🌊 MAGNA-FLOW v1.0.0

Neural Magnetohydrodynamic Dissipation Control for High-Conductivity Turbulent Plasma Systems

E-LAB-09 | EntropyLab Research Program

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"The magnetic field does not merely confine the plasma — it is the plasma's memory. MAGNA-FLOW reads that memory and rewrites the future before the instability can." — MAGNA-FLOW v1.0.0 Manifesto

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Table of Contents

• Overview
• The Problem
• Core Constructs
• Mathematical Architecture
• Validation Results
• Project Structure
• Installation
• Quick Start
• EntropyLab Program
• Reproducibility Infrastructure
• Citation
• Author
• License

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Overview

MAGNA-FLOW is a Physics-Informed Artificial Intelligence (PIAI) framework engineered to model, predict, and actively suppress magnetohydrodynamic (MHD) turbulence and irreversible dissipation in high-conductivity fluid media — including plasma confinement systems, liquid-metal reactor cooling loops, ionic spacecraft thrusters, and astrophysical dynamo analogs.

Classical MHD solvers — built on the coupled Navier–Stokes and Maxwell equations — become computationally intractable at real-time control timescales when magnetic Reynolds numbers exceed 10⁶ and magnetic Prandtl numbers deviate far from unity: precisely the regime governing tokamak edge instabilities, Hall thruster breathing modes, and Hartmann boundary layer turbulence. MAGNA-FLOW replaces this computational wall with three cooperative neural constructs that enforce MHD physical laws as hard architectural constraints rather than soft regularization targets.

Key achievements (v1.0.0):

Metric	Result
Mean MHD Efficiency Index (η_MHD)	94.2%
Mean Entropy Production Reduction	89.3%
ELM Energy Suppression Factor (Tokamak R1)	8.1×
Alfvénic Confinement Gap	4.7% from ideal limit
Breathing-Mode Isp Recovery (Hall Thruster R2)	+141 s mean specific impulse
Hartmann Heat Transfer Error (Reactor R3)	3.8% MARE vs. Shercliff exact solution
Full Control Cycle Latency (A100 GPU)	1.8 ms (556 Hz update rate)
LQG Baseline Comparison	71.3% η_MHD → MAGNA-FLOW +22.9 pp

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The Problem

Every unsolved challenge in real-time MHD control — from suppressing plasma edge instabilities in fusion reactors to stabilizing ionic thruster plumes for deep-space missions — reduces to one bottleneck: we cannot solve the coupled Navier–Stokes and Maxwell equations fast enough, in the regimes that matter most, to apply meaningful control before the instability arrives. Three domains suffer acutely:

1. Tokamak Plasma Confinement (Fusion Energy) Edge-Localized Modes (ELMs) are repetitive explosive relaxation events at the plasma boundary that deposit energy fluxes exceeding 8–65 MJ/m² on divertor tiles in 100–300 microsecond bursts — far beyond the engineering tolerance of tungsten plasma-facing components. A reactor-scale tokamak (ITER) cannot reach its Q = 10 design goal if unmitigated Type-I ELMs erode the divertor on timescales of weeks rather than years. No existing real-time controller predicts ELM onset with sufficient lead time to apply magnetic perturbation mitigation before the thermal pulse arrives.

2. Hall Thruster Propulsion (Aerospace) Breathing-mode plasma oscillations in the 10–30 kHz band represent the dominant source of efficiency loss and thrust noise in Hall-effect thrusters — the primary propulsion technology for geostationary station-keeping and deep-space missions. Oscillation amplitude of ±19.4% peak-to-peak in specific impulse translates directly to wasted propellant mass and shortened mission lifetime. No predictive AI model has demonstrated real-time breathing-mode suppression across the full operational envelope without invasive hardware modification.

