Automated Scientific Discovery

Discover governing equations from experimental data.

Upload time-series data and automatically infer the mathematical laws that govern your system. No physics PhD required.

Upload Dataset See Example

Supports CSV files with time and measurement columns

Validated across 8 scientific domains -- from epidemiology to astrophysics

How it works

1

Upload Data

Upload a CSV containing time-series measurements. One time column, up to 6 measurement columns.

2

Discover Laws

ProtoScience identifies governing equations using sparse symbolic regression. No priors, no assumptions.

3

Analyze Results

Receive differential equations, coefficients, R-squared metrics, and predictive trajectory plots.

See it in action

Three domains. Zero prior knowledge. Same pipeline.

Raw Data Ecology
year, hare_pelts, lynx_pelts
1900, 30.0, 4.0
1901, 47.2, 6.1
1902, 70.2, 9.8
1903, 77.4, 35.2
1904, 36.3, 59.4
1905, 20.6, 41.7
Discovered Equations
dH/dt = +0.46 H − 1.87 H·L
dL/dt = −1.93 L + 2.17 H·L
R² = 0.93
Lotka-Volterra recovered from 1900s fur trading records
Raw Data SIR
day, susceptible, infected, recovered
0, 0.95, 0.05, 0.00
5, 0.89, 0.09, 0.02
10, 0.74, 0.19, 0.07
15, 0.48, 0.33, 0.19
20, 0.22, 0.35, 0.43
25, 0.10, 0.22, 0.68
Discovered Equations
dS/dt = −0.44 S·I
dI/dt = +0.44 S·I − 0.09 I
dR/dt = +0.09 I
R² = 0.99
SIR equations discovered from epidemic curves
Raw Data Gravity
time, x_pos, y_pos
0.00, 0.98, 0.00
0.25, 0.00, 1.00
0.50, -0.98, 0.00
0.75, 0.00, -1.00
1.00, 0.98, 0.00
Discovered Equations
dvx/dt = −39.5 x/r³
dvy/dt = −39.5 y/r³
R² = 0.999
Newton's law of gravity recovered from orbital positions

Validated across domains

Epidemiology
SIR equations
88.6% accuracy
Ecology
Lotka-Volterra
R² = 0.93
Chemistry
BZ Oregonator
R² = 1.0
Synthetic Biology
Hill repressilator
85% accuracy
Climate Science
CO₂ trend + seasonal
R² = 0.99
Astrophysics
Solar 11-year cycle
R² = 0.96
Classical Physics
Hooke's Law F=-kx
12/12 perfect
Gravitational Physics
Newton's gravity
R² = 0.999
Bitcoin daily prices: no governing equation found. R² = 0.00. The system knows when there is no law.

Latest Experiments

Real-time results from the ProtoScience engine

E0532h ago
Real Climate Data (NASA)
R² = 0.90
Climate
E0524h ago
Planetary Orbits
R² = 0.999
Physics
E0515h ago
Radioactive Decay
10/10 perfect
Nuclear
E0506h ago
Spring / Hooke's Law
12/12 perfect
Mechanics
E0497h ago
Ocean Tides
Moon/Sun = 2.22x
Geophysics
E0488h ago
EEG Brain Waves
4/4 states
Neuroscience

Built for researchers

Systems Biology

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Chemical Engineering

Find reaction kinetics from reactor measurements

Ecology

Identify population dynamics from field observations

Physics

Recover force laws from position and velocity data

Turn experimental data into mathematical insight.

Upload your dataset. Get equations in minutes.

Upload Dataset Or email your data: discovery@protoscience.ai