NEUROPIA Documentation

📖 Overview

"If ENTROPIA was the question — how do we understand order from chaos — then NEUROPIA is the answer. It is the state in which artificial intelligence becomes the mirror that reflects the perfection of physical law across every domain simultaneously."

NEUROPIA is the tenth and culminating Physics-Informed Artificial Intelligence framework of the EntropyLab research program (E-LAB-10). It unifies all nine dissipation channels from previous projects into a single learnable operator: the Unified Field Propagator (UFP). Built on three orthogonal neural constructs spanning spectral operator learning, cross-domain symmetry preservation, and Pareto-optimal entropy minimization, NEUROPIA achieves unprecedented efficiency across five multi-physics validation regimes.

🏗️ 3-Core Architecture

NEUROPIA operates on the Physical Coupling Manifold M through three synergistic neural constructs:

UFP — Unified Field Propagator

A gauge-equivariant tensor neural operator acting on sections of a fiber bundle over the Physical Coupling Manifold M. The learnable N_d × N_d complex spectral kernel captures cross-domain coupling between all physical fields simultaneously. Noether projection at the output layer enforces energy, momentum, charge, and information entropy conservation as hard architectural constraints — not penalty terms.

from neuropia import UnifiedFieldPropagator

ufp = UnifiedFieldPropagator(
    n_domains=7,
    n_modes=64,
    n_layers=10,
    hidden_channels=512,
    gauge_group='Poincare x U(1) x SU(3)'
)

CDSP — Cross-Domain Symmetry Preserver

Enforces Noether's theorem across every domain interface architecturally, not through gradient penalties. The Onsager reciprocal matrix L_ij = L_ji is maintained as a hard constraint, preventing unphysical time-irreversible cross-coupling pathways. The Bianchi identity is enforced in the gravitational sector, and coupling consistency checks prevent entropy misattribution between domains.

ECM — Entropy Capstone Module

Integrates all nine EntropyLab dissipation functionals into a single Pareto-optimal master entropy objective. The cross-domain Onsager decomposition ensures that coupling entropy — invisible to any single-domain framework — is explicitly minimized. The Pareto optimizer enforces per-domain performance floors (α_i = 0.15), guaranteeing that no domain is sacrificed for another.

📐 Core Equations (Eq. 1-6)

p = (u, B, T, S, g_μν, ρ_q, H_info) ∈ M

p(x,t+dt) = W·p + F⁻¹[ R_θ(k)·F[p](k) ]

UFP_θ[ρ(g)·p] = ρ(g)·UFP_θ[p]  ∀g ∈ G_phys

Σ_total = Σ_i σ_ii(p) + Σ_{i≠j} L_ij·X_i·X_j

∂_μ J^μ_a = 0  ∀a ∈ {E, p, L, q, H}

σ_ii(p_θ) ≤ α_i · σ_ii(p_baseline)  ∀i, α_i = 0.15

📦 Installation

# From PyPI (stable)
pip install neuropia-engine

# From source
git clone https://gitlab.com/gitdeeper11/NEUROPIA.git
cd NEUROPIA && pip install -e .

# With CUDA acceleration
pip install neuropia-engine[cuda]

🔧 API Reference

UnifiedStateTracker

from neuropia import UnifiedStateTracker

tracker = UnifiedStateTracker(
    spatial_dim=256,
    k_max=64,
    domains=['mhd', 'thermal', 'quantum', 'gravitational'],
    enforce_noether=True,
    pareto_alpha=0.15
)

# E-LAB-X: PCI monitoring
sigma_actual = tracker.get_entropy_production_rate()
sigma_max = 1.0
pci = 1.0 - sigma_actual / sigma_max

tracker.load_weights('experiments/weights/')
tracker.step(dt=1e-6, multi_obs=observation)
ufci = tracker.get_coherence_index()

UnifiedStateTracker Parameters

Processing Capacity Index (E-LAB-X)

from neuropia.elabx import ProcessingCapacityIndex

# Compute PCI from current entropy production
pci = ProcessingCapacityIndex.compute(
    sigma_actual=tracker.get_entropy_production_rate(),
    system_energy=1e-10
)

# PCI range: 0.0 (saturated) to 1.0 (idle)
print(f"Processing Capacity Index: {pci:.3f}")

🧩 Core Modules

📊 Validation Summary

E-LAB-X Validation: Geometric vs. Entropic Gravity

👤 Author

📝 Citation

"If ENTROPIA was the question — how do we understand order from chaos — then NEUROPIA is the answer. It is the state in which artificial intelligence becomes the mirror that reflects the perfection of physical law across every domain simultaneously."