REVIEW 20 cited by
LLM-SR: Scientific Equation Discovery via Programming with Large Language Models
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
read the original abstract
Mathematical equations have been unreasonably effective in describing complex natural phenomena across various scientific disciplines. However, discovering such insightful equations from data presents significant challenges due to the necessity of navigating extremely large combinatorial hypothesis spaces. Current methods of equation discovery, commonly known as symbolic regression techniques, largely focus on extracting equations from data alone, often neglecting the domain-specific prior knowledge that scientists typically depend on. They also employ limited representations such as expression trees, constraining the search space and expressiveness of equations. To bridge this gap, we introduce LLM-SR, a novel approach that leverages the extensive scientific knowledge and robust code generation capabilities of Large Language Models (LLMs) to discover scientific equations from data. Specifically, LLM-SR treats equations as programs with mathematical operators and combines LLMs' scientific priors with evolutionary search over equation programs. The LLM iteratively proposes new equation skeleton hypotheses, drawing from its domain knowledge, which are then optimized against data to estimate parameters. We evaluate LLM-SR on four benchmark problems across diverse scientific domains (e.g., physics, biology), which we carefully designed to simulate the discovery process and prevent LLM recitation. Our results demonstrate that LLM-SR discovers physically accurate equations that significantly outperform state-of-the-art symbolic regression baselines, particularly in out-of-domain test settings. We also show that LLM-SR's incorporation of scientific priors enables more efficient equation space exploration than the baselines. Code and data are available: https://github.com/deep-symbolic-mathematics/LLM-SR
Forward citations
Cited by 20 Pith papers
-
Neuro-Symbolic ODE Discovery with Latent Grammar Flow
Latent Grammar Flow embeds grammar-based ODE representations into a discrete latent space with a behavioural loss and samples candidate equations via discrete flow to fit observed data.
-
LLM-Based Scientific Equation Discovery via Physics-Informed Token-Regularized Policy Optimization
PiT-PO adaptively fine-tunes an LLM during symbolic regression search using physics-validity and token-level redundancy constraints, reporting state-of-the-art benchmark results and a periodic-hill turbulence closure.
-
Autonomous Code Evolution Meets NP-Completeness
An LLM-based agent framework evolved five 2024 SAT solver codebases over 70 cycles and produced solvers that the authors report outperform the 2025 SAT Competition champions.
-
Unified remnant models for aligned-spin, precessing, and eccentric binary black hole mergers
New analytic fits, gwModelRemS/P, predict remnant mass, spin, luminosity, and kick for black hole mergers from equal mass to q=1000, with a neural-flow model for precessing kicks.
-
MOT-SR: Multi-Objective Tool-Augmented Scientific Equation Discovery with Large Language Models
MOT-SR combines tool-augmented data analysis with multi-objective Pareto selection to discover symbolic equations, outperforming LLM-based and classical SR baselines on benchmarks and an EMRI orbital-correction task.
-
Library Reachability in LSR-Synth: How Anti-Memorization Design Changes the Measurement of Symbolic Discovery
A fixed operator library with no access to variable names or domain descriptions solves most LSR-Synth tasks, so LLM candidates rarely expand the solvable set unless the library is deliberately weakened.
-
Program Synthesis for Simulation-Based Inference: Joint Model Selection and Parameter Estimation
An LLM proposes simulator programs and neural simulation-based inference ranks them, enabling joint model selection and parameter estimation.
-
LLM-PDESR: Robust PDE Discovery via Subdomain Weighted Residuals and LLM-Guided Symbolic Hypothesis Generation
LLM-PDESR pairs LLM structural hypotheses with C4 quintic splines and subdomain weighted residuals to recover PDEs from noisy data more robustly than prior symbolic methods.
-
GAE: Graph-Augmented Evolution for Scientific Discovery via Reinforcement Optimization
GAE couples a relational GNN program encoder, a Discrete SAC mutation-type controller, and online GRPO LLM fine-tuning to beat static LLM evolution baselines on nonlinear-oscillator symbolic regression, especially out...
-
DeepInflation: an AI agent for research and model discovery of inflation
An LLM agent with symbolic regression finds simple inflation potentials that match target CMB observables, but the outputs are fitted to the targets rather than independently predicted.
-
HypoSpace: A Diagnostic Benchmark for Set-Valued Hypothesis Generation under Underdetermination and Sublinear Coverage Bounds
A benchmark with exactly enumerated valid hypothesis sets shows LLMs maintain high validity but lose uniqueness and coverage as the admissible solution space grows.
-
EraRAG: Efficient and Incremental Retrieval Augmented Generation for Growing Corpora
EraRAG uses hyperplane-based locality-sensitive hashing to build a hierarchical retrieval graph whose affected regions only are re-summarized when new documents arrive, cutting update cost by up to an order of magnitude.
-
PhySense: Principle-Based Physics Reasoning Benchmarking for Large Language Models
A new benchmark of 380 principle-based physics problems shows that state-of-the-art LLMs struggle to apply symmetry, conservation, and dimensional-analysis shortcuts, achieving under 50 percent average accuracy with h...
-
VisualPatchWorld: Code World Models as Latent Structured Representations for Planning
A two-level induction procedure—active-probe sketch selection plus multi-step rollout fitting—recovers executable code world models that improve CEM planning over prior code baselines on four LeWM tasks.
-
Formula-One Prompting: A Composable Equation-First Prefix for Applied Mathematics
An equation-first prompt beat chain-of-thought and program-of-thought by 5.76 and 8.42 points on average across four applied-math benchmarks, but the body does not include several analyses the abstract promises.
-
SAIL: Sound Abstract Interpreters with LLMs
SAIL synthesizes globally sound abstract transformers for neural-network operators by combining LLM generation with syntactic validation, SMT-based soundness checking, and cost-guided iterative refinement.
-
ExploreGS: Explorable 3D Scene Reconstruction with Virtual Camera Samplings and Diffusion Priors
Adding information-gain-selected virtual views refined by video diffusion priors to 3D Gaussian Splatting improves arbitrary-view rendering quality.
-
DrSR: LLM based Scientific Equation Discovery with Dual Reasoning from Data and Experience
DrSR improves LLM-based symbolic regression by adding data-aware structural insights and a reflective idea library, beating prior methods on six benchmark tasks.
-
Advancing the Scientific Method with Large Language Models: From Hypothesis to Discovery
A perspective review argues that LLMs should be deeply integrated into all stages of science, with human oversight and clear metrics, to become creative engines.
-
Large language models for partial differential equation workflows
A review organizing LLM-assisted PDE research into Discovery, Solving, and Optimization stages, arguing LLMs are most useful as workflow-level interfaces rather than isolated solvers.
Discussion (0). Sign in to comment.