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Data-driven modeling can suffer from a constant demand for data, leading toreduced accuracy and impractical for engineering applications due to the highcost and scarcity of information. To address this challenge, we propose aprogressive reduced order modeling framework that minimizes data cravings andenhances data-driven modeling's practicality. Our approach selectivelytransfers knowledge from previously trained models through gates, similar tohow humans selectively use valuable knowledge while ignoring unusefulinformation. By filtering relevant information from previous models, we cancreate a surrogate model with minimal turnaround time and a smaller trainingset that can still achieve high accuracy. We have tested our framework inseveral cases, including transport in porous media, gravity-driven flow, andfinite deformation in hyperelastic materials. Our results illustrate thatretaining information from previous models and utilizing a valuable portion ofthat knowledge can significantly improve the accuracy of the current model. Wehave demonstrated the importance of progressive knowledge transfer and itsimpact on model accuracy with reduced training samples. For instance, ourframework with four parent models outperforms the no-parent counterpart trainedon data nine times larger. Our research unlocks data-driven modeling'spotential for practical engineering applications by mitigating the datascarcity issue. Our proposed framework is a significant step toward moreefficient and cost-effective data-driven modeling, fostering advancementsacross various fields.

Progressive reduced order modeling: empowering data-driven modeling with selective knowledge transfer