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:
$$
M_{\rm vir},\quad r_s,\quad c
$$
while preserving spectral interpretability and enforcing physical validity.
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 |
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:
$$
V_{\rm obs}^{2}
V_{\rm gas}^{2}
+
V_{\rm disk}^{2}
+
V_{\rm bulge}^{2}
+
V_{\rm halo}^{2}
$$
where the neural network learns the residual halo contribution.
Parameter Space
To improve optimization stability, halo parameters are learned in logarithmic space:
$$
\log_{10}(M_{\rm vir})
$$
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
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 |
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:
$$
10^{7}\ {\rm km,s^{-1}}
$$
to:
$$
15.93\ {\rm km,s^{-1}}
$$
in the final V5 architecture.
MOND Comparison
RRF V5 achieves:
$$
15.93\ {\rm km,s^{-1}}
$$
median RMSE versus:
$$
22.55\ {\rm km,s^{-1}}
$$
for the evaluated MOND benchmark.
This corresponds to an approximate improvement of:
$$
29.4%
$$
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:
$$
37.5%
$$
fewer failures for RRF V5.
Focus Case: NGC2955
RRF V5 successfully recovers a physically plausible halo solution:
$$
M_{\rm vir}=1.52\times10^{11}M_\odot
$$
with:
$$
c = 2.30
$$
while maintaining full physical validity throughout optimization.
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
$$
v_{\rm mean}=141.83~{\rm km,s^{-1}}
$$
$$
v_{\rm std}=88.11~{\rm km,s^{-1}}
$$
Training was performed on 187 processed galaxy samples.
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
Citation
If you use this model in research, please cite:
1@misc{padilla2026rrfphysicalbridgev5,
2 title={RRF Physical Bridge V5: A Hybrid Neural-Physical Framework for Galaxy Rotation Curve Modeling},
3 author={Padilla Morales, Antony},
4 year={2026},
5 publisher={Hugging Face},
6 url={https://huggingface.co/antonypamo}
7}
Contact
Author: Antony Padilla Morales
License
Apache-2.0