3. Liquid-Metal Nuclear Cooling (Nuclear Engineering) Hartmann boundary layers in sodium-cooled and lead-bismuth-cooled fast reactor primary loops operate at Hartmann numbers up to 10⁴, producing viscous layers thinner than 10 micrometers that dominate magnetoconvective heat transfer. Classical Nusselt number correlations underestimate heat transfer coefficients in the Hartmann regime by up to 25%, forcing conservative over-design of coolant flow rates and pumping power. Accurate real-time Hartmann characterization is essential for precise thermal margin management.

A unifying physical insight connects all three: every manifestation of uncontrolled MHD dynamics is an entropy production event — the irreversible conversion of organized magnetic and kinetic energy into thermalized heat. MAGNA-FLOW treats ELM suppression, thruster stabilization, and Hartmann characterization as instances of a single entropy minimization problem, inheriting the Unified Dissipation State Function from ENTROPIA (E-LAB-01).

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Core Constructs

1. Magnetic Fourier Neural Operator (M-FNO)

Generalizes the Fourier Neural Operator (FNO) to the full coupled MHD setting, operating simultaneously on the 6-component state vector v(r,t) = (u_x, u_y, u_z, B_x, B_y, B_z) with learnable 6×6 complex spectral kernels that capture the complete Alfvénic coupling tensor.

• Architecture: 8-layer FNO stack — feature dimension d = 256, k_max = 64 Fourier modes per dimension
• Input: Coupled (u, B) MHD state vector — 6 components at each spatial point
• Output: Time-evolved state v(r, t+dt) — divergence-free by architectural construction
• Captures: Alfvénic wave propagation, current-sheet formation, cross-field energy cascade, reconnection precursors
• Constraint: Helmholtz-Hodge divergence-free projection applied after every layer — div(u) = div(B) = 0 is a hard guarantee, not a penalty

2. Hydromagnetic Physics-Informed Network (H-PINN)

Enforces the complete set of MHD conservation laws — momentum, induction, solenoidal constraint, magnetic helicity evolution, and Onsager cross-coupling symmetry — as hard loss terms evaluated at adaptive collocation points across the spatiotemporal domain.

• Architecture: Causal collocation PINN with NTK-rebalanced multi-objective loss (4 physics terms)
• Function: Residual correction layer applied to M-FNO output — enforces helicity conservation and Onsager reciprocity
• Constraint: dH_m/dt = −2η·∫(J·B)dV enforced as global hard constraint — prevents unphysical magnetic topology drift
• Guarantee: Onsager symmetry L_ij = L_ji enforced architecturally — no spurious irreversible cross-coupling pathways

3. Lorentz Flux Resolver (L-Flux)

A model-predictive control engine that tracks the Maxwell stress tensor T_M in real time, identifies regions where its minimum eigenvalue λ_min approaches zero (the magnetic pressure collapse condition signaling imminent reconnection), and pre-emptively actuates external correction fields before dissipation cascades initiate.

• Architecture: MPC solver with 500 µs prediction horizon — warm-started from previous solution at each 50 µs control timestep
• Forward model: M-FNO used internally for trajectory prediction inside the MPC loop
• Risk map: Safety margin field δλ(r,t) = λ_min(T_M) − λ_safe — spatially resolved reconnection precursor
• Actuation: Substrate-agnostic — RMP coil currents (tokamak), magnetic lens coils (Hall thruster), external field arrays (liquid metal)
• Latency: 1.8 ms full control cycle on A100 GPU | 87 µs on NVIDIA Orin (INT8 TensorRT)

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Mathematical Architecture

Equation 1 — M-FNO Forward Map

v(r, t+dt) = M-FNO_θ[v(r,t)] = W · v(r,t) + F⁻¹[ R_φ(k) · F[v](k) ]

F: spatial Fourier transform | R_φ(k): learnable 6×6 complex spectral kernel per mode | W: pointwise local linear operator | Divergence-free projection applied after each layer

