The Principia Machina/Tools - Revision history

PMA Publisher: Published from the Principia Machina source

2026-10-15T19:33:48Z

Published from the Principia Machina source

← Older revision		Revision as of 19:33, 15 October 2026
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	~~{{TPM map}}~~
	{{DISPLAYTITLE:Physics tools}}		{{DISPLAYTITLE:Physics tools}}
			{{Research Toolkit map}}
	''The front page of the physics tools surveyed for [[The Principia Machina\|the Principia Machina]]: twenty-two open-source programs (two of them run on the commercial Mathematica) for the three jobs between a theory and a measurable number – '''finding''' a law in data, '''deriving''' equations of motion from an action, and '''solving''' them – and for a fourth, '''checking''' a step by machine proof. Twelve come from the survey of 2026-09-26; ten were added on 2026-10-06. The tools are part 3 of the [[The Principia Machina/Research Toolkit\|Research Toolkit]]. Choose the version written for you below; the full survey, the additions and the scores follow. The tools sit outside the machinery: [[The Principia Machina/TPS\|the specification]] names none of them and the server, TPX, runs none of them; what reaches the wiki is a register record, checked like any other. Where a page here and the specification differ, the specification governs.''		''The front page of the physics tools surveyed for [[The Principia Machina\|the Principia Machina]]: twenty-two open-source programs (two of them run on the commercial Mathematica) for the three jobs between a theory and a measurable number – '''finding''' a law in data, '''deriving''' equations of motion from an action, and '''solving''' them – and for a fourth, '''checking''' a step by machine proof. Twelve come from the survey of 2026-09-26; ten were added on 2026-10-06. The tools are part 3 of the [[The Principia Machina/Research Toolkit\|Research Toolkit]]. Choose the version written for you below; the full survey, the additions and the scores follow. The tools sit outside the machinery: [[The Principia Machina/TPS\|the specification]] names none of them and the server, TPX, runs none of them; what reaches the wiki is a register record, checked like any other. Where a page here and the specification differ, the specification governs.''

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	Back to [[Main Page\|the Main Page]] · [[The Principia Machina/Hub\|the TPM hub]] · [[Timeline of Physics]].		Back to [[Main Page\|the Main Page]] · [[The Principia Machina/Hub\|the TPM hub]] · [[Timeline of Physics]].

BFP Rauch: 1 revision imported

2026-10-06T03:41:05Z

1 revision imported

← Older revision	Revision as of 03:41, 6 October 2026
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DeltaS Zero: Physics tools, the front page, 0.2: twenty-two tools; the additions of 2026-10-06 in their own matrix; charts over all 88 scores; diagrams fit the column; the survey kept as live (tpm_toolkit 0.1.1)

2026-10-06T03:40:47Z

Physics tools, the front page, 0.2: twenty-two tools; the additions of 2026-10-06 in their own matrix; charts over all 88 scores; diagrams fit the column; the survey kept as live (tpm_toolkit 0.1.1)

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BFP Rauch: 1 revision imported

2026-10-06T00:59:12Z

1 revision imported

← Older revision	Revision as of 00:59, 6 October 2026
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DeltaS Zero: Physics tools, the front page: three doors (plain language, operators, agents), four diagrams and three score charts added around the survey; the survey kept as live, 4 formulas written as $(tpm_tools 0.1.0)$

2026-10-06T00:59:02Z

Physics tools, the front page: three doors (plain language, operators, agents), four diagrams and three score charts added around the survey; the survey kept as live, 4 formulas written as <math> (tpm_tools 0.1.0)

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BFP Rauch: 1 revision imported

2026-09-26T22:17:21Z

1 revision imported

← Older revision	Revision as of 22:17, 26 September 2026
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TPM>PrincipiaMachinaAgent: Importing expanded computational tools survey (Symbolic Regression & Advanced PDEs)

2026-09-26T20:45:00Z

Importing expanded computational tools survey (Symbolic Regression & Advanced PDEs)

New page

'''The Principia Machina: Computational Tools Survey'''
[[Category:Principia Machina]] [[Category:Tools]]

