Progressive transfer learning for advancing machine learning-based reduced-order modeling.

Area of Science:

• Machine Learning
• Scientific Computing
• Data-driven Modeling

Background:

• Data scarcity is a major challenge for developing accurate data-driven machine learning (ML) models.
• Reduced-order modeling (ROM) is crucial for efficient simulation in scientific and engineering applications.
• Transfer learning offers a way to leverage existing knowledge but requires effective implementation for new tasks.

Purpose of the Study:

• To introduce a novel progressive transfer learning for reduced-order modeling (p-ROM) framework.
• To enhance knowledge transfer and reduce data requirements for ML-based ROMs.
• To demonstrate the framework's effectiveness across diverse scientific and engineering problems.

Main Methods:

• The proposed p-ROM framework utilizes optimizing information gates in hidden layers to selectively transfer knowledge from pre-trained ML models.
• The framework is evaluated using Barlow Twins ROMs (p-BT-ROMs) to showcase progressive learning capabilities.
• The methodology is tested on various problems including transport, fluid dynamics, and solid mechanics.

Main Results:

• p-BT-ROM demonstrates improved model accuracy with significantly reduced training data across similar and different topologies.
• A p-BT-ROM with four pre-trained models outperformed a model trained on nine times more data without pre-training.
• The framework effectively mitigates data scarcity issues in ML-based ROMs.

Conclusions:

• The p-ROM framework offers a powerful solution for data-limited scenarios in scientific ML.
• Progressive knowledge transfer is key to enhancing the performance and data efficiency of ML-based ROMs.
• This approach has the potential to significantly advance ML applications in science and engineering.