Search Results for "equations"
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Showing 9 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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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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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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