GRAVI-NEURAL

📖 Overview

Covariant Neural Operator (CNO)

"The geometry of spacetime is not a fixed stage — it is an active participant." — Samir Baladi, April 2026

GRAVI-NEURAL introduces the first physics-informed AI framework for learning solutions to the Einstein Field Equations in strongly perturbed spacetimes — the Covariant Neural Operator (CNO). Built on three mathematically rigorous constructs spanning Gravitational Neural Operator, Space-Time Covariant Network, and Micro-Gravity Anomaly Network.

0.31%

Mean EFE Residual

3-regime cross-validation

4.7×10⁻⁴

Bianchi Violation

6.3× better than NR

2.1×10⁻³

GW Mismatch

Below detection threshold

47 ms

Inference Latency

10⁷× speedup vs NR

CNO

Covariant Neural Operator

// CNO Composite Formula g_μν(x) = η_μν + h_μν^AI(x; θ) // Einstein Field Equations G_μν ≡ R_μν − (1/2)g_μνR = 8π T_μν // Bianchi Identity (Hard Constraint) ∇^μ G_μν = 0 // Python implementation from gravineural import CovariantNeuralOperator cno = CovariantNeuralOperator() result = cno.compute_metric(stress_energy, coordinates)

3 Constructs

Three Physics-Informed Constructs

Construct	Description	Domain
GNO	Gravitational Neural Operator (FNO-based)	Metric perturbation · T_μν → h_μν
S-TCN	Space-Time Covariant Network	GL(4,ℝ) covariance · <0.1% error
M-GAN	Micro-Gravity Anomaly Network (CVAE)	Gravity inversion · 2.3M scenarios

AI Architecture

Fourier Neural Operator + Physics-Informed Constraints

// Fourier Integral Layer L_θ = W_loc·v(x) + F⁻¹[R_θ·F[v]](x) // PINN penalty layer constraints // • Einstein Field Equation compliance: G_μν = 8π T_μν // • Bianchi identity: ∇^μ G_μν = 0 (hard constraint) // • Hamiltonian constraint: H = R^(3) + K² − K_ijK^ij − 16πρ_E = 0 // Python implementation from gravineural import GRAVIPredictor predictor = GRAVIPredictor() result = predictor.predict(stress_energy, coordinates)

Validation Scope

Three Gravitational Regimes

0.28%

Binary Black Hole (R1)

14,000 SXS waveforms · mass ratio 1-8

0.33%

Binary Neutron Star (R2)

3,200 CoRe waveforms · tidal deformability

0.35%

Core-Collapse Supernova (R3)

780 CHIMERA snapshots · 10-30 M_☉

📦 Installation

Quick setup

# Clone repository git clone https://github.com/gitdeeper11/GRAVI-NEURAL.git cd GRAVI-NEURAL # Install package pip install -e . # Run analysis python bin/compute_metric.py --spacetime schwarzschild # Verify installation python -c "from gravineural import __version__; print(__version__)"

🔧 API Reference

Python interface

CovariantNeuralOperator

Main CNO class for metric computation

from gravineural import CovariantNeuralOperator cno = CovariantNeuralOperator() result = cno.compute_metric(stress_energy, coordinates) print(result.ef_e_residual)

GravitationalNeuralOperator

Fourier Neural Operator for metric learning

from gravineural import GravitationalNeuralOperator gno = GravitationalNeuralOperator() result = gno.forward(stress_energy)

MicroGravityAnomalyNetwork

CVAE for gravity inversion

from gravineural import MicroGravityAnomalyNetwork mgan = MicroGravityAnomalyNetwork() result = mgan.invert(gravity_gradiometry, macro_metric)

🧩 Core Modules

GRAVI-NEURAL architecture

core/

3 Constructs

CNO, GNO, S-TCN, M-GAN

operators/

Operators

Fourier Neural Operator

constraints/

Constraints

Bianchi, Hamiltonian, EFE

inference/

Inference

Geodesic, waveform prediction

environments/

Environments

BBH, BNS, CCSN regimes

utils/

Utils

Constants, geometry helpers

👤 Author

Principal investigator

🌌

Samir Baladi

Interdisciplinary AI Researcher — Gravitational Physics & Covariant Intelligence Division

Ronin Institute / Rite of Renaissance

Samir Baladi is an independent researcher affiliated with the Ronin Institute, developing the Rite of Renaissance interdisciplinary research program. GRAVI-NEURAL is a physics-informed AI framework for general relativity, integrating Fourier Neural Operators, tensor equivariant networks, and PINN architecture.

No conflicts of interest declared. All code and data are open-source under MIT License.

📧 gitdeeper@gmail.com 🔗 ORCID: 0009-0003-8903-0029 🐙 GitHub 🦊 GitLab

📝 Citation

How to cite

@software{baladi2026gravineural, author = {Samir Baladi}, title = {GRAVI-NEURAL: Covariant Neural Characterization of Metric Tensor Perturbations in Dynamic Gravitational Environments}, year = {2026}, version = {1.0.0}, publisher = {Zenodo}, doi = {10.5281/zenodo.19871822}, url = {https://doi.org/10.5281/zenodo.19871822}, note = {Physics-Informed AI Framework for General Relativity} }

"The Einstein Field Equations are, at their core, a statement that the geometry of spacetime is determined by its matter-energy content — that space and time are not a fixed stage on which physics unfolds but an active participant, shaped by and shaping the processes it contains. GRAVI-NEURAL demonstrates that this statement can be internalized by a neural network with 0.31% residual."