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Gosl is a Go library to develop Artificial Intelligence and High-Performance Scientific Computations. The library tries to be as general and easy as possible. Gosl considers the use of both Go concurrency routines and parallel computing using the message passing interface (MPI). Gosl has several modules (sub-packages) for a variety of tasks in scientific computing, image analysis, and data post-processing.

scientific-computing visualization linear-algebra differential-equations sparse-systems plotting mkl parallel-computations computational-geometry graph-theory tensor-algebra fast-fourier-transform eigenvalues eigenvectors hacktoberfest machine-learning artificial-intelligence optimization optimization-algorithms linear-programmingThis library provides stochastic differential equation (SDE) solvers with GPU support and efficient backpropagation. Requirements: Python >=3.6 and PyTorch >=1.6.0.

deep-neural-networks deep-learning pytorch dynamical-systems differential-equations stochastic-differential-equations stochastic-processes stochastic-volatility-models neural-differential-equationsThe 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-systemsThey are straightforward to implement and evaluate using existing tools, in particular PyTorch and the torchcde library. See torchcde.

machine-learning deep-neural-networks deep-learning time-series pytorch neural-networks dynamical-systems differential-equations rough-paths neural-differential-equations controlled-differential-equationsBrian is a free, open source simulator for spiking neural networks. It is written in the Python programming language and is available on almost all platforms. We believe that a simulator should not only save the time of processors, but also the time of scientists. Brian is therefore designed to be easy to learn and use, highly flexible and easily extensible. Brian2 is released under the terms of the CeCILL 2.1 license.

neuroscience science differential-equations spiking-neural-networks biological-simulations code-generation simulation-framework brianIntegrate 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 calculusA solver for differential algebraic equations (DAE). This wraps the original DASKR FORTRAN solver. DASKR is a derivative of the DASSL solver with root finding. An interface to the JuliaDiffEq common interface is also provided.

differential-equations differential-algebraic daskrThis is a library of callbacks for extending the solvers of DifferentialEquations.jl. For more information on using callbacks, see the manual page.

callback differential-equationsDiffEqJump.jl is a component package in the DifferentialEquations ecosystem. It holds the utilities for building jump equations, like Gillespie SSA and jump diffusions. Users interested in using this functionality should check out DifferentialEquations.jl.

gillespie ssa jump-diffusion stochastic differential-equationsdiffeqr 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-equationsParameterizedFunctions.jl is a component of the JuliaDiffEq ecosystem which allows for parameters to be explicitly present within functions. The interface which ParameterizedFunctions describes allows for functionality which requires parameters, such as parameter sensitivity analysis and parameter estimation, to be added to the differential equation solvers of DifferentialEquations.jl. While the interface itself is of importance to ecosystem developers, ParameterizedFunctions.jl provides user-facing macros which make a ParameterizedFunction easy to define, and automatically include optimizations like explicit Jacobian functions and explicit inverse Jacobian functions for the differential equation solvers to take advantage of. The result is an easy to use API which allows for more functionality and more performance optimizations than could traditionally be offered. ParameterizedFunction is a type which can be used in various JuliaDiffEq solvers where the parameters must be accessible by the solver function. These use call overloading generate a type which acts like a function f(t,u,du) but has access to many more features. For example, a ParameterizedFunction can contain a function for the Jacobian or Inverse Jacobian. If such functions exist, the solvers can use them to increase the speed of computations. If they don't exist, the solvers will ignore them. Since ParameterizedFunction is a subtype of Function, these can be used anywhere that a function can be used, just with the extra functionality ignored.

differential-equations jacobian parametersThe code behind @pendulum_bot Twitter bot which posts animations of a double pendulum released from a random position to swing for 30 seconds. The animation is saved as .mp4 video in animations subdirectory.

numpy matplotlib animation numerics numerical-methods differential-equations twitter twitter-botAn ordinary differential equation solving library in golang.

ode solving-library multivariate differential-equationsFor installation instructions and user guides, see the package website.

pomp mathematical-modelling statistical-inference dynamical-systems stochastic-processes state-space markov-model particle-filter likelihood-free likelihood r simulation-modeling time-series abc markov-chain-monte-carlo sequential-monte-carlo sobol-sequence b-spline differential-equations measurement-errorDelay Differential Equations in Haskell

simulation delay differential-equationsThis package contains bindings for ODEInterface.jl to allow it to be used with the JuliaDiffEq common interface. For more information on using the solvers from this package, see the DifferentialEquations.jl documentation. The options available in solve are documented at the common solver options page. The available methods are documented at the ODE solvers page.

julia radau rodas hairer differential-equationsWrangle non-linear differential equations while writing maintainable, simple code. ODE solvers seem to fill the niche of simple system solvers in your numerical packages such as scipy's odeint/solve_ivp.

simulation ode differential-equations runge-kutta newton-raphson-multivariable ode-solver ivp runge-kutta-fehlberg initial-value-problem dormand-princeBackpropagation through a Neural ODE/CDE can be performed via the "adjoint method", which involves solving another differential equation backwards in time. However it turns out that default numerical solvers are unnecessarily stringent when solving the adjoint equation, and take too many steps, that are too small. That's it.

machine-learning deep-neural-networks deep-learning pytorch dynamical-systems differential-equations ordinary-differential-equations numerical-methods numerical-analysis neural-differential-equations controlled-differential-equations
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