Energy-Consistent Neural Networks with Fenchel-Young Loss for Physics-Guided Energy Prediction in Sheet Metal Forming...

Area of Science:

• Mechanical Engineering
• Materials Science
• Computational Science

Background:

• Sheet metal forming simulations are computationally intensive and data acquisition is limited.
• Predicting energy response accurately is crucial for process optimization.
• Existing methods struggle with small-data conditions.

Purpose of the Study:

• To develop a computationally efficient and accurate surrogate model for energy-response prediction in sheet metal forming.
• To address the challenges of limited data availability in conventional simulation-based approaches.
• To propose an Energy-Informed Neural Network (EINN) framework.

Main Methods:

• Developed an Energy-Informed Neural Network (EINN) framework.
• Integrated energy consistency constraints into the neural network.
• Utilized a Fenchel-Young duality-based loss function for physically consistent learning.
• Generated a dataset from 54 finite element simulations across 18 materials and three friction conditions.

Main Results:

• The EINN framework achieved an RMSE of 0.0096, MAE of 0.0065, and R² of 0.9778.
• Demonstrated approximately a 48% reduction in RMSE compared to the best baseline model.
• Achieved approximately 50% reduction in prediction error and improved stability compared to an energy-constrained neural network without the Fenchel-Young term.

Conclusions:

• Embedding energy-consistent dual structures enhances prediction accuracy and robustness in neural networks.
• The EINN framework provides a practical surrogate modeling approach for sheet metal forming under limited data.
• This approach offers significant improvements over conventional methods for process optimization.