Search Results for "equations"

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. ...

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. ...

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. ...

...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.

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...

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...

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.

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.