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RheOPT: Few-Shot Non-Newtonian Flow Prediction via Newtonian Pretraining of RheOFormer

Maedeh Saberi, Amir Barati Farimani, Safa Jamali · 2026 · arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.31465 · cited by 0 works (OpenAlex) · open-access PDF

French

Malgré les progrès du régime fluctuant établi dans les méthodes numériques, les simulations de flux non-Newtoniennes restent computablement coûteuses parce que la vitesse et le stress doivent être avancés ensemble à travers la dynamique constitutive dépendante du rythme et de l'histoire. Les surrogates d'opérateur neuronal réduisent les coûts d'inférence après l'entraînement, mais leurs données de formation nécessitent les mêmes simulations Newtoniennes coûteuses qu'elles visent à remplacer, ce qui rend l'apprentissage efficace des données essentiel lorsque seules quelques simulations non-Newtoniennes peuvent être fournies. Ici, nous introduisons le Transformer de l'opérateur rhéologique prétrainé (RheOP

Machine translation (Meta M2M100); the English original follows.

Abstract

Despite advances in numerical methods, non-Newtonian flow simulations remain computationally expensive because velocity and stress must be advanced together through rate- and history-dependent constitutive dynamics. Neural-operator surrogates reduce inference cost after training, but their training data require the same expensive simulations they aim to replace, making data-efficient learning essential when only a few non-Newtonian simulations can be afforded. Here, we introduce the Rheological Operator Pretrained Transformer (RheOPT), which pretrains a transformer-based neural operator on inexpensive Newtonian simulations and fine-tunes it on a small number of non-Newtonian samples. Rather than transferring the Newtonian constitutive response itself, RheOPT reuses geometry-conditioned transport structure that remains useful after the stress model changes. We evaluate RheOPT in two geometry-matched settings: a $4{:}1$ contraction channel for Giesekus, Oldroyd-B, and Bingham fluids, and the oscillatory wake behind a triangular obstacle for Oldroyd-B flow. In the contraction, Newtonian pretraining substantially improves few-shot prediction, and a model fine-tuned on four target samples can match or exceed a from-scratch model trained on four times as many. This benefit is reliable under reversible instance normalization (RevIN) but dataset dependent under Global normalization, a difference we trace to the dynamic range of each fluid's velocity and stress fields. In the wake, where relative $L_2$ error alone cannot verify that vortex shedding is recovered, phase-insensitive diagnostics show that pretraining recovers the shedding frequency and wake fluctuation amplitude that are suppressed by the from-scratch model in the few-shot regime. Overall, RheOPT establishes Newtonian simulation as a physically grounded pretraining source for data-efficient non-Newtonian operator learning.

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Topics: Bingham plastic, Non-Newtonian fluid, Wake, Newtonian fluid, Computer science, Operator (biology)

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