The Principia Machina/Tools/PySR - Revision history

PMA Publisher: Published from the Principia Machina source

2026-10-15T19:34:10Z

Published from the Principia Machina source

← Older revision		Revision as of 19:34, 15 October 2026
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			{{DISPLAYTITLE:PySR / SymbolicRegression.jl}}
	'''PySR / SymbolicRegression.jl: High-Performance Symbolic Discovery'''		'''PySR / SymbolicRegression.jl: High-Performance Symbolic Discovery'''
	[[Category:Principia Machina]] [[Category:Tools]]		[[Category:Principia Machina]] [[Category:Tools]]
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	''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.''		''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#PYSR23\|PYSR23]]''' – Cranmer, M. (2023). Interpretable Machine Learning for Science with PySR and SymbolicRegression.jl. arXiv preprint (astro-ph.IM), v1 2 May 2023, v3 5 May 2023, no journal-ref. [https://arxiv.org/abs/2305.01582 arXiv:2305.01582], [https://doi.org/10.48550/arXiv.2305.01582 doi:10.48550/arXiv.2305.01582].		* '''[[The Principia Machina/Research Toolkit/Bibliography#PYSR23\|PYSR23]]''' – Cranmer, M. (2023). Interpretable Machine Learning for Science with PySR and SymbolicRegression.jl. arXiv preprint (astro-ph.IM), v1 2 May 2023, v3 5 May 2023, no journal-ref. [https://arxiv.org/abs/2305.01582 arXiv:2305.01582], [https://doi.org/10.48550/arXiv.2305.01582 doi:10.48550/arXiv.2305.01582].

BFP Rauch: 1 revision imported

2026-10-06T03:41:05Z

1 revision imported

← Older revision	Revision as of 03:41, 6 October 2026
(No difference)

DeltaS Zero: References added: the tool's citation as its project asks, each checked 2026-10-06; the survey's text unchanged (tpm_toolkit 0.1.1)

2026-10-06T03:40:47Z

References added: the tool's citation as its project asks, each checked 2026-10-06; the survey's text unchanged (tpm_toolkit 0.1.1)

← Older revision		Revision as of 03:40, 6 October 2026
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	# '''Variational Loss Enforcement:''' Evaluate candidates against action stationarity constraints.		# '''Variational Loss Enforcement:''' Evaluate candidates against action stationarity constraints.
	# '''Analytical Verification:''' Pass discovered symbolic candidate expressions to [[The Principia Machina/Tools/Cadabra2\|Cadabra2]] for formal Noether symmetry evaluation.		# '''Analytical Verification:''' Pass discovered symbolic candidate expressions to [[The Principia Machina/Tools/Cadabra2\|Cadabra2]] for formal Noether symmetry evaluation.

			== 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#PYSR23\|PYSR23]]''' – Cranmer, M. (2023). Interpretable Machine Learning for Science with PySR and SymbolicRegression.jl. arXiv preprint (astro-ph.IM), v1 2 May 2023, v3 5 May 2023, no journal-ref. [https://arxiv.org/abs/2305.01582 arXiv:2305.01582], [https://doi.org/10.48550/arXiv.2305.01582 doi:10.48550/arXiv.2305.01582].

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: Formulas written for the wiki's math renderer: 1 $$..$$ and 7 $..$ as $, 4 numbered lines as # items; no other text changed (tpm_tools 0.1.0)$

2026-10-06T00:59:02Z

Formulas written for the wiki's math renderer: 1 $$..$$ and 7 $..$ as <math>, 4 numbered lines as # items; no other text changed (tpm_tools 0.1.0)

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

'''PySR / SymbolicRegression.jl: High-Performance Symbolic Discovery'''
[[Category:Principia Machina]] [[Category:Tools]]

== Overview & Architectural Fit ==
'''PySR''' (interfaced via Python to the high-performance Julia backend '''SymbolicRegression.jl''') is an open-source symbolic regression framework utilizing Multi-Population Genetic Algorithms and Pareto Frontier optimization. In the [[The Principia Machina|Principia Machina]] architecture, PySR addresses the inverse theoretical problem: given a field dataset or trajectory simulation, what analytical scalar expression or Lagrangian density $\mathcal{L}(q, \dot{q}, t)$ or $\mathcal{L}(\phi, \partial_\mu \phi)$ governs the system?

== Mathematical Evaluation for TPM & SVD ==
* '''Lagrangian & Action Discovery (9.5/10):''' PySR can search candidate functional spaces for invariant quantities. By setting loss functions to penalize violations of Euler-Lagrange dynamics or Hamilton's principle ($\delta S = 0$), PySR directly extracts analytical scalar Lagrangians from observational state trajectories.
* '''Pareto Complexity Optimization:''' Automatically balances accuracy against expression complexity using score metrics:
$$\text{Score} = -\frac{\Delta \log(\text{MSE})}{\Delta \text{Complexity}}$$
This directly prevents the discovery of unphysical "overfitted" mathematical artifacts.
* '''Custom Operator Ingestion:''' Supports specialized physical operators (e.g., spatial gradients $\nabla \phi$, d'Alembertian operators $\Box \phi$, or relativistic dot products $u^\mu u_\mu$).

