monopole.ai
A single magnetic charge, modeled by machine intelligence.
We use generative physics models and lattice gauge networks to predict, locate, and characterize magnetic monopoles — the particles Dirac demanded but the universe has yet to confirm.
Premise
A particle that should exist
In 1931, Paul Dirac showed that the existence of a single magnetic monopole would explain why electric charge is quantized. Ninety-five years later, the monopole has not been observed in any laboratory, in any cosmic ray detector, in any frozen corner of antarctic ice. And yet every consistent grand unified theory predicts them.
monopole.ai is a computational research collective applying contemporary AI — diffusion models on lattice gauge configurations, transformer-based field reconstruction, and neural posterior estimation — to the question Dirac left open.
North Pole · Sourced
Sources of B
An isolated north monopole is a true source of the magnetic field — a point from which field lines emerge and never return. In Maxwell's equations as taught, ∇ · B = 0. With a monopole, ∇ · B = ρm, and the equations become symmetric under electric ↔ magnetic exchange.
∇ · E = ρe / ε0
∇ · B = μ0 ρm
∇ × E = -∂B/∂t - μ0 Jm
∇ × B = μ0(Je + ε0 ∂E/∂t)Restored Maxwell system with magnetic charge density ρm and current Jm.
South Pole · Sunk
Sinks of B
Where there is a north, there is a south — but only as the terminus of every field line. A south monopole, in isolation, would be where magnetic field disappears into a point. Our networks treat north/south asymmetry as a learnable representation: separate embedding spaces, joined by a polarity-conserving projection head.
In the trained model, a candidate event in detector data is scored against both poles independently. Confidence in a monopole detection requires high agreement across the polarity-conjugate pair.
Method
Holographic field reconstruction
Our generative model is trained on synthetic lattice gauge configurations seeded with 't Hooft-Polyakov monopole solutions in SU(2) Yang-Mills-Higgs theory. The network learns to reconstruct full 3D field geometries from sparse detector slices — a holographic inversion from boundary measurements to bulk topology.
Encoder
3D U-Net over 32³ gauge field cells, with rotation-equivariant convolutions preserving the topological winding number.
Diffusion
Score-based sampler in field-strength space, conditioned on detector residuals, with monopole charge as a conserved scalar.
Decoder
Inverse projection back to (E, B, φ) on the lattice, with a topological loss term over Π2(SU(2)/U(1)).
Lattice
Quantization condition, learned
e · g = n · (h c / 2) ← Dirac quantization
ΦB = ∮ B · dA = 4π g ← flux through enclosing surface
Qm = (1/4π) ∮ εijk ∂i na ∂j na dSk ← topological chargeThe model treats the integer winding number Qm as a discrete latent variable. Sampling is constrained to integer charges, enforcing Dirac's condition not as a prior but as an architectural symmetry.
Active Research
Where we are looking
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MoEDAL
Re-analysis of nuclear track detector arrays from LHC Run 3 with our diffusion-based event reconstruction. Mass window 1–3 TeV.
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IceCube
Cosmic monopole signatures in &Cherenkov; light cones — relativistic monopoles produce a distinctive radiative profile our model is trained to recognize.
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Polar Cap
Spin-ice condensed matter analogs — emergent monopole excitations in Dy2Ti2O7 as a controlled testbed for our reconstruction networks.
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Lattice
Generative sampling of SU(2) gauge configurations at finite temperature, near the deconfinement transition where monopole condensation is hypothesized.
End of Field
If they exist, we will see them.
monopole.ai is a private research collective. Our models are open. Our datasets are open. Our predictions are timestamped. The next monopole — predicted, unobserved — will not stay unobserved for long.
contact → field@monopole.ai