Physics-informed two-tier neural network for non-linear model order reduction.

Area of Science:

• Computational Science and Engineering
• Machine Learning Applications
• Physics-Informed Modeling

Background:

• Machine learning (ML) significantly impacts non-intrusive model order reduction (MOR), but faces high offline training costs and generalization issues.
• Current methods often neglect physical information and struggle with efficiency, with some techniques being intrusive or computationally expensive.
• Existing hyper-reduction methods for efficient online stages are either intrusive or demand substantial offline computation.

Purpose of the Study:

• To propose a non-intrusive, physics-informed, two-tier deep network (TTDN) method to address the limitations of current ML-based MOR techniques.
• To develop a method that reduces offline computational costs and enhances generalization capabilities.
• To integrate physical laws directly into the neural network training process for improved MOR.

Main Methods:

• A two-tier deep network (TTDN) architecture is proposed, inspired by physics-informed neural networks.
• The first tier performs regression of the quantity of interest, while the second tier reconstructs the physical constitutive law.
• The network is trained using pretraining and semi-supervised learning strategies.

Main Results:

• The TTDN method demonstrates efficiency in handling challenging non-linear and non-affine problems.
• Numerical experiments confirm the effectiveness of the proposed physics-informed approach.
• The method successfully addresses high computational costs associated with the offline training phase.

Conclusions:

• The proposed non-intrusive, physics-informed TTDN method offers an effective solution for computationally expensive ML-based MOR.
• TTDN improves generalization and reduces training costs by incorporating physical laws.
• This approach shows promise for complex multi-scale mechanics problems and other non-linear systems.