antonypamo/v1-V5

RRF Physical Bridge (V5)

Model Summary

RRF Physical Bridge (V5) is a hybrid neural-physical framework for galaxy mass modeling and rotation curve prediction using the SPARC dataset.

The model combines:

• Multi-channel baryonic decomposition
• Spectral manifold learning
• Stiefel manifold orthogonality constraints
• Physics-informed parameter prediction
• Log-space optimization for numerical stability

The framework maps galactic kinematic observations into physically meaningful halo parameters:

$$M_{\mathrm{v}\mathrm{i}\mathrm{r}},r_s,cM\_\{\backslash rm\; vir\},\backslash quad\; r\_s,\backslash quad\; c$$

while preserving spectral interpretability and enforcing physical validity.

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Evolution Roadmap

Version	Major Intervention	Outcome	Status
V1	Initial Baseline	Predicted negligible virial masses ($M_{\rm vir}\sim10^{-9}M_\odot$)	❌ Failure
V2	Normalization Correction	Fixed contaminated velocity scaling ($v_{\rm std}$)	⚠️ Partial
V3	Multi-Channel Integration + Physical Constraints	Added $V_{\rm gas}$, $V_{\rm disk}$, $V_{\rm bulge}$ and enforced positivity	⚠️ Partial
V4	Stiefel Manifold + Direct Physics Loss	Preserved orthogonality but suffered gradient explosions	⚠️ Unstable
V5	Log-Space Refactoring	Stable training and physically meaningful outputs	✅ Success

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Technical Specifications

Architecture

• 36-node spectral manifold
• Stiefel manifold parameterization
• Cayley-transform orthogonality preservation
• Multi-layer neural encoder
• Physics-constrained parameter heads

Input Channels

The model uses four synchronized velocity channels:

• Observed velocity ($V_{\rm obs}$)
• Gas contribution ($V_{\rm gas}$)
• Stellar disk contribution ($V_{\rm disk}$)
• Bulge contribution ($V_{\rm bulge}$)

Physical Decomposition

The observed rotation curve is modeled as:

$$V_{\mathrm{o}\mathrm{b}\mathrm{s}}^2===============V_{\mathrm{g}\mathrm{a}\mathrm{s}}^2+V_{\mathrm{d}\mathrm{i}\mathrm{s}\mathrm{k}}^2+V_{\mathrm{b}\mathrm{u}\mathrm{l}\mathrm{g}\mathrm{e}}^2+V_{\mathrm{h}\mathrm{a}\mathrm{l}\mathrm{o}}^{2}V\_\{\backslash rm\; obs\}^\{2\}\; ===============\; V\_\{\backslash rm\; gas\}^\{2\}\; +\; V\_\{\backslash rm\; disk\}^\{2\}\; +\; V\_\{\backslash rm\; bulge\}^\{2\}\; +\; V\_\{\backslash rm\; halo\}^\{2\}$$

where the neural network learns the residual halo contribution.

Parameter Space

To improve optimization stability, halo parameters are learned in logarithmic space:

$${\log }_{10}(M_{\mathrm{v}\mathrm{i}\mathrm{r}})\backslash log\_\{10\}(M\_\{\backslash rm\; vir\})$$

This refactoring eliminates the catastrophic gradient explosions observed in V4 and allows stable optimization across multiple orders of magnitude in halo mass.

Loss Function

• Direct Physics Loss
• Log-MSE Objective
• Spectral Manifold Constraints
• Physical Positivity Enforcement

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Benchmarking Results

Evaluation performed on the SPARC galaxy sample.

Method	Median RMSE (km/s)	Mean RMSE (km/s)	Stability Failures
RRF V5 (Log-Space)	15.93	31.94	10
MOND Benchmark	22.55	44.37	10
NFW Traditional Fit	6.08	14.37	16

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Performance Highlights

Numerical Stability

The transition from linear-space optimization to log-space parameterization resolved the catastrophic failures observed during V4 training.

