Equilibrium Conserving Neural Operators for Super-Resolution Learning

• URL: http://arxiv.org/abs/2504.13422v1
• Date: Fri, 18 Apr 2025 02:47:53 GMT
• Title: Equilibrium Conserving Neural Operators for Super-Resolution Learning
• Authors: Vivek Oommen, Andreas E. Robertson, Daniel Diaz, Coleman Alleman, Zhen Zhang, Anthony D. Rollett, George E. Karniadakis, Rémi Dingreville,
• Abstract summary: We introduce a framework for super-resolution learning in solid mechanics problems.<n>Our approach allows one to train a high-resolution neural network using only low-resolution data.<n>We evaluate this ECO-based super-resolution framework that strongly enforces conservation-laws in the predicted solutions.
• Score: 2.062348453578637
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Neural surrogate solvers can estimate solutions to partial differential equations in physical problems more efficiently than standard numerical methods, but require extensive high-resolution training data. In this paper, we break this limitation; we introduce a framework for super-resolution learning in solid mechanics problems. Our approach allows one to train a high-resolution neural network using only low-resolution data. Our Equilibrium Conserving Operator (ECO) architecture embeds known physics directly into the network to make up for missing high-resolution information during training. We evaluate this ECO-based super-resolution framework that strongly enforces conservation-laws in the predicted solutions on two working examples: embedded pores in a homogenized matrix and randomly textured polycrystalline materials. ECO eliminates the reliance on high-fidelity data and reduces the upfront cost of data collection by two orders of magnitude, offering a robust pathway for resource-efficient surrogate modeling in materials modeling. ECO is readily generalizable to other physics-based problems.

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