Relying on paired synthetic data, existing learning-based Computational Aberration Correction (CAC) methods are confronted with the intricate and multifaceted synthetic-to-real domain gap, which leads to suboptimal performance in real-world applications. In this paper, in contrast to improving the simulation pipeline, we deliver a novel insight into real-world CAC from the perspective of Unsupervised Domain Adaptation (UDA). By incorporating readily accessible unpaired real-world data into training, we formalize the Domain Adaptive CAC (DACAC) task, and then introduce a comprehensive Real-world aberrated images (Realab) dataset to benchmark it. The setup task presents a formidable challenge due to the intricacy of understanding the target aberration domain. To this intent, we propose a novel Quntized Domain-Mixing Representation (QDMR) framework as a potent solution to the issue. QDMR adapts the CAC model to the target domain from three key aspects: (1) reconstructing aberrated images of both domains by a VQGAN to learn a Domain-Mixing Codebook (DMC) which characterizes the degradation-aware priors; (2) modulating the deep features in CAC model with DMC to transfer the target domain knowledge; and (3) leveraging the trained VQGAN to generate pseudo target aberrated images from the source ones for convincing target domain supervision. Extensive experiments on both synthetic and real-world benchmarks reveal that the models with QDMR consistently surpass the competitive methods in mitigating the synthetic-to-real gap, which produces visually pleasant real-world CAC results with fewer artifacts. Codes and datasets will be made publicly available.

Data-driven modeling approaches can produce fast surrogates to study large-scale physics problems. Among them, graph neural networks (GNNs) that operate on mesh-based data are desirable because they possess inductive biases that promote physical faithfulness, but hardware limitations have precluded their application to large computational domains. We show that it is possible to train a class of GNN surrogates on 3D meshes. We scale MeshGraphNets (MGN), a subclass of GNNs for mesh-based physics modeling, via our domain decomposition approach to facilitate training that is mathematically equivalent to training on the whole domain under certain conditions. With this, we were able to train MGN on meshes with millions of nodes to generate computational fluid dynamics (CFD) simulations. Furthermore, we show how to enhance MGN via higher-order numerical integration, which can reduce MGN's error and training time. This work presents a practical path to scaling MGN for real-world applications. Understanding physical systems and engineering processes often requires extensive numerical simulations of their underlying models. However, these simulations are typically computationally expensive to generate, which can hinder their applicability to large-scale problems.