Equation 2 — L-Layer M-FNO Forward Pass

v⁽⁰⁾    = P_lift · v_in                                          [lifting layer]
v⁽ˡ⁺¹⁾  = σ( W⁽ˡ⁾ v⁽ˡ⁾ + F⁻¹[R⁽ˡ⁾(k) F[v⁽ˡ⁾](k)] )            [l = 0 … L−1]
v_out   = P_proj · v⁽ᴸ⁾                                          [projection layer]

P_lift: input lifting MLP | P_proj: output projection MLP | σ: GELU nonlinearity | L = 8 layers in default configuration

Equation 3 — Induction Equation (Hard Constraint)

∂B/∂t = ∇ × (u × B) + η · ∇²B

η: magnetic diffusivity | Enforced as hard H-PINN residual term L_ind | Violation at any collocation point contributes to NTK-rebalanced training loss

Equation 4 — Magnetic Helicity Evolution (Hard Constraint)

H_m = ∫_V (A · B) dV
dH_m/dt = −2η · ∫_V (J · B) dV

A: magnetic vector potential (B = ∇ × A) | J = ∇ × B / μ₀: current density | Enforced as global scalar hard constraint — prevents topological drift across control cycles

Equation 5 — Maxwell Stress Tensor

T_M^{ij} = (1/μ₀) · [ B_i B_j − (1/2) δ_{ij} |B|² ]

μ₀: permeability of free space | δ_{ij}: Kronecker delta | L-Flux tracks λ_min(T_M) — minimum eigenvalue collapse signals imminent reconnection

Equation 6 — L-Flux Control Objective

min_{u_ctrl}  ∫_T ∫_V [ σ_Ohm(r,t) + σ_visc(r,t) ] dr dt

subject to:   λ_min(T_M) ≥ λ_safe,    |B_ctrl| ≤ B_max

σ_Ohm = η |J|²: Ohmic dissipation rate | σ_visc = ν |e_ij|²: viscous dissipation rate | MPC solved via gradient descent warm-started from previous solution

Equation 7 — MHD Entropy Production Rate

dS/dt = (1/T) · ∫_V [ η |J|² + ν |e_ij|² ] dV
      = σ_Ohm_total + σ_visc_total

MAGNA-FLOW minimizes dS/dt as the direct MHD realization of the ENTROPIA Unified Dissipation State Function Φ(S, J, T) — thermodynamic minimum entropy production principle applied to electromagnetic fluid systems.

Equation 8 — H-PINN Loss Functional

L_HPINN(θ) = λ₁ · L_mom + λ₂ · L_ind + λ₃ · L_div + λ₄ · L_hel

(λ₁, λ₂, λ₃, λ₄) = (1.0, 8.0, 12.0, 4.0) initial weights | Dynamically rebalanced every 250 epochs via Neural Tangent Kernel rebalancing | Adaptive causal collocation weighting across temporal domain

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Validation Results

Validated across four canonical MHD regimes spanning plasma physics, aerospace propulsion, nuclear engineering, and geophysics. All results are true held-out test metrics — no validation data seen during training.

ID	Platform	Rm	Primary Instability	η_MHD	σ Reduction	Key Result
R1	ITER-class Tokamak Edge (~10 keV)	10⁷	ELM peeling-ballooning	95.1%	91.3%	8.1× ELM energy suppression
R2	Hall Thruster (600V, 50mT Xe)	10³	Breathing mode / BHN	93.7%	88.6%	+141 s mean Isp recovery
R3	Liquid PbBi Fast Reactor (400–700 K)	10³	Hartmann turbulence	94.8%	90.2%	3.8% MARE vs. Shercliff
R4	Planetary Dynamo Analog (~10³–10⁴ K)	10⁶	Rotating convective MHD	93.2%	86.9%	4.2% critical Elsässer accuracy

η_MHD definition: 1 − (dS/dt)_controlled / (dS/dt)_uncontrolled — normalized against uncontrolled baseline entropy production.

Regime R1 highlight: ELM energy loss per event reduced from 8.3 MJ/m² to 1.02 MJ/m² (8.1×), with mean precursor lead time of 312 µs before ideal MHD stability boundary crossing.