Median RMSE improved from unstable values exceeding:

$${10}^7\mathrm{k}\mathrm{m},{\mathrm{s}}^{-1}10^\{7\}\backslash \; \{\backslash rm\; km,s^\{-1\}\}$$

to:

$$15.93\mathrm{k}\mathrm{m},{\mathrm{s}}^{-1}15.93\backslash \; \{\backslash rm\; km,s^\{-1\}\}$$

in the final V5 architecture.

MOND Comparison

RRF V5 achieves:

$$15.93\mathrm{k}\mathrm{m},{\mathrm{s}}^{-1}15.93\backslash \; \{\backslash rm\; km,s^\{-1\}\}$$

median RMSE versus:

$$22.55\mathrm{k}\mathrm{m},{\mathrm{s}}^{-1}22.55\backslash \; \{\backslash rm\; km,s^\{-1\}\}$$

for the evaluated MOND benchmark.

This corresponds to an approximate improvement of:

$$29.429.4\%$$

under the evaluation protocol used in this project.

Robustness

Although traditional NFW fitting achieves lower RMSE values, it exhibits more catastrophic fitting failures.

Method	Stability Failures
RRF V5	10
NFW Traditional Fit	16

This represents approximately:

$$37.537.5\%$$

fewer failures for RRF V5.

Focus Case: NGC2955

RRF V5 successfully recovers a physically plausible halo solution:

$$M_{\mathrm{v}\mathrm{i}\mathrm{r}}=1.52\times {10}^{11}{M}_{\odot }M\_\{\backslash rm\; vir\}=1.52\backslash times10^\{11\}M\_\backslash odot$$

with:

$$c=2.30c\; =\; 2.30$$

while maintaining full physical validity throughout optimization.

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Training Data

Training and evaluation were conducted using the SPARC dataset.

Dataset

SPARC (Spitzer Photometry and Accurate Rotation Curves)

Reference:

Lelli, F., McGaugh, S. S., & Schombert, J. M. (2016).

SPARC: Mass Models for 175 Disk Galaxies with Spitzer Photometry and Accurate Rotation Curves.

The Astronomical Journal, 152(6), 157.

Normalization Statistics

$$v_{\mathrm{m}\mathrm{e}\mathrm{a}\mathrm{n}}=141.83\mathrm{k}\mathrm{m},{\mathrm{s}}^{-1}v\_\{\backslash rm\; mean\}=141.83~\{\backslash rm\; km,s^\{-1\}\}$$

$$v_{\mathrm{s}\mathrm{t}\mathrm{d}}=88.11\mathrm{k}\mathrm{m},{\mathrm{s}}^{-1}v\_\{\backslash rm\; std\}=88.11~\{\backslash rm\; km,s^\{-1\}\}$$

Training was performed on 187 processed galaxy samples.

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Current Status

RRF Physical Bridge V5 represents the first fully stabilized version of the framework.

Validated features include:

• Log-space optimization
• Spectral manifold learning
• Stiefel orthogonality constraints
• Multi-channel baryonic integration
• Physically constrained outputs
• Stable physical parameter prediction
• Dark matter residual modeling

Future work includes:

• Cross-validation studies
• Bayesian uncertainty estimation
• External dataset validation
• Expanded astrophysical benchmarking
• Large-scale survey deployment
• Integration with future RRF manifold architectures

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Citation

If you use this model in research, please cite:

@misc{padilla2026rrfphysicalbridgev5,
  title={RRF Physical Bridge V5: A Hybrid Neural-Physical Framework for Galaxy Rotation Curve Modeling},
  author={Padilla Morales, Antony},
  year={2026},
  publisher={Hugging Face},
  url={https://huggingface.co/antonypamo}
}

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Contact

Author: Antony Padilla Morales

Email: (mailto:antonypamo@gmail.com)

Hugging Face: https://huggingface.co/antonypamo

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License

Apache-2.0