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Accepted paper · NeurIPS 2026 workshop

Does Text Steer Neural PDE Surrogates? A Controlled Diagnostic with OperatorCLIP

Aadi Dash, Lennon J. Shikhman, Michael Galarnyk

Poster presentation · session and time TBD

13 December 2026 · Paris, France

Abstract

Lower error from a text-conditioned neural surrogate does not, by itself, show that the model uses the meaning of the text. We examine this attribution problem with *OperatorCLIP*, a CLIP-style text–data conditioning system, by comparing an unconditioned FNO, a constant-sentence FiLM control, and a fixed task description trained with contrastive alignment. Three-seed experiments cover Darcy2D, ShallowWater2D, and three-dimensional compressible Navier–Stokes (CNS3D). The constant control lowers mean relative $L^2$ error by $19.0$% on Darcy2D and $17.7$% on ShallowWater2D, showing that conditioning-pathway and capacity changes can produce apparent gains. Alignment improves ShallowWater2D by $18.9$%, worsens Darcy2D by $5.1$%, and has no mean benefit on CNS3D. Each dataset supplies only one task-level description. In this regime, pairwise InfoNCE cannot identify positive text–data pairs and is minimized at $\log B$; shuffled prompts are unchanged, and semantically corrupted descriptions remain close to correct ones. These results diagnose architectural and optimization effects, but do not demonstrate semantic steering.

Paper

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