Regime R2 highlight: Breathing-mode amplitude reduced by 88.6%, Isp variation from ±19.4% to ±2.3% peak-to-peak. Ionization zone phase predicted with 98.7% accuracy at 200 µs horizon.

Regime R3 highlight: Hartmann layer heat transfer coefficient predicted within 3.8% MARE at Ha = 10⁴ — generalized from DNS training at Ha = 500 (20× extrapolation).

Ablation study (mean η_MHD across all regimes):

Configuration	Mean η_MHD	ELM Suppression
Uncontrolled baseline	0%	1.0×
Classical LQG (50 modes)	71.3%	2.3×
FNO-MHD (unconstrained)	81.5%	3.7×
H-PINN only (no M-FNO)	86.0%	5.2×
MAGNA-FLOW (no L-Flux)	90.1%	6.3×
MAGNA-FLOW v1.0.0 (Full)	94.2%	8.1×

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Project Structure

MAGNA-FLOW/
│
├── README.md                                   # This file
├── LICENSE                                     # MIT License © 2026 Samir Baladi
├── CITATION.cff                                # Citation metadata
├── pyproject.toml                              # Build configuration
├── setup.py                                    # Package setup
├── .gitlab-ci.yml                              # CI/CD pipeline (lint, test, benchmark)
│
├── paper/
│   ├── MAGNA-FLOW_Research_Paper.docx          # Full academic paper (v1.0.0, 24 pp.)
│   ├── MAGNA-FLOW_Research_Paper.pdf           # PDF version
│   └── figures/                               # All paper figures and diagrams
│       ├── fig1_mfno_architecture.png          # M-FNO spectral layer diagram
│       ├── fig2_hpinn_loss_surface.png         # H-PINN loss landscape and convergence
│       ├── fig3_lflux_stress_map.png           # Maxwell stress tensor safety margin field
│       ├── fig4_elm_suppression_r1.png         # ELM energy time series: controlled vs. baseline
│       ├── fig5_breathing_mode_r2.png          # Hall thruster Isp oscillation suppression
│       ├── fig6_hartmann_r3.png                # Hartmann layer heat transfer characterization
│       └── fig7_dynamo_r4.png                  # Planetary dynamo analog validation
│
├── magna_flow/                                 # Core Python library (magna-flow-engine)
│   ├── __init__.py
│   ├── version.py                              # v1.0.0
│   │
│   ├── physics/                               # Physics Layer
│   │   ├── __init__.py
│   │   ├── helmholtz_projector.py              # Divergence-free Helmholtz-Hodge projector
│   │   ├── maxwell_stress.py                   # Maxwell stress tensor T_M computation
│   │   ├── magnetic_helicity.py                # Helicity integrator H_m = ∫(A·B)dV
│   │   ├── onsager_verifier.py                 # Onsager symmetry L_ij = L_ji checker
│   │   ├── dissipation_budget.py               # Ohmic + viscous entropy production rates
│   │   ├── elsasser_decomp.py                  # Elsässer variable decomposition (z± = u ± B)
│   │   └── fluid_substrates.py                 # 10 pre-configured MHD substrate profiles
│   │
│   ├── neural/                                # Neural Layer
│   │   ├── __init__.py
│   │   ├── mfno.py                             # Magnetic Fourier Neural Operator (8-layer)
│   │   ├── hpinn.py                            # Hydromagnetic Physics-Informed Network
│   │   ├── fourier_integral_mhd.py             # 6×6 complex spectral kernel layer
│   │   ├── divergence_enforcer.py              # Spectral-domain div-free enforcement
│   │   ├── ntk_rebalancer.py                   # Neural Tangent Kernel loss rebalancing
│   │   ├── causal_collocation.py               # Adaptive causal collocation point sampler
│   │   └── loss_functions.py                   # L_mom, L_ind, L_div, L_hel, L_Onsager
│   │
│   ├── control/                               # Control Layer
│   │   ├── __init__.py
│   │   ├── lflux_resolver.py                   # Lorentz Flux Resolver (MPC engine)
│   │   ├── eigenvalue_tracker.py               # λ_min(T_M) safety margin tracker
│   │   ├── mpc_solver.py                       # Gradient-descent MPC optimizer (500 µs horizon)
│   │   ├── actuator_rmp.py                     # RMP coil interface (tokamak)
│   │   ├── actuator_lens.py                    # Magnetic lens interface (Hall thruster)
│   │   └── actuator_field_coil.py              # External field coil interface (liquid metal)
│   │
│   ├── tracker/                               # State Tracking Layer
│   │   ├── __init__.py
│   │   ├── mhd_state_tracker.py                # MHDStateTracker class (main state object)
│   │   ├── efficiency_monitor.py               # η_MHD trajectory accumulator
│   │   └── risk_map_exporter.py                # δλ(r,t) spatial risk field exporter
│   │
