aiqbench analysis
Newtonian pretraining of a transformer neural operator appears to cut the number of costly non-Newtonian simulations needed for accurate few-shot prediction, with the benefit depending on normalization choice. The paper also adds phase-insensitive diagnostics to show that the surrogate recovers vortex-shedding frequency and amplitude, which relative L2 error alone cannot confirm. For ML readers, the main question is whether transfer from cheap physics simulations to harder physical regimes generalizes beyond these two geometry-matched benchmarks.
RheOPT: Few-Shot Non-Newtonian Flow Prediction via Newtonian Pretraining of RheOFormer
arXiv:2610.31465v1 Announce Type: new 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.
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.
Machine Learning (cs.LG)
arXiv:2610.31465 [cs.LG]
(or arXiv:2610.31465v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2610.31465 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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Full text under the publisher's open licence · 345 words