Search Results for "differential equation python"

Opacus is a library that enables training PyTorch models with differential privacy. It supports training with minimal code changes required on the client, has little impact on training performance, and allows the client to online track the privacy budget expended at any given moment. Vectorized per-sample gradient computation that is 10x faster than micro batching. Supports most types of PyTorch models and can be used with minimal modification to the original neural network. Open source,...

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...

DeepXDE is a library for scientific machine learning and physics-informed learning. DeepXDE includes the following algorithms. Physics-informed neural network (PINN). Solving different problems. Solving forward/inverse ordinary/partial differential equations (ODEs/PDEs) [SIAM Rev.] Solving forward/inverse integro-differential equations (IDEs) [SIAM Rev.] fPINN: solving forward/inverse fractional PDEs (fPDEs) [SIAM J. Sci. Comput.] NN-arbitrary polynomial chaos (NN-aPC): solving...

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.

CasADi is a symbolic framework for numeric optimization implementing automatic differentiation in forward and reverse modes on sparse matrix-valued computational graphs. It supports self-contained C-code generation and interfaces state-of-the-art codes such as SUNDIALS, IPOPT, etc. It can be used in C++, Python, or Matlab/Octave. CasADi's backbone is a symbolic framework implementing forward and reverse modes of AD on expression graphs to construct gradients, large-and-sparse Jacobians, and Hessians. These expression graphs, encapsulated in Function objects, can be evaluated in a virtual machine or exported to stand-alone C code. Initial value problems in ordinary or differential-algebraic equations (ODE/DAE) can be calculated using explicit or implicit Runge-Kutta methods or interfaces to IDAS/CVODES from the SUNDIALS suite. ...

CFD Python, a.k.a. the 12 steps to Navier-Stokes, is a practical module for learning the foundations of Computational Fluid Dynamics (CFD) by coding solutions to the basic partial differential equations that describe the physics of fluid flow. The module was part of a course taught by Prof. Lorena Barba between 2009 and 2013 in the Mechanical Engineering department at Boston University (Prof.

A lightweight C++ and Python library for finance, statistics and linear algebra. Finance features include compound rate present/future value, annuity, various present/future value coefficients ... Statistics features include mean, median, variance, standard deviation, covariance, correlation, linear regression, probabilities and random variates of various distributions ...