Attaining physics-driven convolutional operators by architecture design

Operator learning is key to leveraging artificial intelligence for scientific discovery by enabling the solution of partial differential equations that express core principles of physical modeling. However, conventional data-driven methods rely heavily on costly, high-fidelity simulations for training. Here, we introduce a physics-driven convolutional operator, leveraging a recurrent convolutional neural network framework to bypass this data reliance for multiscale predictive modeling. Trained entirely through physics-based constraints, this operator accurately learns equations characterizing complex systems, acquiring robust physical inference capabilities to serve as a surrogate applicable to a family of partial differential equations across various microstructures and initial conditions. It exhibits great accuracy and efficiency by solving the micromechanics problem, elastic wave propagation, and microstructure evolution, outperforming previous operator learners in rigorous quantitative comparisons. This labeled-data-free, fully knowledge-based operator learning provides a systematic approach for developing surrogate models, significantly benefiting physical prediction via forward modeling and engineering design via inverse modeling. Operator learning is essential for advancing AI-driven scientific discovery by solving partial differential equations that underpin physical modeling. Here, the authors introduce a label-free physics-driven convolutional operator (PDCO) that leverages a recurrent convolutional neural network to efficiently approximate neural operators, with its performance demonstrated on the Eshelby inclusion problem, elastic wave propagation, and the Allen–Cahn equations for predicting microstructure evolution.