SciML/ModelingToolkit.jl
ModelingToolkit.jl
ModelingToolkit.jl is a symbolic modeling framework and computer algebra system designed for the definition and simulation of complex mathematical systems. It provides a foundational environment for constructing multi-domain physical models and differential equation systems, enabling users to represent scientific problems through symbolic graphs that facilitate automated analysis and transformation.
The framework distinguishes itself through its acausal component composition, which allows for the assembly of large-scale models by connecting modular elements rather than defining explicit data flows. It employs automated system tearing and index reduction to simplify complex differential-algebraic equations, ensuring numerical stability. By utilizing just-in-time symbolic compilation, the system maps these high-level definitions directly into optimized machine code for execution by specialized numerical solvers.
Beyond standard simulation, the project integrates scientific machine learning utilities to combine symbolic physics models with neural networks. It supports automated equation discovery, allowing for the extraction of governing mathematical structures from experimental data. The framework also includes comprehensive tools for numerical optimization, including automated derivative generation and sparsity exploitation, to accelerate the solving of large-scale systems.
Features
- Acausal Modeling Frameworks - Provides a framework for composing multi-domain physical systems by connecting modular components that automatically generate efficient numerical solvers.
- Computer Algebra Systems - Acts as a symbolic engine performing automated mathematical transformations, system simplification, and code generation.
- Symbolic Equation Discoverers - Identifies the symbolic structure or functional form of differential equations directly from experimental data.
- Symbolic Modeling Frameworks - Provides a system for defining and transforming differential equations and physical models using symbolic mathematics.
- Symbolic Compilation - Utilizes just-in-time symbolic compilation to lower high-level mathematical definitions into optimized machine code.
- Multi-Domain Physical Modeling - Enables construction of multi-domain physical simulations by connecting modular components into a unified mathematical representation.
- Acausal Composition - Provides an acausal component composition system for assembling large-scale physical models by connecting modular elements.
- Symbolic - Constructs symbolic representations of differential equations, nonlinear systems, and optimization problems.
- Symbolic Graphs - Represents models as directed acyclic graphs of mathematical expressions to enable automated algebraic analysis.
- Differential Algebraic Equation Solving - Provides automated index reduction and system lowering to solve complex differential-algebraic equations efficiently.
- Index Reduction - Performs automated index reduction to simplify differential-algebraic equations for compatibility with standard numerical solvers.
- Differential Equation Optimization - Automates symbolic simplification and numerical transformation of complex differential equations to improve simulation performance.
- Numerical Solver Generators - Converts symbolic model definitions into executable numerical problems compatible with high-performance solvers.
- Numerical Computation Optimizers - Accelerates mathematical solving by automatically generating efficient functions for derivatives and applying sparsity techniques.
- Physical Model Composition - Constructs mathematical representations of multi-domain physical systems by connecting modular components.
- Scientific Machine Learning - Integrates symbolic physics models with neural networks to accelerate scientific discovery and physics-informed machine learning.
- Libraries - Provides tools for integrating symbolic physics models with neural networks to perform automated discovery and parameter estimation.
- Symbolic Expression Manipulators - Performs automated symbolic manipulations like alias elimination and system tearing to simplify nonlinear models for numerical execution.
- Governing Equation Discovery - Supports automated equation discovery to extract governing mathematical structures from experimental data.
- Numerical - Maps symbolic models to specialized numerical solvers using multiple dispatch to select the most efficient algorithm.
- Lazy System Composition - Connects reusable components through a lazy connection system to build large-scale models supporting causal and acausal approaches.
- Equation System Tearing - Employs automated system tearing to decompose complex nonlinear equations into smaller, solvable subsets.
Star history
How this analysis was created: This summary and feature list are AI-generated from collected project material and can contain mistakes. Stars, license and language are imported from GitHub. Inclusion does not mean that we have tested or audited this project. Check the source documentation for any feature you depend on. Learn more on our About page.