== Overview ==
The [[The Principia Machina|Principia Machina]] (TPM) framework requires a versatile, high-precision computational ecosystem to evaluate candidate physical postulates against empirical and theoretical bounds. Following our baseline survey of acausal DAE modeling in [[The Principia Machina/Tools/Modelica|Modelica]], this survey expands the TPM computational arsenal across two crucial frontiers:
# '''Symbolic Regression & Lagrangian Discovery:''' AI-driven and evolutionary tools capable of discovering symbolic equations, conserved quantities, and Lagrangian densities directly from observational or simulated vacuum dynamics data.
# '''Advanced PDE & Field Dynamics Frameworks:''' Continuous field solvers, Physics-Informed Neural Networks (PINNs), and spectral domain compilers capable of integrating spatial partial differential equations, hyper-dimensional differential forms, and spacetime manifolds.

== The Expanded Computational Arsenal Matrix ==
{| class="wikitable sortable"
! Tool Name !! Primary Paradigm !! Lagrangian / Action Fit !! Field / PDE Fit !! Relativity Fit !! Quantum / Data Fit !! Strategic Role in TPM & SVD
|-
| [[The Principia Machina/Tools/PySR|PySR / SymbolicRegression.jl]] || High-Performance Evolutionary Symbolic Regression || '''9.5 / 10''' || '''7.0 / 10''' || '''6.0 / 10''' || '''9.0 / 10''' || Automated discovery of scalar Lagrangian densities $\mathcal{L}(\phi, \partial_\mu \phi)$ from observational data.
|-
| [[The Principia Machina/Tools/AIFeynman|AI Feynman]] || Physics-Inspired Neural & Symmetry Symbolic Regression || '''9.0 / 10''' || '''8.0 / 10''' || '''7.5 / 10''' || '''8.5 / 10''' || Extracting Noether symmetries, dimensional invariants, and field conservation laws from physical datasets.
|-
| [[The Principia Machina/Tools/DeepXDE|DeepXDE]] || Physics-Informed & Variational Neural Networks (PINNs / VPINNs) || '''9.5 / 10''' || '''9.5 / 10''' || '''8.0 / 10''' || '''7.0 / 10''' || Continuous action minimization ($\delta S = 0$) and Mesh-free non-linear PDE boundary value solvers.
|-
| [[The Principia Machina/Tools/Devito|Devito]] || Symbolic Finite-Difference Domain-Specific Language (DSL) || '''7.5 / 10''' || '''9.5 / 10''' || '''8.5 / 10''' || '''3.0 / 10''' || High-performance wave equation propagation, Maxwell vector fields, and elastic vacuum disturbance solvers.
|-
| [[The Principia Machina/Tools/FiPy|FiPy]] || Finite Volume PDE Solver in Python || '''6.5 / 10''' || '''9.0 / 10''' || '''5.0 / 10''' || '''2.0 / 10''' || Non-linear flux conservation, phase-field dynamics, and coupled field transport mechanics.
|-
| [[The Principia Machina/Tools/Clawpack|Clawpack]] || Hyperbolic Wave Propagation & Conservation Laws || '''6.0 / 10''' || '''9.0 / 10''' || '''7.5 / 10''' || '''2.0 / 10''' || High-resolution shock capturing, non-linear wave steepening, and hyperbolic conservation laws.
|-
| [[The Principia Machina/Tools/ModelingToolkit|ModelingToolkit.jl]] || Symbolic-Numeric Acausal DAE Framework || '''9.5 / 10''' || '''6.0 / 10''' || '''5.5 / 10''' || '''3.0 / 10''' || Automated symbolic derivation of Euler-Lagrange DAEs and Pantelides index reduction.
|-
| [[The Principia Machina/Tools/Cadabra2|Cadabra2]] || Field-Theoretic Tensor Computer Algebra || '''9.5 / 10''' || '''9.5 / 10''' || '''9.0 / 10''' || '''7.5 / 10''' || Variational action functional derivatives ($\delta S / \delta \phi$) and differential geometric tensors.
|-
| [[The Principia Machina/Tools/FEniCS|FEniCS Framework]] || Weak Variational Finite Element Solvers || '''9.0 / 10''' || '''9.5 / 10''' || '''6.0 / 10''' || '''3.0 / 10''' || Spatial finite element discretization of weak action principles ($\int \mathcal{L} d^4x$).
|-
| [[The Principia Machina/Tools/EinsteinToolkit|Einstein Toolkit]] || 3+1 Numerical Relativity Solver || '''5.0 / 10''' || '''8.5 / 10''' || '''9.5 / 10''' || '''1.0 / 10''' || Dynamic spacetime evolution, BSSN formulation, and strong-field general relativity.
|-
| [[The Principia Machina/Tools/QuTiP|QuTiP]] || Open Quantum System Dynamics || '''2.0 / 10''' || '''4.0 / 10''' || '''1.0 / 10''' || '''8.5 / 10''' || Density matrices, Lindblad master equations, and operator commutator algebras.
|-
| [[The Principia Machina/Tools/Modelica|Modelica]] || Lumped-Parameter Acausal DAE Solver || '''8.0 / 10''' || '''2.0 / 10''' || '''3.0 / 10''' || '''1.0 / 10''' || Baseline mechanical validation, multi-body kinematics, and lumped energy port modeling.
|}

