Equilibrium Conserving Neural Operators for Super-Resolution Learning
This addresses the problem of high data acquisition costs for researchers and engineers in materials modeling, offering a resource-efficient surrogate modeling pathway, though it is incremental as it builds on existing neural operator methods.
The paper tackles the need for extensive high-resolution training data in neural surrogate solvers for partial differential equations in solid mechanics by introducing a super-resolution learning framework that trains high-resolution networks using only low-resolution data. The result is the Equilibrium Conserving Operator (ECO) architecture, which embeds physics to enforce conservation laws, reducing data collection costs by two orders of magnitude in examples like embedded pores and polycrystalline materials.
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.