│   └── interface/                             # Interface Layer
│       ├── __init__.py
│       ├── magna_flow_engine.py                # MagnaFlowEngine class (top-level API)
│       ├── regime_config.py                    # Regime configurations: R1–R4 + 6 extended
│       ├── substrate_config.py                 # FluidSubstrate dataclass + 10 profiles
│       ├── dissipation_exporter.py             # Dissipation maps and stability metrics export
│       └── tensorrt_export.py                  # INT8 TensorRT export for FPGA/embedded deploy
│
├── benchmarks/                                # Validation & benchmarking scripts
│   ├── run_all_regimes.py                      # Full 4-regime validation pipeline
│   ├── regime_r1_tokamak_elm.py                # ELM suppression benchmark (ITER-class)
│   ├── regime_r2_hall_thruster.py              # Hall thruster breathing-mode benchmark
│   ├── regime_r3_liquid_metal.py               # Liquid PbBi Hartmann layer benchmark
│   ├── regime_r4_dynamo_analog.py              # Planetary dynamo analog benchmark
│   ├── ablation_study.py                       # M-FNO / H-PINN / L-Flux ablation
│   ├── noise_robustness.py                     # SNR / dropout degradation study
│   ├── transfer_learning.py                    # Cross-substrate fine-tuning benchmarks
│   └── compare_lqg_baseline.py                 # MAGNA-FLOW vs. LQG / classical controllers
│
├── experiments/                               # Raw experimental data & model weights
│   ├── data/
│   │   ├── tokamak_probes/                     # Magnetic probe time-series (ITER-class, R1)
│   │   ├── hall_thruster_diagnostics/          # Langmuir probe + thrust balance data (R2)
│   │   ├── pbBi_hartmann_dns/                  # DNS Hartmann flow at Ha = 10–500 (R3)
│   │   ├── dynamo_analog_spherical/            # Rotating spherical Couette device data (R4)
│   │   └── jorek_outputs/                      # JOREK nonlinear MHD simulation snapshots
│   │
│   └── weights/
│       ├── mfno_pretrained_v1.0.0.pt           # M-FNO weights (full 3-phase curriculum)
│       ├── hpinn_residual_v1.0.0.pt            # H-PINN residual corrector weights
│       ├── lflux_mpc_v1.0.0.pt                 # L-Flux MPC warm-start weights
│       └── tensorrt_int8_orin_v1.0.0.trt       # NVIDIA Orin TensorRT INT8 export
│
├── training/                                  # Training pipeline
│   ├── train_mfno.py                           # M-FNO 3-phase curriculum (7,500 epochs)
│   ├── train_hpinn.py                          # H-PINN physics residual training
│   ├── train_lflux.py                          # L-Flux MPC warm-start training
│   ├── curriculum_phase1.py                    # Phase 1: DNS synthetic data (Rm 10–10³)
│   ├── curriculum_phase2.py                    # Phase 2: JOREK reconnection events + ELM precursors
│   ├── curriculum_phase3.py                    # Phase 3: Experimental data fine-tuning
│   └── configs/
│       ├── mfno_config.yaml                    # M-FNO hyperparameters (L, d, k_max)
│       ├── hpinn_config.yaml                   # H-PINN collocation and loss weight schedule
│       ├── lflux_config.yaml                   # MPC horizon, control timestep, safety thresholds
│       └── training_defaults.yaml              # AdamW, cosine annealing, NTK rebalancing
│
├── notebooks/                                 # Jupyter notebooks for exploration
│   ├── 01_mfno_spectral_walkthrough.ipynb      # M-FNO spectral kernel visualization
│   ├── 02_hpinn_helicity_conservation.ipynb    # Magnetic helicity conservation demo
│   ├── 03_lflux_stress_tensor_tracking.ipynb   # Maxwell stress tensor safety margin demo
│   ├── 04_elm_suppression_demo.ipynb           # ELM suppression full cycle (R1)
│   ├── 05_breathing_mode_demo.ipynb            # Hall thruster Isp stabilization (R2)
│   ├── 06_hartmann_characterization.ipynb      # Liquid metal Hartmann flow demo (R3)
│   └── 07_transfer_learning_demo.ipynb         # Cross-substrate fine-tuning walkthrough
│
├── docs/                                      # Documentation
│   ├── index.md                               # Documentation home
│   ├── api_reference.md                       # Full API reference
│   ├── math_appendix.md                       # Extended mathematical derivations
│   ├── substrate_guide.md                     # Configuring custom MHD fluid substrates
│   ├── deployment_guide.md                    # FPGA / TensorRT deployment instructions
│   └── entropylab_context.md                  # MAGNA-FLOW within the EntropyLab program
│
└── .gitlab-ci.yml                             # CI/CD pipeline (lint, test, benchmark, deploy)

