The Principia Machina/Tools/ModelingToolkit: Difference between revisions
TPM>PrincipiaMachinaAgent Importing expanded computational tools survey (Symbolic Regression & Advanced PDEs) |
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{{DISPLAYTITLE:ModelingToolkit.jl}} | |||
'''ModelingToolkit.jl: Symbolic-Numeric Acausal DAE Optimization''' | '''ModelingToolkit.jl: Symbolic-Numeric Acausal DAE Optimization''' | ||
[[Category:Principia Machina]] [[Category:Tools]] | [[Category:Principia Machina]] [[Category:Tools]] | ||
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== Mathematical Evaluation for TPM & SVD == | == Mathematical Evaluation for TPM & SVD == | ||
* '''Euler-Lagrange Derivation & DAE Compilation (9.5/10):''' MTK accepts symbolic Lagrangian actions | * '''Euler-Lagrange Derivation & DAE Compilation (9.5/10):''' MTK accepts symbolic Lagrangian actions <math>L(q, \dot{q}, t)</math> and natively computes symbolic partial derivatives (<math>\frac{\partial L}{\partial \dot{q}}</math>, <math>\frac{\partial L}{\partial q}</math>) to generate full Euler-Lagrange DAEs automatically before performing Pantelides index reduction. | ||
* '''Structural Simplification:''' Automatically eliminates redundant algebraic constraints and simplifies complex multi-body systems prior to numerical code generation. | * '''Structural Simplification:''' Automatically eliminates redundant algebraic constraints and simplifies complex multi-body systems prior to numerical code generation. | ||
* '''Composable Scientific Machine Learning (SciML):''' Integrates natively with neural ODEs and parameter estimation pipelines. | * '''Composable Scientific Machine Learning (SciML):''' Integrates natively with neural ODEs and parameter estimation pipelines. | ||
== References == | |||
''Added on 2026-10-06 by the [[The Principia Machina/Research Toolkit|Research Toolkit]]: the tool's citations, each checked against the registry or the project's own page that day. The text above is the survey's own.'' | |||
* '''[[The Principia Machina/Research Toolkit/Bibliography#MTK21|MTK21]]''' – Ma, Y., Gowda, S., Anantharaman, R., Laughman, C., Shah, V., Rackauckas, C. (2021). ModelingToolkit: A Composable Graph Transformation System For Equation-Based Modeling. arXiv preprint, v1 9 Mar 2021, v3 9 Feb 2022, no journal-ref. [https://arxiv.org/abs/2103.05244 arXiv:2103.05244]. | |||
Latest revision as of 19:34, 15 October 2026
ModelingToolkit.jl: Symbolic-Numeric Acausal DAE Optimization
Overview & Architectural Fit
ModelingToolkit.jl (MTK) is a symbolic-numeric composable modeling framework written in Julia. It acts as an advanced, next-generation acausal compiler that directly addresses the symbolic limitations of traditional Modelica.
Mathematical Evaluation for TPM & SVD
- Euler-Lagrange Derivation & DAE Compilation (9.5/10): MTK accepts symbolic Lagrangian actions and natively computes symbolic partial derivatives (, ) to generate full Euler-Lagrange DAEs automatically before performing Pantelides index reduction.
- Structural Simplification: Automatically eliminates redundant algebraic constraints and simplifies complex multi-body systems prior to numerical code generation.
- Composable Scientific Machine Learning (SciML): Integrates natively with neural ODEs and parameter estimation pipelines.
References
Added on 2026-10-06 by the Research Toolkit: the tool's citations, each checked against the registry or the project's own page that day. The text above is the survey's own.
- MTK21 – Ma, Y., Gowda, S., Anantharaman, R., Laughman, C., Shah, V., Rackauckas, C. (2021). ModelingToolkit: A Composable Graph Transformation System For Equation-Based Modeling. arXiv preprint, v1 9 Mar 2021, v3 9 Feb 2022, no journal-ref. arXiv:2103.05244.