python and Julia
...Symbolic regression works best on low-dimensional datasets, but one can also extend these approaches to higher-dimensional spaces by using "Symbolic Distillation" of Neural Networks, as explained in 2006.11287, where we apply it to N-body problems. Here, one essentially uses symbolic regression to convert a neural net to an analytic equation. Thus, these tools simultaneously present an explicit and powerful way to interpret deep neural networks. -
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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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FEniCS.jl
A scientific machine learning (SciML) wrapper for the FEniCS
...Interfaces have been provided for the main functions and their attributes, and instructions to add further ones can be found here. A high-level API for usage with DifferentialEquations. An example can be seen in solving the heat equation with high-order adaptive time-stepping. Various gists/jupyter notebooks have been created to provide a brief overview of the overall functionality and of any differences between the pythonic FEniCS and the Julian wrapper. DifferentialEquations.jl ecosystem. Paraview can also be used to visualize various results just like in FEniCS. -
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Physical Symbolic Optimization (Φ-SO)
Physical Symbolic Optimization
Physical Symbolic Optimization (Φ-SO) - A symbolic optimization package built for physics. Symbolic regression module uses deep reinforcement learning to infer analytical physical laws that fit data points, searching in the space of functional forms. -
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Hyperf
A coroutine framework that focuses on hyperspeed and flexibility
Hyperf is an extremely performant and flexible PHP CLI framework, powered by a state-of-the-art coroutine server and a large number of battle-tested components. Aside from decisively beating PHP-FPM frameworks in benchmarks, Hyperf is unique in its focus on flexibility and composition. Hyperf ships with an AOP-enabling (aspect-oriented programming) dependency injector to ensure components and classes are pluggable and meta-programmable. All of Hyperf's core components strictly follow PSR... -
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latexify
A library to generate LaTeX expression from Python code
latexify_py converts small, math-heavy pieces of Python code into human-readable LaTeX that mirrors the intent of the computation, not just its surface syntax. It parses Python functions and expressions into an abstract syntax tree (AST), applies symbolic rewrites for common mathematical constructs, and then emits LaTeX that compiles cleanly in standard environments. Typical use cases include turning analytical utilities—like probability mass functions, activation formulas, or recurrence... -
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canonical-ellipse
Canonical Ellipse equation and more
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Bounds on Interbay Buckling
Bounds on the effect of initial geometric imperfections
An Excel spreadsheet compares the following four bounds on the yield onset pressure due to Interbay imperfections in thin-wall monocoque and ring-stiffened cylindrical pressure vessels: • Bodner-Berks method [1] • Galletly-Bart method [2] • Gordon’s simply supported method [3] • Gordon’s clamped end method [3] Because the first two methods are based on Donnell's equation of equilibrium, they are applicable only for shallow shells—that is for relatively short thin-wall cylinders whose critical buckling mode shapes are characterized by a large number of circumferential lobes. (Reference [1] claims greater than 8 lobes.) This restriction does not apply to the second two methods because they are based on Morley’s equation of equilibrium [4] rather than Donnell’s. ... -
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DAE Tools Project
Object-oriented equation-based modelling and optimisation software
DAE Tools is a cross-platform equation-based object-oriented modelling, simulation and optimisation software. It is not a modelling language nor a collection of numerical libraries but rather a higher level structure – an architectural design of interdependent software components providing an API for: - Model development/specification - Activities on developed models, such as simulation, optimisation, sensitivity analysis and parameter estimation - Processing of the results, such as plotting and exporting to various file formats - Report generation - Code generation, co-simulation and model exchange The following class of problems can be solved by DAE Tools: - Initial value problems of implicit form - Index-1 DAE systems - With lumped or distributed parameters - Steady-state or dynamic - Continuous with some elements of event-driven systems -
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crowdEgress
Complex systems of social groups with opinion exchange
Inspired by the well-known microscopic models of Brownian particles and social-force model, this project presents a force-based method to characterize social groups and opinion exchange in collective behavior of many individual units. The problem is complex because opinions and actions are described as different features for each individual, and opinions interact and shape action with a time delay. The social topology among individuals is described by a set of matrices, which provide...
