Physics-informed neural operator solver and super-resolution for solid mechanics

Physics-Informed Neural Networks (PINNs) have solved numerous mechanics problems by training to minimize the loss functions of governing partial differential equations (PDEs). Despite successful development of PINNs in various systems, computational efficiency and fidelity prediction have remained profound challenges. To fill such gaps, this study proposed a Physics-Informed Neural Operator Solver (PINOS) to achieve accurate and fast simulations without any required data set. The training of PINOS adopts a weak form based on the principle of least work for static simulations and a strong form for dynamic systems in solid mechanics. Results from numerical examples indicated that PINOS is capable of approximating solutions notably faster than the benchmarks of PINNs in both static an dynamic systems. The comparisons also showed that PINOS reached a convergence speed of over 20 times faster than finite element software in two-dimensional and three-dimensional static problems. Furthermore, this study examined the zero-shot super-resolution capability by developing Super-Resolution PINOS (SR-PINOS) that was trained on a coarse mesh and validated on fine mesh. The numerical results demonstrate the great performance of the model to obtain accurate solutions with a speed up, suggesting effectiveness in increasing sampling points and scaling a simulation. This study also discusses the differentiation methods of PINOS and SR-PINOS and suggests potential implementations related to forward applications for promising machine learning methods for structural designs and optimization.