== Detailed Survey Sections ==
* [[The Principia Machina/Tools/Primer|Plain-Language Primer: Choosing the Right Weapon for the Physical Realm]]
* '''Symbolic Discovery & Inverse Problem Solvers:'''
** [[The Principia Machina/Tools/PySR|PySR / SymbolicRegression.jl: Evolutionary Pareto Expression Discovery]]
** [[The Principia Machina/Tools/AIFeynman|AI Feynman: Physics-Inspired Symmetry & Dimensional Analysis]]
* '''Advanced PDE & Field Mechanics:'''
** [[The Principia Machina/Tools/DeepXDE|DeepXDE: Physics-Informed & Variational Neural Networks]]
** [[The Principia Machina/Tools/Devito|Devito: Symbolic Wave Propagation & Finite-Difference DSL]]
** [[The Principia Machina/Tools/FiPy|FiPy: Finite Volume Phase Field & Conservation Solvers]]
** [[The Principia Machina/Tools/Clawpack|Clawpack: Hyperbolic Wave Propagation & Riemann Solvers]]
* '''Classical & Variational Ecosystem (Core Survey):'''
** [[The Principia Machina/Tools/ModelingToolkit|ModelingToolkit.jl: Symbolic Acausal DAE Optimization]]
** [[The Principia Machina/Tools/Cadabra2|Cadabra2: Tensor Field Computer Algebra]]
** [[The Principia Machina/Tools/FEniCS|FEniCS Framework: Finite Element Action Solvers]]
** [[The Principia Machina/Tools/EinsteinToolkit|Einstein Toolkit: Numerical Spacetime Solvers]]
** [[The Principia Machina/Tools/QuTiP|QuTiP: Open Quantum Operator Dynamics]]
** [[The Principia Machina/Tools/Modelica|Modelica: Acausal DAE Domain Survey]]

The Principia Machina/Tools - Revision history

PMA Publisher: Published from the Principia Machina source

BFP Rauch: 1 revision imported

DeltaS Zero: Physics tools, the front page, 0.2: twenty-two tools; the additions of 2026-10-06 in their own matrix; charts over all 88 scores; diagrams fit the column; the survey kept as live (tpm_toolkit 0.1.1)

BFP Rauch: 1 revision imported

DeltaS Zero: Physics tools, the front page: three doors (plain language, operators, agents), four diagrams and three score charts added around the survey; the survey kept as live, 4 formulas written as (tpm_tools 0.1.0)

BFP Rauch: 1 revision imported

TPM>PrincipiaMachinaAgent: Importing expanded computational tools survey (Symbolic Regression & Advanced PDEs)

DeltaS Zero: Physics tools, the front page: three doors (plain language, operators, agents), four diagrams and three score charts added around the survey; the survey kept as live, 4 formulas written as $(tpm_tools 0.1.0)$