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

arXiv: https://arxiv.org/abs/2609.38517 · HTML: https://mlsanity.com/paper/2609.38517/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 28 of its 36 references that are in the map.
- First posted on arXiv 29 Sep 2026.

## Builds on (most cited first, 28 of 28)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Fourier Neural Operator with Learned Deformations for PDEs on General Geometries](https://mlsanity.com/paper/2207.05209/) (2022)
- [PDEBENCH: An Extensive Benchmark for Scientific Machine Learning](https://mlsanity.com/paper/2210.07182/) (2022)
- [GNOT: A General Neural Operator Transformer for Operator Learning](https://mlsanity.com/paper/2302.14376/) (2023)
- [Transformer for Partial Differential Equations' Operator Learning](https://mlsanity.com/paper/2205.13671/) (2022)
- [Convolutional Neural Operators for robust and accurate learning of PDEs](https://mlsanity.com/paper/2302.01178/) (2023)
- [Poseidon: Efficient Foundation Models for PDEs](https://mlsanity.com/paper/2405.19101/) (2024)
- [Towards Multi-spatiotemporal-scale Generalized PDE Modeling](https://mlsanity.com/paper/2209.15616/) (2022)
- [DPOT: Auto-Regressive Denoising Operator Transformer for Large-Scale PDE Pre-Training](https://mlsanity.com/paper/2403.03542/) (2024)
- [The Well: a Large-Scale Collection of Diverse Physics Simulations for Machine Learning](https://mlsanity.com/paper/2412.00568/) (2024)
- [In-Context Operator Learning with Data Prompts for Differential Equation Problems](https://mlsanity.com/paper/2304.07993/) (2023)
- [APEBench: A Benchmark for Autoregressive Neural Emulators of PDEs](https://mlsanity.com/paper/2411.00180/) (2024)
- [CFDBench: A Large-Scale Benchmark for Machine Learning Methods in Fluid Dynamics](https://mlsanity.com/paper/2310.05963/) (2023)
- [Hypernetwork-based Meta-Learning for Low-Rank Physics-Informed Neural Networks](https://mlsanity.com/paper/2310.09528/) (2023)
- [Unisolver: PDE-Conditional Transformers Towards Universal Neural PDE Solvers](https://mlsanity.com/paper/2405.17527/) (2024)
- [PROSE-FD: A Multimodal PDE Foundation Model for Learning Multiple Operators for Forecasting Fluid Dynamics](https://mlsanity.com/paper/2409.09811/) (2024)
- [GPT-PINN: Generative Pre-Trained Physics-Informed Neural Networks toward non-intrusive Meta-learning of parametric PDEs](https://mlsanity.com/paper/2303.14878/) (2023)
- [OmniArch: Building Foundation Model For Scientific Computing](https://mlsanity.com/paper/2402.16014/) (2024)
- [Explain Like I'm Five: Using LLMs to Improve PDE Surrogate Models with Text](https://mlsanity.com/paper/2410.01137/) (2024)
- [Diagnosing Failure Modes of Neural Operators Across Diverse PDE Families](https://mlsanity.com/paper/2601.11428/) (2026)
- [PICL: Physics Informed Contrastive Learning for Partial Differential Equations](https://mlsanity.com/paper/2401.16327/) (2024)
- [One Operator to Rule Them All? On Boundary-Indexed Operator Families in Neural PDE Solvers](https://mlsanity.com/paper/2603.01406/) (2026)
- [Semigroup Consistency as a Diagnostic for Learned Physics Simulators](https://mlsanity.com/paper/2605.26324/) (2026)
- [ArGEnT: Arbitrary Geometry-encoded Transformer for Operator Learning](https://mlsanity.com/paper/2602.11626/) (2026)

## Abstract (arXiv)

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.