ArticleMaterials (Basel, Switzerland)2026
Energy-Consistent Neural Networks with Fenchel-Young Loss for Physics-Guided Energy Prediction in Sheet Metal Forming Under Small-Data Conditions.
Article in Materials (Basel, Switzerland), 2026. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Not yet cited in PubMed.
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Abstract
This study addresses energy-response prediction in sheet metal forming under small-data conditions, where conventional simulation-based approaches are computationally expensive and data acquisition is limited. We propose an Energy-Informed Neural Network (EINN) framework that integrates energy consistency constraints and a Fenchel-Young duality-based loss to enforce physically consistent learning without relying on explicit governing equations. Using a dataset generated from 54 finite element simulations across 18 materials and three friction conditions, the proposed model demonstrates significant performance improvements. Specifically, EINN achieves an RMSE of 0.0096, MAE of 0.0065, and R
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