SURFACEBENCH: A Geometry-Aware Benchmark for Symbolic Surface Discovery
Sanchit Kabra, Shobhnik Kriplani, Parshin Shojaee, Chandan K. Reddy

TL;DR
SURFACEBENCH is a new geometry-aware benchmark for symbolic surface discovery that evaluates methods on 3D surface equations using geometric and structural metrics, revealing current approaches' limitations.
Contribution
It introduces the first geometry-aware benchmark for 3D surface symbolic discovery, incorporating diverse representations and geometric metrics for evaluation.
Findings
No current method performs well across all representations.
LLM-based approaches have strong structural priors but limited robustness.
The benchmark reveals gaps in existing symbolic surface discovery methods.
Abstract
Equation discovery from data is a central challenge in machine learning for science, which requires the recovery of concise symbolic expressions that govern complex physical and geometric phenomena. Recent large language model (LLM) approaches have shown promise in symbolic regression, yet existing benchmarks predominantly evaluate low-dimensional scalar functions and rely on string-level or regression-based metrics that fail to capture structural and geometric equivalence. We introduce SURFACEBENCH, the first geometry-aware benchmark for symbolic discovery of three-dimensional surfaces. Unlike scalar curve-fitting tasks, SURFACEBENCH targets surface-level reasoning, where multi-variable coupling, coordinate transformations, and geometric structure must be inferred directly from data. The benchmark comprises 183 analytically constructed, science-inspired surface equations across 15…
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Taxonomy
TopicsMachine Learning in Materials Science · Model Reduction and Neural Networks · Advanced Graph Neural Networks
