SciLaws-Bench

Data for Can LLMs Discover Scientific Laws in Real and Parallel Worlds?

118 scientific law-discovery problems curated from 381 papers, covering 291 candidate laws and ~8.2M real measurements across six disciplines. Every problem comes from active, data-driven literature where the published law still leaves room for improvement — not from textbook equations.

• Code and harness: https://github.com/yiyihum/SciLaws-Bench
• Project page: https://yiyihum.github.io/SciLaws-Bench/
• Paper: https://yiyihum.github.io/SciLaws-Bench/assets/scilaws_bench_paper.pdf

Two settings per problem

SciLaws-Real — propose a closed-form law from fixed published records. Published formulas are reference baselines to beat, not recovery targets. Scored on numeric fit S_N (best published formula = 0.5, perfect predictor = 1.0) and scientific validity S_V (a frozen, source-grounded rubric behind an anti-hacking gate).

SciLaws-Parallel — the same problem as a queryable simulator whose generating mechanism is a newly synthesized structural variant of the published form, absent from the literature. Scored on structure recovery S_S at five levels: 0 unrelated, 0.25 right variables or trends, 0.5 published base form, 0.75 base plus most added terms, 1.0 the complete hidden structure.

Composition

Discipline	Tasks
Earth & Physics	24
Ecology & Hydrology	22
Astronomy	20
Materials & Engineering	19
Social Sciences	17
Biology	16

66 tasks are Type I (single-group: one global law), 52 are Type II (multi-group: one shared functional form, a few per-group parameters). All 118 ship a calibrated simulator.

task_index.csv in this repository lists every task with its discipline, target variable, input count, row counts and license.

Layout

tasks/typeI/<task>/
├── metadata.yaml            # solver-facing: context, target, inputs, units, ranges
├── data/
│   ├── train.csv            # column 0 = target, columns 1..N = inputs
│   └── test.csv
├── eval/
│   ├── reference_metrics.json   # published-baseline anchors used to normalize S_N
│   ├── validity_rubrics.json    # frozen source-grounded validity rubric
│   └── metadata_full.yaml       # grader-facing task record: adds `references`, i.e.
│                                #   which published law each baseline id comes from
└── simulator/
    ├── state.joblib         # simulator state, loaded by harness/sim_runtime.py
    ├── sample.csv           # fixed free sample
    └── formula.py           # the hidden law — grader-only

tasks/typeII/<task>/
└── data/{train,test_fit,test_test}.csv    # otherwise identical

For Type II, test_fit calibrates per-group parameters on held-out groups and test_test scores the shared functional form on those same groups. predict() never receives group_id.

eval/ and simulator/ are grader-facing — and this release publishes them. eval/ holds the reference anchors and the frozen validity rubric. simulator/ holds the Parallel setting's hidden law: not only in formula.py, but inside state.joblib itself, whose formula_source field is the law's source text that sim_runtime executes to generate y. Removing it does not hide the law, it breaks the simulator. So a locally runnable Parallel world necessarily ships its own answer.

If you evaluate a system on SciLaws-Parallel, withhold eval/ and simulator/ from it and mediate every query through harness/sim_runtime.py. Treat scores obtained by a system that had filesystem access to these directories as invalid.

Usage

hf download RealSR/SciLaws-Bench --repo-type dataset --local-dir . --include 'tasks/*'

Load one task directly:

import pandas as pd, yaml

task = "tasks/typeI/mauna_loa_co2_keeling_curve_noaa__co2_ppm"
meta = yaml.safe_load(open(f"{task}/metadata.yaml"))
train = pd.read_csv(f"{task}/data/train.csv")
y, X = train.iloc[:, 0], train.iloc[:, 1:]

Scoring is done by the harness in the code repository, not by a metric in this dataset.

Licensing

Each task carries the license of its upstream dataset, listed per task in LICENSES.md and in the task's own metadata.yaml. Terms vary, several are share-alike or non-commercial, so check the task you use, and cite its upstream source.

Citation

@article{huang2026scilaws,
  title   = {Can LLMs Discover Scientific Laws in Real and Parallel Worlds?},
  author  = {Huang, Yiming and Liu, Ziche and Wu, Zhuohang and Wang, Yiqian and
             Cui, Junxia and Zou, Xinkai and Mao, Lingjun and Huang, Nan and
             Yu, Naicheng and Zhu, Kaijie and Ma, Yue and Zhou, Kun and
             Peng, Letian and Shang, Jingbo},
  journal = {arXiv preprint},
  year    = {2026}
}