Physics-Informed Generative Adversarial Network to Super-Resolve General Transient Simulations

Artificial Intelligence methods, such as Generative Adversarial Networks (GANs), have revolutionised image Super Resolution (SR), yet the generated images often lack the physical consistency required for scientific applications. We developed a physics-informed SR method, PI-SRGAN, that explicitly accounts for the governing partial differential equations, boundary conditions and time integrator for discrete time-marching strategy. We implemented our approach on top of an existing non-physics method named SRGAN. Targeting general transient initial-boundary-value problems with first-order time derivatives, we validated our approach with two standard problem types: Allen-Cahn and Eriksson-Johnson. PI-SRGAN significantly outperformed SRGAN across different metrics. For the Allen-Cahn problem with periodic boundaries, PI-SRGAN with a Backward Differentiation Formula integrator achieved a Peak Signal-to-Noise Ratio (PSNR) of 37.27, Structural Similarity Index Measure (SSIM) of 0.9652, Mean Squared Error (MSE) of 0.0041 and Mean Squared Gradient Error (MSGE) of 7.24, compared to SRGAN's 32.44, 0.9084, 0.0111, and 18.14, respectively. Similar performance improvements are also achieved in Allen-Cahn with Neumann boundaries and Eriksson-Johnson with Dirichlet boundaries. PI-SRGAN has surrogate capabilities, producing valid initial solutions for further simulations. The error while surrogating from PI-SRGAN images was an order of magnitude smaller than those from SRGAN images. PI-SRGAN advances scientific machine learning by improving performance and efficiency (requiring only 13% of training data to reach SRGAN) while ensuring physical consistency. Despite the need for problem-specific training, the method offers significant benefits. Applications include enhancing the resolution of simulation results, serving as a computationally cheaper surrogate (up to 10^8 times in three dimensions) and preconditioning for simulations.