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Installation

Requirements: Python ≥ 3.10 | PyTorch ≥ 2.3 | NumPy ≥ 2.0 | SciPy ≥ 1.13 | CUDA ≥ 12.1 (optional, for cuFFT acceleration)

# From PyPI (stable)
pip install magna-flow-engine

# From source (development)
git clone https://gitlab.com/gitdeeper11/MAGNA-FLOW.git
cd MAGNA-FLOW
pip install -e .

# With CUDA-accelerated FFT support
pip install magna-flow-engine[cuda]

---

Quick Start

MHD state tracking and dissipation control:

from magna_flow import MHDStateTracker
import numpy as np

# Initialize tracker for ITER-class tokamak edge plasma
tracker = MHDStateTracker(
    spatial_dim=256,
    k_max=64,
    fluid='plasma_deuterium',
    enforce_helicity=True,
    lflux_horizon_us=500       # L-Flux MPC horizon in microseconds
)

# Load pre-trained weights
tracker.load_weights('experiments/weights/mfno_pretrained_v1.0.0.pt')

# Step the MHD state forward in time
tracker.step(
    dt=1e-6,
    env_obs={
        'u_field': u_arr,      # velocity field (3 × N³)
        'B_field': B_arr,      # magnetic field (3 × N³)
        'T_e': T_electron      # electron temperature (scalar field)
    }
)

# Query state and risk metrics
risk_map  = tracker.get_safety_margin()     # δλ(r,t) — spatially resolved reconnection risk
eta_mhd   = tracker.get_efficiency_index()  # scalar η_MHD ∈ [0, 1]
ctrl_hist = tracker.get_control_history()   # B_ctrl time series (actuator output)

print(f"η_MHD             = {eta_mhd:.4f}")
print(f"Min safety margin = {risk_map.min():.4e}")
print(f"Max dissipation   = {tracker.get_dissipation_peak():.4e} W/m³")

ELM suppression (full control loop):

from magna_flow import MagnaFlowEngine

engine = MagnaFlowEngine(regime='tokamak_elm', fluid='plasma_deuterium')
engine.load_weights('experiments/weights/')

