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

Aadi Dash; Lennon J. Shikhman; Michael Galarnyk

cs.LGSep 29, 2026

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

Authors: Aadi Dash, Lennon J. Shikhman, Michael Galarnyk

Organizations: College of Computing, Georgia Institute of Technology · Department of Mathematics and Systems Engineering, Florida Institute of Technology · Wallace H. Coulter Department of Biomedical Engineering, Georgia Institute of Technology

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, 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). Constant conditioning has lower mean test error on both 2D tasks. Relative to this control, task text plus alignment has a similar mean on ShallowWater2D and CNS3D and a higher mean on Darcy2D; these descriptive comparisons have substantial seed uncertainty. The latter comparison changes both prompt content and loss, so it isolates neither effect. The text encoder is trained from scratch, and each conditioned model sees only one description during training. In this regime, pairwise InfoNCE cannot identify matched pairs and has minimum $\log B$ . Prompt interventions show no reliable semantic ordering. This methodological caution demonstrates why pathway controls are needed; it neither establishes semantic competence of the encoder nor tests the effectiveness of text under varying physical context.

Figures & tables

Panel of Figure 1 — Figure 1: Diagnostic comparisons. Unconditioned-to-constant changes pathway and capacity together; constant-to-aligned changes both text and loss. Interventions probe prompt sensitivity.

Task	Unconditioned	Constant	Fixed prompt + align.	$\Delta_{\rm U\to C}$	$\Delta_{\rm C\to A}$
Darcy2D	$.03714\!\pm\!.00744$	$.03009\!\pm\!.00064$	$.03903\!\pm\!.00941$	$+19.0\%$	$-29.7\%$
ShallowWater2D	$.001694\!\pm\!.000242$	$.001394\!\pm\!.000272$	$.001373\!\pm\!.000099$	$+17.7\%$	$+1.5\%$
CNS3D	$.40446\!\pm\!.00485$	$.40675\!\pm\!.00789$	$.40458\!\pm\!.01458$	$-0.6\%$	$+0.5\%$

Table 1: Test relative

L^{2}

(mean

\pm

sample s.d., three seeds). Positive

\Delta_{\rm U\to C}

and

\Delta_{\rm C\to A}

denote lower mean error in constant versus unconditioned and aligned versus constant. Percentages are descriptive ratios of means, not isolated causal effects or significance claims.

Figure 2: Prompt sensitivity of the aligned models. Cells show the paired change in test relative $L^{2}$ error from the correct description (mean $\pm$ sample standard deviation over the same three seeds); positive values indicate higher error. Missing and constant modes use the same sentence.

Appendix figures & tables1 asset

Supplementary material from the paper’s appendix.

Appendix

Task	Seed	Unconditioned	Constant	Fixed prompt + align.
Darcy2D	7	0.032205	0.030741	0.049860
	17	0.033520	0.030068	0.034352
	27	0.045690	0.029452	0.032868
ShallowWater2D	7	0.00155104	0.00118240	0.00135158
	17	0.00155618	0.00129879	0.00128726
	27	0.00197349	0.00170078	0.00148120

Appendix

Table 2: All 27 existing runs: final-epoch test relative

L^{2}

, lower is better. Each row contains three separately trained models.

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