lululxvi/deepxde

Features

• Physics-Informed Architectures - Implements a physics-informed neural network library for solving forward and inverse differential equations.
• Differential Equation Solvers - Computes numerical solutions for forward and inverse ordinary, partial, and integro differential equations.
• Automatic Differentiation - Provides an automatic differentiation engine supporting both forward and reverse mode for evaluating differential operators.
• Automatic Differentiation Frameworks - Provides a comprehensive system for computing derivatives using forward and reverse mode differentiation.
• Deep Operator Network Frameworks - Provides a dedicated framework for learning operator mappings that approximate function relationships in multiphysics.
• Deep Operator Networks - Implements deep operator networks to approximate relationships between functions in multiphysics problems.
• Model Performance Evaluators - Measures prediction accuracy using relative error, absolute percentage error, and other statistical metrics.
• Model Predictions - Generates predictions for input samples and computes residuals of differential operators for validation.
• Operator Mapping Learning - Trains neural networks to approximate mathematical operators that map functions to other functions using aligned datasets.
• Loss Function Calculators - Computes the difference between predicted and true values using loss functions like mean squared error.
• Tensor Computation Backends - Implements a backend-agnostic wrapper that allows switching between TensorFlow, PyTorch, and JAX tensor backends.
• Tensor Libraries - Provides a multi-backend tensor library for hardware-accelerated scientific computing and neural network operations.
• Neural Networks and Deep Learning - Implements deep operator learning to approximate operator mappings for complex multiphysics problems.
• Physics and PDE Solvers - Functions as a deep learning PDE solver for partial, ordinary, and integro differential equations.
• Time-Dependent PDE Solvers - Implements solvers for evolving physical systems using adaptive refinement and training point resampling.
• Boundary Condition Enforcement - Implements constraints like Dirichlet or Neumann using hard constraints or approximate distance functions.
• Computational Backend Integrations - Allows the selection of underlying tensor libraries for numerical operations via environment variables or detection.
• Deep Operator Networks - Implements deep operator networks to approximate mappings between functions in multiphysics problems.
• Forward PDE Solvers - Computes solutions for differential equations given specified parameters and boundary conditions.
• Inverse PDE Solvers - Estimates unknown parameters or forcing fields within differential equations by training on observed data.
• Physics-Informed Operator Solving - Combines operator learning with physics-based constraints to solve differential equations across spatial dimensions.
• Time-Independent PDE Solvers - Computes steady-state solutions for partial differential equations across various boundary conditions.
• Automatic Differentiation - Calculates derivatives using reverse-mode backpropagation, forward-mode, or zero coordinate shift methods.
• Scientific Machine Learning - Combines data-driven neural networks with mathematical constraints to model complex physical systems.
• Distributed Training - Splits training workloads across multiple GPUs using data-parallel processing to accelerate computation.
• Residual-Based Adaptive Resampling - Implements adaptive resampling of training coordinates to improve accuracy in high-residual regions of the spatial domain.
• Multi-Fidelity Optimization - Integrates multi-fidelity data to improve the overall accuracy of the learned mathematical models.
• Multi-Fidelity Data Modeling - Improves model accuracy by combining low- and high-fidelity datasets through transfer learning.
• Multi-Fidelity Training - Combines data of varying accuracy levels through transfer learning across scales to enhance model performance.
• Custom Architectures - Implements specialized neural network structures and custom loss functions tailored for complex mathematical problems.
• Multi-Fidelity - Combines low- and high-accuracy datasets through transfer learning to improve the precision of physical system models.
• Fractional PDE Solving - Computes solutions for partial differential equations involving fractional order derivatives across multiple dimensions.
• Integro-Differential Equation Solving - Calculates solutions for equations containing both derivatives and integrals, such as Volterra types.
• Ordinary Differential Equation Solving - Computes solutions for systems of ordinary differential equations including second order systems.
• Mathematical Function Approximations - Learns mathematical mappings using explicit formulas or datasets to represent target functions.
• Mathematical Point Sampling - Generates training datasets using specialized mathematical sampling sequences like Latin Hypercube and Sobol.
• Constructive Solid Geometry Operations - Uses constructive solid geometry and boolean operations to define complex spatial domains for differential equations.

Star history