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This chapter intends to introduce the main objects and concepts in TensorFlow. We also introduce how to access the data for the rest of the book and provide additional resources for learning about TensorFlow. After we have established the basic objects and methods in TensorFlow, we now want to establish the components that make up TensorFlow algorithms. We start by introducing computational graphs, and then move to loss functions and back propagation. We end with creating a simple classifier and then show an example of evaluating regression and classification algorithms.

tensorflow tensorflow-cookbook linear-regression neural-network tensorflow-algorithms rnn cnn svm nlp packtpub machine-learning tensorboard classification regression kmeans-clustering genetic-algorithm odeThe well-optimized DifferentialEquations solvers benchmark as the some of the fastest implementations, using classic algorithms and ones from recent research which routinely outperform the "standard" C/Fortran methods, and include algorithms optimized for high-precision and HPC applications. At the same time, it wraps the classic C/Fortran methods, making it easy to switch over to them whenever necessary. It integrates with the Julia package sphere, for example using Juno's progress meter, automatic plotting, built-in interpolations, and wraps other differential equation solvers so that many different methods for solving the equations can be accessed by simply switching a keyword argument. It utilizes Julia's generality to be able to solve problems specified with arbitrary number types (types with units like Unitful, and arbitrary precision numbers like BigFloats and ArbFloats), arbitrary sized arrays (ODEs on matrices), and more. This gives a powerful mixture of speed and productivity features to help you solve and analyze your differential equations faster. For information on using the package, see the stable documentation. Use the latest documentation for the version of the documentation which contains the un-released features.

differential-equations differentialequations julia ode sde pde dae stochastic dde spde delay monte-carlo-simulation stochastic-processes stochastic-differential-equations delay-differential-equations partial-differential-equations differential-algebraic-equations simulation numerical-integration dynamical-systemsIntegrate a system of ODEs using the Euler method

scijs ode euler integration differential-equations calculus first-orderFor a similar adaptive method using the fifth order Cash-Karp Runge-Kutta method with fourth order embedded error estimator, see ode45-cash-karp.Returns: Initialized integrator object.

scijs ode rk4 runge-kutta integration differential-equations calculuswhere is a vector of length . Given time step , the Cash-Karp method uses a fifth order Runge-Kutta scheme with a fourth order embedded estimator in order to control the error. In other words, the same intermediate values used in calculating the fifth order update can be used to calculate a fourth order estimate. The difference yields an error estimate, and the error estimate controls the timestep .Initialized integrator object.

scijs ode rk4 runge-kutta adaptive rk45 cash-karp ode45 integration differential-equations calculusWant one that's not there? Open an issue, or better yet, a pull request adding it. All of the methods are hand-written in asm.js, so they should be fast. Not that your integration method would ever be your bottleneck anyway, but hey... why not.

numerical integrate integration rk4 runge kutta euler physics ode ordinary differential equationGame Engine Framework for the D programming language

enet ode game-engine-framework imgui gamedev dlangJava 3D Physics Engine and Library.

3d-game-engine 3d ode physics stepper java-ports turbulenz-enginediffeqr is a package for solving differential equations in R. It utilizes DifferentialEquations.jl for its core routines to give high performance solving of ordinary differential equations (ODEs), stochastic differential equations (SDEs), delay differential equations (DDEs), and differential-algebraic equations (DAEs) directly in R. If you have any questions, or just want to chat about solvers/using the package, please feel free to chat in the Gitter channel. For bug reports, feature requests, etc., please submit an issue.

differential-equations ode sde dae dde differential-algebraic-equations ordinary-differential-equations stochastic-differential-equations delay-differential-equationsOrdinaryDiffEq.jl is a component package in the DifferentialEquations ecosystem. It holds the ordinary differential equation solvers and utilities. While completely independent and usable on its own, users interested in using this functionality should check out DifferentialEquations.jl. Other refined forms are IMEX and semi-linear ODEs (for exponential integrators).

ordinary-differential-equations differentialequations ode event-handling adaptive high-performanceThis is a modern object-oriented Fortran implementation of the DDEABM Adams-Bashforth-Moulton ODE solver. The original Fortran 77 code was obtained from the SLATEC library. It has been extensively refactored. DDEABM uses the Adams-Bashforth-Moulton predictor-corrector formulas of orders 1 through 12 to integrate a system of first order ordinary differential equations of the form dx/dt = f(t,x). Also included is an event-location capability, where the equations can be integrated until a specified function g(t,x) = 0. Dense output is also supported.

ode adams-bashforth root-findingThis is a modern Fortran (2003/2008) implementation of Hairer's DOP853 ODE solver. The original FORTRAN 77 code has been extensively refactored, and is now object-oriented and thread-safe, with an easy-to-use class interface. DOP853 is an explicit Runge-Kutta method of order 8(5,3) due to Dormand & Prince (with stepsize control and dense output). This project is hosted on GitHub.

ode runge-kuttaAn ordinary differential equation solving library in golang.

ode solving-library multivariate differential-equationsmrgsolve facilitates simulation in R from hierarchical, ordinary differential equation (ODE) based models typically employed in drug development. See the example below. Please see mrgsolve.github.io for additional resources.

ode simulated-data r cran mrgsolveThis library provides Stan language functions that calculate amounts in each compartment, given an event schedule and an ODE system. We are working with Stan development team to create a system to add and share Stan packages. In the mean time, the current repo contains forked version of Stan with Torsten. The latest version of Torsten (v0.87) is compatible with Stan v2.19.1. Torsten is agnostic to which Stan interface you use. Here we provide command line and R interfaces.

mcmc pharmacometrics autodiff stan inference-engine pkpd mpi ode openmp
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