Data-driven modeling can suffer from a constant demand for data, leading to reduced accuracy and impractical for engineering applications due to the high cost and scarcity of information. To address this challenge, we propose a progressive reduced order modeling framework that minimizes data cravings and enhances data-driven modeling's practicality. Our approach selectively transfers knowledge from previously trained models through gates, similar to how humans selectively use valuable knowledge while ignoring unuseful information. By filtering relevant information from previous models, we can create a surrogate model with minimal turnaround time and a smaller training set that can still achieve high accuracy. We have tested our framework in several cases, including transport in porous media, gravity-driven flow, and finite deformation in hyperelastic materials. Our results illustrate that retaining information from previous models and utilizing a valuable portion of that knowledge can significantly improve the accuracy of the current model. We have demonstrated the importance of progressive knowledge transfer and its impact on model accuracy with reduced training samples. For instance, our framework with four parent models outperforms the no-parent counterpart trained on data nine times larger. Our research unlocks data-driven modeling's potential for practical engineering applications by mitigating the data scarcity issue. Our proposed framework is a significant step toward more efficient and cost-effective data-driven modeling, fostering advancements across various fields.

翻译：数据驱动建模常受制于对数据的持续需求，因信息获取成本高昂且稀缺，导致工程应用中精度下降且不切实际。针对这一挑战，我们提出渐进式降阶建模框架，旨在最小化数据依赖并增强数据驱动建模的实用性。该方法通过门控机制选择性迁移先前训练模型的知识，其原理类似于人类仅保留有价值信息而过滤无用知识。通过筛取先前模型中的关联信息，我们能够以最短周转时间和更小训练集构建高精度替代模型。我们在多孔介质输运、重力驱动流及超弹性材料有限变形等案例中验证了该框架。结果表明，保留并利用先前模型中的有效知识可显著提升当前模型的精度。我们证明了渐进式知识迁移对减少训练样本后模型精度的重要影响：例如，采用四个父模型的框架性能优于使用九倍数据训练的无父模型。本研究通过缓解数据稀缺问题，释放了数据驱动建模在实际工程应用中的潜力。所提框架为更高效、低成本的数据驱动建模迈出了关键一步，将推动多领域的进步。