Algorithms

KD puts seven equation-discovery algorithms behind one intermediate representation and one API: switching algorithms means changing kd.Model(algorithm=...), with the same dataset and the same way of reading the result. The derivatives are computed by the platform to each algorithm's declared requirement, so their source can differ (see derivative sources). Each algorithm constructs its own final score, so those numbers do not line up across algorithms; refit the same terms in one context with evaluate_terms first, as described in score conventions and comparability.

Algorithm list

All seven are stated in the same terms, column by column, under the name each one is published as; the last column links its paper. The identifier kd.Model(algorithm=...) takes is in the spec strip at the top of every algorithm page, and the authors' code repository is in the references on the same page.

Algorithm	Score	Cost	Derivatives	Equation form	Data layout	Source
SGA-PDE	AIC min	medium	finite_diff autograd	EVOLUTION	grid	Chen et al. (2022)
DLGA-PDE	DLGA fitness min	heavy	autograd	EVOLUTION	grid	Xu et al. (2020)
DISCOVER	reward max	heavy	finite_diff	EVOLUTION REGRESSION	grid tabular	Du et al. (2024)
EqGPT	EqGPT reward max	heavy	finite_diff	EVOLUTION HOMOGENEOUS	grid scattered	Xu et al. (2025)
LLM4ED	LLM4ED sparse reward max	medium	finite_diff	EVOLUTION	grid	Du et al. (2024)
PySR	NMSE min	medium	finite_diff	EVOLUTION REGRESSION	grid tabular	Cranmer (2023)
PySINDy	NMSE min	light	finite_diff	EVOLUTION	grid	de Silva et al. (2020)

Algorithm pages

AICmediumfinite_diff autograd

SGA-PDE

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

DLGA fitnessheavyautograd

DLGA-PDE

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

rewardheavyfinite_diff

DISCOVER

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

EqGPT

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

LLM4ED sparse rewardmediumfinite_diff

LLM4ED

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

NMSEmediumfinite_diffexternal package

PySR

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

NMSElightfinite_diffexternal package

PySINDy

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