发表机构
Massachusetts Institute of Technology（麻省理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对RUDE框架训练不稳定、外推差和不可解释的问题，提出多模式mmRUDEs，通过对数压缩、分裂网络和投影层保证热力学稳定，引入rheome增强可解释性，在合成与实验数据上验证了稳定性和准确性。
AI 中文摘要
流变学通用微分方程（RUDE）框架将神经网络嵌入到框架无关的张量本构骨架中，从而能够以数据驱动的方式发现复杂材料的流变行为。然而，使RUDE框架具有吸引力的灵活性也使其难以部署：学习到的神经网络修正项可能使本构方程在训练期间数值上变得刚性，将修正分布到张量基项的非唯一组合中，并且随着非线性增加而外推性能变差，尤其是对于具有宽弛豫谱的工业相关材料。我们开发了一个以稳定性和可靠性为重点的多模式RUDE框架，解决了三个关键挑战：热力学可容许性、分布外预测和可解释性。输入不变量的对数压缩和分裂网络架构改善了训练期间的数值条件，而可微投影层在每个时间步强制执行Clausius-Duhem不等式。我们使用合成数据（多模式Giesekus模型）和纠缠硅聚合物熔体的实验数据来展示该框架。两个模型均在LAOS上训练；它们在未见过的流动条件下保持稳定和准确，包括稳态剪切、瞬态应力增长和拉伸流动，在这些条件下，无约束模型可能数值发散。为了帮助解释每个学习修正对流变行为的贡献，我们引入了rheome，一种紧凑表示对整体流变行为起主导作用的加权张量基贡献的方式。对RUDE框架的这些改进导致了稳定且可解释的训练模型，为在计算流体动力学模拟中的实施以及指导软材料加工操作的合理设计铺平了道路。
英文摘要
The Rheological Universal Differential Equation (RUDE) framework embeds neural networks within a frame-indifferent tensorial constitutive backbone and so enables data-driven discovery of complex material rheological behavior. However, the flexibility that makes the RUDE framework attractive also makes it difficult to deploy: the learned neural network correction can make the constitutive equation numerically stiff during training, distribute corrections across non-unique combinations of tensor-basis terms, and extrapolate poorly with increasing nonlinearity, especially for industrially relevant materials with broad relaxation spectra. We develop a stability- and reliability-focused multi-mode RUDE framework that addresses three key challenges: thermodynamic admissibility, out-of-distribution prediction, and interpretability. Logarithmic compression of the input invariants and a split-network architecture improve numerical conditioning during training, while a differentiable projection layer enforces the Clausius--Duhem inequality at every time step. We illustrate the framework with both synthetic (a multi-mode Giesekus model) and experimental data on an entangled silicone polymer melt. Both models were trained on LAOS; they remain stable and accurate under unseen flow conditions, including steady shear, transient stress growth, and extensional flows, for which the unconstrained models may diverge numerically. To aid in interpretation of the contributions of each learned correction to the rheological behavior, we introduce the rheome, a compact way of representing the dominant weighted tensor-basis contributions to the overall rheological behavior. These improvements to the RUDE framework lead to stable and interpretable trained models, paving the way for implementation in computational fluid dynamics simulations and for guiding the rational design of soft material processing operations.
