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. ...

...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. ...

...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.

...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...