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KD A platform for Knowledge Discovery

KD is a plug-in platform for equation discovery. It gives different discovery algorithms a consistent, easy-to-use interface and provides shared services such as visualization, evaluation, and experiment management, while leaving each algorithm free to implement its own search procedure.

SGA-PDE · kdv · seed 42 generation 200 / 200 · nmse 2.70e-06 · AIC -19.42

Heatmap of the kdv field u over x and t

\(u_t =\)\(-u\,u_x\)\(-0.0025\,u_{xxx}\)

An SGA-PDE run on the KdV dataset, showing the field it was given and the equation it returned.

Quick start Examples

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Quick start

Install KD and run your first equation-discovery experiment in a few lines of Python. The example below uses a Burgers dataset bundled with KD.

1 install

git clone -b trunk https://github.com/Scientific-Artificial-Intelligence-Lab/kd.git
cd kd && uv sync

2 fit

import kd

# a 256 × 201 (x, t) field; for your own arrays, PDEDataset.from_arrays
data = kd.load_burgers()

model = kd.Model(algorithm="sga", generations=5, seed=0)
model.fit(data)

5 generations · AIC -28.78

\(u_t =\)\(-u\,u_x\)\(+0.1002\,u_{xx}\)

Examples

Getting started

Load a bundled benchmark, fit in one call, read the result.

worked exampleDISCOVERPySR

Column chromatography

Two algorithms on one 74-row table, both recovering the published formula.

Use your own data

Two coordinate arrays and one field array, from NumPy to a fitted equation.

The published EqGPT equation, reproduced on 12 wave-tank experiments.

Algorithms

KD currently provides seven equation-discovery algorithms through a common interface.

AICmediumfinite_diff autograd

A genetic search over expression trees; the coefficients come from the algorithm's own sparse regression.

DLGA fitnessheavyautograd

A neural network fits the field and supplies derivatives; a genetic algorithm searches term sets over a candidate library.

rewardheavyfinite_diff

A recurrent controller writes expression trees token by token and is trained on its own best-rewarded draws; the coefficients come from a platform refit.

EqGPT rewardheavyfinite_diff

A pretrained transformer reads the field and proposes equations, then fine-tunes on reward.

LLM4ED sparse rewardmediumfinite_diff

A large language model proposes and revises candidate equations round by round, filtered by a sparse reward.

NMSEmediumfinite_diffexternal package

Multi-population evolutionary search returning a complexity/error Pareto front.

NMSElightfinite_diffexternal package

Sparse regression over a supplied candidate library, solved in one pass.

Design

Platform and plugins

Seven algorithms as plugins over one set of shared services, and the decisions that let them share it.

Data requirements

Fields, coordinate axes, grid or scattered points, and how the left-hand side is chosen.

Score conventions and comparability

Each algorithm builds its own final score. Refit the terms in one shared context before comparing.