SciML/ModelingToolkit.jl
ModelingToolkit.jl
ModelingToolkit.jl ist ein symbolisches Modellierungs-Framework und Computeralgebrasystem, das für die Definition und Simulation komplexer mathematischer Systeme konzipiert wurde. Es bietet eine grundlegende Umgebung für die Konstruktion physikalischer Multi-Domain-Modelle und Differentialgleichungssysteme, die es Nutzern ermöglicht, wissenschaftliche Probleme durch symbolische Graphen darzustellen, die eine automatisierte Analyse und Transformation erleichtern.
Das Framework zeichnet sich durch seine akausale Komponentenkomposition aus, die den Zusammenbau groß angelegter Modelle durch das Verbinden modularer Elemente ermöglicht, anstatt explizite Datenflüsse zu definieren. Es verwendet automatisierte System-Tearing- und Index-Reduktionsverfahren, um komplexe differential-algebraische Gleichungen zu vereinfachen und die numerische Stabilität sicherzustellen. Durch die Nutzung von Just-in-Time-symbolischer Kompilierung bildet das System diese hochgradigen Definitionen direkt in optimierten Maschinencode für die Ausführung durch spezialisierte numerische Löser ab.
Über die Standardsimulation hinaus integriert das Projekt wissenschaftliche Machine-Learning-Dienstprogramme, um symbolische physikalische Modelle mit neuronalen Netzen zu kombinieren. Es unterstützt die automatisierte Gleichungsentdeckung, was die Extraktion zugrunde liegender mathematischer Strukturen aus experimentellen Daten ermöglicht. Das Framework enthält zudem umfassende Tools für die numerische Optimierung, einschließlich automatisierter Ableitungsgenerierung und Sparsity-Exploitation, um die Lösung groß angelegter Systeme zu beschleunigen.
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.
