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

Mr. Md Rakibul Hasan1,2, Dr. Pouria Behnoudfar2, Dr. Dan MacKinlay3, Dr. Thomas Poulet2

1School of Electrical Engineering, Computing and Mathematical Sciences, Curtin University, Bentley, Australia, 2Commonwealth Scientific and Industrial Research Organisation (CSIRO) Mineral Resources, Kensington, Australia, 3Commonwealth Scientific and Industrial Research Organisation (CSIRO) Data61, Eveleigh, Australia

Biography:

Md Rakibul Hasan (Rakib) is a doctoral researcher in Computing at the 'Human-Centric Group in AI' at Curtin University, Western Australia, where he builds robust AI models to detect empathy from multimodal data, including video, audio, and textual content. His overarching research interest includes advancing affective computing and multimodal systems using deep learning algorithms.

In addition to research, Rakib is keen on teaching. He has been tutoring as a casual academic at Curtin University and Murdoch University. He is on leave from BRAC University, Bangladesh, where he currently holds a full-time senior lecturer position. He also lectured full-time at the Bangladesh Army International University of Science & Technology.

Rakib received his BSc (2019) and MSc (2021) degrees from Khulna University of Engineering & Technology, Bangladesh. In 2024, he received the 'Quality Journal Publication Award' from BRAC University for two of his publications between January and June 2023. As a CI, he received two grants on computational power for 2024 from the Pawsey Supercomputing Research Centre, Australia. Earlier, he championed the 'Seeds for the Future 2018' program by Huawei Technologies Co. Ltd., leading to a two-week sponsored visit to China.

Abstract:

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.

 

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