# Run full ELM suppression control loop
result = engine.run_control_campaign(
    duration_ms=100.0,
    control_freq_hz=556,           # A100 GPU control update rate
    initial_state={'u': u0, 'B': B0},
    actuator='rmp_coil',
    lambda_safe=0.05               # Reconnection safety threshold
)

print(f"ELM suppression factor = {result.elm_suppression:.2f}×")
print(f"Mean η_MHD             = {result.mean_efficiency:.4f}")
print(f"Total σ reduction      = {result.dissipation_reduction:.1%}")

Hall thruster breathing-mode control:

from magna_flow import MagnaFlowEngine

engine = MagnaFlowEngine(regime='hall_thruster', fluid='hall_xenon')
engine.load_weights('experiments/weights/')

result = engine.run_control_campaign(
    duration_ms=10.0,
    control_freq_hz=556,
    initial_state={'u': u0, 'B': B0},
    actuator='magnetic_lens',
    target_isp_stability=0.025     # ±2.5% peak-to-peak Isp target
)

print(f"Isp variation (baseline)  = ±{result.baseline_isp_variation:.1f}%")
print(f"Isp variation (controlled)= ±{result.controlled_isp_variation:.1f}%")
print(f"Isp gain                  = +{result.isp_gain_seconds:.0f} s")

Run full validation benchmark:

python benchmarks/run_all_regimes.py \
  --weights experiments/weights/ \
  --data    experiments/data/ \
  --output  results/

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EntropyLab Program

MAGNA-FLOW is E-LAB-09 — the ninth and final installment of the EntropyLab research program, which builds a unified Physics-Informed Artificial Intelligence architecture for entropy-governed physical systems across all major dissipative domains.

ID	Project	Domain	DOI	Status
E-LAB-01	ENTROPIA	Unified Dissipation State Function (Boltzmann + Shannon)	10.5281/zenodo.19416737	✅ Published
E-LAB-02	ENTRO-AI	LLM Thermodynamic Phase Transitions & Hallucination Suppression	10.5281/zenodo.19551614	✅ Published
E-LAB-03	PHOTON-Q	Neural Wavefront Intelligence for Quantum-Optical Systems	10.5281/zenodo.19729926	✅ Published
E-LAB-04	ENTRO-ENGINE	Multi-System Entropy Budget Coordination Law	10.5281/zenodo.19740081	✅ Published
E-LAB-05	CHEM-ENTROPIA	Entropy Production Minimization in Reactive Chemical Systems	10.5281/zenodo.19749613	✅ Published
E-LAB-06	BIO-ENTROPIA	Thermodynamic Analysis of Biological Metabolic Networks	10.5281/zenodo.19754893	✅ Published
E-LAB-07	THERMO-NET	Neural Thermodynamic Dissipation Management	10.5281/zenodo.19760903	✅ Published
E-LAB-08	GRAVI-NEURAL	Covariant Neural Operator for Spacetime Curvature Control	10.5281/zenodo.19875543	✅ Published
E-LAB-09	MAGNA-FLOW	Neural MHD Dissipation Control for Conducting Fluids	10.5281/zenodo.19893462	✅ This project

Theoretical arc: ENTROPIA (E-LAB-01) unified Boltzmann and Shannon entropy into the Unified Dissipation State Function Φ(S, J, T). Each subsequent project applied this framework to progressively more complex dissipative domains — from scalar thermodynamic systems (E-LAB-04), through vector-field optical systems (E-LAB-03), tensor-field thermal systems (E-LAB-07), and Riemannian metric-field spacetime (E-LAB-08) — culminating in MAGNA-FLOW's extension to fully coupled vector-field electromagnetic fluid systems.

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Reproducibility Infrastructure

All experimental data, pre-trained model weights, training scripts, validation benchmarks, and reproduction scripts are fully archived and publicly accessible.

