Equations Discovered From Raw Data

Browse closed-form formulas Superset has discovered across physics, astrophysics, materials science, and engineering. Each entry includes a link to the underlying data and the published paper or known physics that validates the result.

Upload your dataset →   Discover equations hidden in your own data. No account required.

Nuclear Physics R² = 0.9976

Nuclear Charge Radii

A 4-parameter algebraic formula that maps the charge radii of the entire nuclear chart, autonomously deriving the neutron skin effect and detecting magic number shell structure.

R(Z, N) = f(Z, N, A) [4-parameter formula]
Input Data 952 isotopes from hydrogen to curium
Astrophysics Mathematical proof

MOND Acceleration Constant

Independently derived that a hidden acceleration constant must exist in the M-sigma relation, the foundation of Modified Newtonian Dynamics (MOND).

M_BH = C · σ⁴ / (G · a₀)
Input Data 42 supermassive black hole measurements
Multi-Domain Engineering R² = 0.801 to 0.9997

Universal Friction Equation

One equation governs ten different physical systems across fifteen orders of magnitude: bearings, blood flow, earthquakes, pipes, metal fatigue, jet engines, heat transfer, and concrete.

Log-quadratic scaling law (3 parameters)
Input Data 193 measurements, 12 research groups, 1918 to 2013
Astrophysics / Nuclear Hard mathematical bound

Neutron Star QCD Transition

Proved that the QCD phase transition inside neutron stars must occur between 1.2 and 2.6 times nuclear saturation density, regardless of mechanism.

1.2 ≤ ρ₀ ≤ 2.6 ρ_sat
Input Data Boundary conditions + general relativity + causality
Quantum Physics R² = 1.0000 (exact)

BEC Condensation Law

Recovered Einstein's 1924 Bose-Einstein condensate law from numerical data alone. Both coefficients exact to six decimal places.

N₀/N = 1 - (T/T_c)^(3/2)
Input Data 100 points of T/T_c vs condensate fraction
Astrophysics R² = 0.76

Pulsar Spin-Down ISM Dependence

Pulsar spin-down depends on the surrounding interstellar medium density, a relationship not predicted by the standard magnetic dipole model.

log(Ṗ) ∝ 0.81 · (log(DM) + log(P))
Input Data 2,797 pulsars from ATNF Pulsar Catalogue
Aerodynamics R² = 0.453 (validation)

Wind Turbine Blade Noise

A simple 3-term formula for wind turbine blade noise, replacing hours of CFD simulation with instant calculation.

3-term formula (chord, frequency × thickness)
Input Data 1,503 NASA wind tunnel experiments
Field Theory Exact derivation

Maxwell, Einstein, Yang-Mills from Symmetry

Derived the fundamental field equations of electromagnetism, general relativity, and the strong nuclear force from nothing but a field and its symmetry.

Fμν F^μν, R, Yang-Mills Lagrangian
Input Data A field and a symmetry rule

Have your own dataset?

Upload a CSV and Superset will attempt to discover the underlying equation. Free for researchers. No account required to start.

Upload Dataset