Search Results for "equations"
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Showing 15 open source projects for "equations"
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DiffEqFlux.jl
Pre-built implicit layer architectures with O(1) backprop, GPUs
DiffEqFlux.jl is a Julia library that combines differential equations with neural networks, enabling the creation of neural differential equations (neural ODEs), universal differential equations, and physics-informed learning models. It serves as a bridge between the DifferentialEquations.jl and Flux.jl libraries, allowing for end-to-end differentiable simulations and model training in scientific machine learning. -
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PySINDy
A package for the sparse identification of nonlinear dynamical systems
PySINDy is a Python library that implements the Sparse Identification of Nonlinear Dynamics (SINDy) method for discovering mathematical models of dynamical systems from data. The framework focuses on identifying governing equations that describe the behavior of complex physical systems by selecting sparse combinations of candidate functions. Instead of fitting a purely predictive machine learning model, PySINDy attempts to recover interpretable differential equations that explain how a system evolves over time. This approach is particularly valuable in scientific fields such as physics, engineering, and biology where researchers seek both predictive accuracy and theoretical insight. ... -
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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. 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. ... -
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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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Lux.jl
Elegant and Performant Deep Learning
...Unlike traditional machine learning libraries that bundle training logic and models, Lux separates model definitions from training routines, encouraging modularity and ease of experimentation. It integrates seamlessly with SciML and other Julia packages, supporting neural differential equations and scientific machine learning workflows. -
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NVIDIA PhysicsNeMo
Open-source deep-learning framework for building and training
NVIDIA PhysicsNeMo is an open-source deep learning framework designed for building artificial intelligence models that incorporate physical laws and scientific knowledge into machine learning workflows. The framework focuses on the emerging field of physics-informed machine learning, where neural networks are used alongside physical equations to model complex scientific systems. PhysicsNeMo provides modular Python components that allow developers to create scalable training and inference pipelines for models that combine data-driven learning with physics-based constraints. It is built on top of the PyTorch ecosystem and integrates with GPU-accelerated computing environments to handle computationally demanding simulations and datasets. ... -
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DeepXDE
A library for scientific machine learning & 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 forward/inverse stochastic PDEs (sPDEs) [J. Comput. Phys.] PINN with hard constraints (hPINN): solving inverse design/topology optimization [SIAM J. ... -
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NeuralPDE.jl
Physics-Informed Neural Networks (PINN) Solvers
NeuralPDE.jl is a Julia library for solving partial differential equations (PDEs) using physics-informed neural networks and scientific machine learning. Built on top of the SciML ecosystem, it provides a flexible and composable interface for defining PDEs and training neural networks to approximate their solutions. NeuralPDE.jl enables hybrid modeling, data-driven discovery, and fast PDE solvers in high dimensions, making it suitable for scientific research and engineering applications. -
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Optax
Optax is a gradient processing and optimization library for JAX
...Others may build upon these basic components in more complicated abstractions. Whenever reasonable, implementations prioritize readability and structuring code to match standard equations, over code reuse. -
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Flow Matching
A PyTorch library for implementing flow matching algorithms
...The underlying idea is to parameterize a flow (a time-dependent vector field) that transports samples from a simple base distribution to a target distribution, and train via matching of flows without requiring score estimation or noisy corruption—this can lead to more efficient or stable generative training. The library supports both continuous-time flows (via differential equations) and discrete-time analogues, giving flexibility in design and tradeoffs. It provides examples across modalities (images, toy 2D distributions) to help users understand how to apply flow matching in practice. The codebase includes notebooks illustrating 2D flow matching, discrete flows, and Riemannian flow matching on curved manifolds (e.g. flat torus) for non-Euclidean support. -
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Qwen2.5-Coder
Qwen2.5-Coder is the code version of Qwen2.5, the large language model
Qwen2.5-Coder, developed by QwenLM, is an advanced open-source code generation model designed for developers seeking powerful and diverse coding capabilities. It includes multiple model sizes—ranging from 0.5B to 32B parameters—providing solutions for a wide array of coding needs. The model supports over 92 programming languages and offers exceptional performance in generating code, debugging, and mathematical problem-solving. Qwen2.5-Coder, with its long context length of 128K tokens, is... -
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Gorgonia
Gorgonia is a library that helps facilitate machine learning in Go
Write and evaluate mathematical equations involving multidimensional arrays easily. Gorgonia is a library that helps facilitate machine learning in Go. Write and evaluate mathematical equations involving multidimensional arrays easily. If this sounds like Theano or TensorFlow, it's because the idea is quite similar. Specifically, the library is pretty low-level, like Theano, but has higher goals like Tensorflow. -
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BayesianCortex
simple algorithm for a realtime interactive visual cortex for painting
A paint program where the canvas is the visual cortex of a simple kind of artificial intelligence. You paint with the mouse into its dreams and it responds by changing what you painted gradually. There will also be an API for using it with other programs as a general high-dimensional space. Each pixel's brightness is its own dimension. Bayesian nodes have exactly 3 childs because that is all thats needed to do NAND in a fuzzy way as Bayes' Rule which is NAND at certain extremes. NAND can be... -
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A branch-and-prune method to find all solutions to systems of nonlinear equations. The number of variables must equal the number of equations. The variables must have proper lower and upper bounds. The solver has an interface to the AMPL environment.
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The JSparse Matrix Package, developed by Philipp Geigenmüller during an internship at the prudsys AG in Chemnitz, Germany, is an extension of the well-known Java Matrix Package (JAMA) and allows the use of sparse matrices and related algorithms.
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