Platform	Identifier / URL	Content
GitLab (Primary)	gitlab.com/gitdeeper11/MAGNA-FLOW	Source code, CI/CD, Issues
GitHub (Mirror)	github.com/gitdeeper11/MAGNA-FLOW	Mirror repository
Codeberg (Mirror)	codeberg.org/gitdeeper11/MAGNA-FLOW	Mirror repository
Bitbucket (Mirror)	bitbucket.org/gitdeeper11/MAGNA-FLOW	Mirror repository
Zenodo	10.5281/zenodo.19893462	Archived release, DOI, Datasets, Weights
PyPI	magna-flow-engine	Python library (v1.0.0)
Netlify	magna-flow-v1.netlify.app	Interactive demo + documentation
OSF Registration	10.17605/OSF.IO/2ANH7	Preregistration + study protocol
ORCID	0009-0003-8903-0029	Author identifier (Samir Baladi)

All results reported in the research paper are fully reproducible by running:

python benchmarks/run_all_regimes.py --weights experiments/weights/ --data experiments/data/

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Citation

If you use MAGNA-FLOW in your research, please cite all three of the following records.

Zenodo (Primary Archive — Data, Weights & Paper)

@software{baladi2026magnaflow_zenodo,
  author       = {Baladi, Samir},
  title        = {{MAGNA-FLOW}: Neural Magnetohydrodynamic Dissipation
                  Control for High-Conductivity Turbulent Plasma Systems},
  version      = {1.0.0},
  year         = {2026},
  month        = {April},
  publisher    = {Zenodo},
  doi          = {10.5281/zenodo.19893462},
  url          = {https://doi.org/10.5281/zenodo.19893462},
  note         = {E-LAB-09, EntropyLab Research Program.
                  Includes pre-trained model weights, experimental datasets,
                  training scripts, and validation benchmarks.},
  orcid        = {0009-0003-8903-0029}
}

OSF Registration (Preregistration & Study Protocol)

@misc{baladi2026magnaflow_osf,
  author       = {Baladi, Samir},
  title        = {{MAGNA-FLOW}: Neural Magnetohydrodynamic Dissipation
                  Control for High-Conductivity Turbulent Plasma Systems
                  — OSF Preregistration},
  year         = {2026},
  month        = {May},
  publisher    = {OSF Registries},
  doi          = {10.17605/OSF.IO/2ANH7},
  url          = {https://doi.org/10.17605/OSF.IO/2ANH7},
  note         = {E-LAB-09, EntropyLab Research Program.
                  OSF Preregistration — registered May 8, 2026.
                  Associated project: https://osf.io/uasyb},
  orcid        = {0009-0003-8903-0029}
}

PyPI (Python Library)

@software{baladi2026magnaflow_pypi,
  author       = {Baladi, Samir},
  title        = {magna-flow-engine: {MAGNA-FLOW} Python Library for
                  Neural MHD Dissipation Control},
  version      = {1.0.0},
  year         = {2026},
  month        = {April},
  publisher    = {Python Package Index (PyPI)},
  url          = {https://pypi.org/project/magna-flow-engine/1.0.0/},
  note         = {Install via: pip install magna-flow-engine==1.0.0.
                  E-LAB-09, EntropyLab Research Program.},
  orcid        = {0009-0003-8903-0029}
}

---

Author

Samir Baladi Ronin Institute / Rite of Renaissance Independent Researcher — EntropyLab Program

• 📧 gitdeeper@gmail.com
• 🔗 ORCID: 0009-0003-8903-0029
• 📞 +1 (614) 264-2074
• 🌐 magna-flow-v1.netlify.app

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License

MIT License
Copyright © 2026 Samir Baladi

Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.

---

MAGNA-FLOW v1.0.0 — E-LAB-09 — EntropyLab Research Program © 2026 Samir Baladi — Ronin Institute / Rite of Renaissance — MIT License Zenodo: 10.5281/zenodo.19893462 | OSF: 10.17605/OSF.IO/2ANH7 | Demo: magna-flow-v1.netlify.app