== SVD Integration Pipeline ==
1. '''Data Generation:''' Extract spatial perturbation profiles from vacuum disturbance simulations.
2. '''Operator Set Specification:''' Define admissible operators $\{+, -, \times, \div, \nabla, \partial_t, \text{exp}\}$.
3. '''Variational Loss Enforcement:''' Evaluate candidates against action stationarity constraints.
4. '''Analytical Verification:''' Pass discovered symbolic candidate expressions to [[The Principia Machina/Tools/Cadabra2|Cadabra2]] for formal Noether symmetry evaluation.

← Older revision		Revision as of 00:59, 6 October 2026
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	== Overview & Architectural Fit ==		== Overview & Architectural Fit ==
	'''PySR''' (interfaced via Python to the high-performance Julia backend '''SymbolicRegression.jl''') is an open-source symbolic regression framework utilizing Multi-Population Genetic Algorithms and Pareto Frontier optimization. In the [[The Principia Machina\|Principia Machina]] architecture, PySR addresses the inverse theoretical problem: given a field dataset or trajectory simulation, what analytical scalar expression or Lagrangian density $\mathcal{L}(q, \dot{q}, t)$ or $\mathcal{L}(\phi, \partial_\mu \phi)$ governs the system?		'''PySR''' (interfaced via Python to the high-performance Julia backend '''SymbolicRegression.jl''') is an open-source symbolic regression framework utilizing Multi-Population Genetic Algorithms and Pareto Frontier optimization. In the [[The Principia Machina\|Principia Machina]] architecture, PySR addresses the inverse theoretical problem: given a field dataset or trajectory simulation, what analytical scalar expression or Lagrangian density <math>\mathcal{L}(q, \dot{q}, t)</math> or <math>\mathcal{L}(\phi, \partial_\mu \phi)</math> governs the system?

	== Mathematical Evaluation for TPM & SVD ==		== Mathematical Evaluation for TPM & SVD ==
	* '''Lagrangian & Action Discovery (9.5/10):''' PySR can search candidate functional spaces for invariant quantities. By setting loss functions to penalize violations of Euler-Lagrange dynamics or Hamilton's principle ($\delta S = 0$), PySR directly extracts analytical scalar Lagrangians from observational state trajectories.		* '''Lagrangian & Action Discovery (9.5/10):''' PySR can search candidate functional spaces for invariant quantities. By setting loss functions to penalize violations of Euler-Lagrange dynamics or Hamilton's principle (<math>\delta S = 0</math>), PySR directly extracts analytical scalar Lagrangians from observational state trajectories.
	* '''Pareto Complexity Optimization:''' Automatically balances accuracy against expression complexity using score metrics:		* '''Pareto Complexity Optimization:''' Automatically balances accuracy against expression complexity using score metrics:
	$$\text{Score} = -\frac{\Delta \log(\text{MSE})}{\Delta \text{Complexity}}$$		<math display="block">\text{Score} = -\frac{\Delta \log(\text{MSE})}{\Delta \text{Complexity}}</math>
	This directly prevents the discovery of unphysical "overfitted" mathematical artifacts.		This directly prevents the discovery of unphysical "overfitted" mathematical artifacts.
	* '''Custom Operator Ingestion:''' Supports specialized physical operators (e.g., spatial gradients $\nabla \phi$, d'Alembertian operators $\Box \phi$, or relativistic dot products $u^\mu u_\mu$).		* '''Custom Operator Ingestion:''' Supports specialized physical operators (e.g., spatial gradients <math>\nabla \phi</math>, d'Alembertian operators <math>\Box \phi</math>, or relativistic dot products <math>u^\mu u_\mu</math>).

	== SVD Integration Pipeline ==		== SVD Integration Pipeline ==
	1. '''Data Generation:''' Extract spatial perturbation profiles from vacuum disturbance simulations.		# '''Data Generation:''' Extract spatial perturbation profiles from vacuum disturbance simulations.
	2. '''Operator Set Specification:''' Define admissible operators $\{+, -, \times, \div, \nabla, \partial_t, \text{exp}\}$.		# '''Operator Set Specification:''' Define admissible operators <math>\{+, -, \times, \div, \nabla, \partial_t, \text{exp}\}</math>.
	3. '''Variational Loss Enforcement:''' Evaluate candidates against action stationarity constraints.		# '''Variational Loss Enforcement:''' Evaluate candidates against action stationarity constraints.
	4. '''Analytical Verification:''' Pass discovered symbolic candidate expressions to [[The Principia Machina/Tools/Cadabra2\|Cadabra2]] for formal Noether symmetry evaluation.		# '''Analytical Verification:''' Pass discovered symbolic candidate expressions to [[The Principia Machina/Tools/Cadabra2\|Cadabra2]] for formal Noether symmetry evaluation.

The Principia Machina/Tools/PySR - Revision history

PMA Publisher: Published from the Principia Machina source

BFP Rauch: 1 revision imported

DeltaS Zero: References added: the tool's citation as its project asks, each checked 2026-10-06; the survey's text unchanged (tpm_toolkit 0.1.1)

BFP Rauch: 1 revision imported

DeltaS Zero: Formulas written for the wiki's math renderer: 1 $$..$$ and 7 $..$ as , 4 numbered lines as # items; no other text changed (tpm_tools 0.1.0)

BFP Rauch: 1 revision imported

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

DeltaS Zero: Formulas written for the wiki's math renderer: 1 $$..$$ and 7 $..$ as $, 4 numbered lines as # items; no other text changed (tpm_tools 0.1.0)$