Design

KD is a platform for discovering partial differential equations from data, organized as a set of algorithm plugins. Each plugin implements the algorithm-specific search procedure and scientific logic, while the platform provides the data processing, execution, visualization, and experiment infrastructure shared across algorithms. Seven algorithms are currently integrated: five published by our group (SGA-PDE, DLGA-PDE, DISCOVER, EqGPT, LLM4ED) and two external baselines (PySR, PySINDy).

Inputs flow into a dataset, an algorithm searches it, and a result carries the equation, the score and the run record. Platform services are used as each algorithm's declaration states. The package layers behind this view are on the Architecture page. Open the figure in a new tab for full size.

Data is prepared once and an algorithm is chosen by name:

model = kd.Model(algorithm="sga").fit(data)

The fitted model carries the equation, the score, and the record of the run. Selecting a different algorithm changes only the algorithm argument; the surrounding code and the way the result is read stay the same.

Division of responsibility

Algorithms own their search, scoring and final fit. Platform services are optional; each algorithm declares which services and data forms its modes use. The platform and plugin contract describes the required members, shared services and per-algorithm responsibilities.

Shared machinery

Datasets hold observations. Derivative providers compute derivatives from those observations or from a trained field model when requested. The data requirements and derivative sources describe these choices; optional services cover the evaluation and fitting components.

Shared notation

Public equations use term strings such as mul(u, u_x) and diff_x(diff2_x(u)), paired with coefficients and a left-hand side. Checkpoints preserve the plugin's native search state. Equation representation explains the term syntax, input contracts and structural comparison.

Score comparability

The fitted model retains the algorithm's own score. Comparisons require matching data, derivative and scoring conventions. Score conventions explains how to refit candidate terms in a shared context with kd.evaluate_terms.

Figures from one call

model.report renders the supported figures and an HTML report from a fitted model. Visualization explains the shared figures and algorithm-specific panels; Figure generation covers the report and individual plotting calls.

Checkpoints and resuming

A checkpoint restores search state; the new model supplies the configuration for the resumed segment. Parameter tiers and resuming explains the checkpoint manifest, resume-safe parameters, identity checks and branching.

Batch studies

Batch experiments describes ordered plans across seeds, algorithms and datasets, sealed evidence stores and consensus from the recorded results.

Architecture

The Architecture page contains the complete component diagram, package layers and conventions that cross layers. The detailed SVG can be opened at full size from that page.

The path of one fit

The execution sequence follows dataset construction, component assembly, search, result assembly and subsequent analysis.