Accurate simulation of turbulent flows is of immense importance in a variety of scientific and engineering fields. Within the realm of turbulent flow simulation, direct numerical simulation (DNS) is widely considered to be the most reliable approach, but it is prohibitively expensive and thus has limited applicability to long-term and fine-scale simulation over various configurations. Given the pressing need for efficient simulation, there is an increasing interest in building machine learning models for simulating turbulence, either by reconstructing DNS from alternative low-fidelity simulations or sequentially predicting DNS from historical data. However, conventional machine learning models are not designed for capturing complex spatio-temporal characteristics of turbulent flows. This results in their limited performance and generalizability, especially when applied to complex flow data and various flow configurations. This paper presents a novel physics-enhanced neural operator (PENO) that efficiently models the complex flow dynamics while leveraging physical knowledge of partial differential equations (PDEs) to enhance the simulation process. We further introduce a self-augmentation mechanism to reduce the accumulated errors in long-term simulations. The proposed method is evaluated on multiple turbulent flow datasets, showcasing the model's capability to reconstruct high-resolution DNS data, maintain the inherent physical properties of flow transport, and transfer across various resolution settings and simulation configurations. These encouraging results confirm its applicability to a wide range of real-world scenarios in which extensive simulations are needed under diverse settings.

Accurate simulation of turbulent flows is of crucial importance in many branches of science and engineering. Direct numerical simulation (DNS) provides the highest fidelity means of capturing all intricate physics of turbulent transport. However, the method is computationally expensive because of the wide range of turbulence scales that must be accounted for in such simulations. Large eddy simulation (LES) provides an alternative. In such simulations, the large scales of the flow are resolved, and the effects of small scales are modelled. Reconstruction of the DNS field from the low-resolution LES is needed for a wide variety of applications. Thus the construction of super-resolution methodologies that can provide this reconstruction has become an area of active research. In this work, a new physics-guided neural network is developed for such a reconstruction. The method leverages the partial differential equation that underlies the flow dynamics in the design of spatio-temporal model architecture. A degradation-based refinement method is also developed to enforce physical constraints and to further reduce the accumulated reconstruction errors over long periods. Detailed DNS data on two turbulent flow configurations are used to assess the performance of the model.

Direct numerical simulation (DNS) of turbulent flows is computationally expensive and cannot be applied to flows with large Reynolds numbers. Low-resolution large eddy simulation (LES) is a popular alternative, but it is unable to capture all of the scales of turbulent transport accurately. Reconstructing DNS from low-resolution LES is critical for large-scale simulation in many scientific and engineering disciplines, but it poses many challenges to existing super-resolution methods due to the complexity of turbulent flows and computational cost of generating frequent LES data. We propose a physics-guided neural network for reconstructing frequent DNS from sparse LES data by enhancing its spatial resolution and temporal frequency. Our proposed method consists of a partial differential equation (PDE)-based recurrent unit for capturing underlying temporal processes and a physics-guided super-resolution model that incorporates additional physical constraints. We demonstrate the effectiveness of both components in reconstructing the Taylor-Green Vortex using sparse LES data. Moreover, we show that the proposed recurrent unit can preserve the physical characteristics of turbulent flows by leveraging the physical relationships in the Navier-Stokes equation.

Direct numerical simulation (DNS) of turbulent flows is computationally expensive and cannot be applied to flows with large Reynolds numbers. Large eddy simulation (LES) is an alternative that is computationally less demanding, but is unable to capture all of the scales of turbulent transport accurately. Our goal in this work is to build a new data-driven methodology based on super-resolution techniques to reconstruct DNS data from LES predictions. We leverage the underlying physical relationships to regularize the relationships amongst different physical variables. We also introduce a hierarchical generative process and a reverse degradation process to fully explore the correspondence between DNS and LES data. We demonstrate the effectiveness of our method through a single-snapshot experiment and a cross-time experiment. The results confirm that our method can better reconstruct high-resolution DNS data over space and over time in terms of pixel-wise reconstruction error and structural similarity. Visual comparisons show that our method performs much better in capturing fine-level flow dynamics.

With the explosion of large, dynamic graph datasets from various fields, graph partitioning and repartitioning are becoming more and more critical to the performance of many graph-based Big Data applications, such as social analysis, web search, and recommender systems. However, well-studied graph (re)partitioners usually assume a homogeneous and contention-free computing environment, which contradicts the increasing communication heterogeneity and shared resource contention in modern, multicore high performance computing clusters. To bridge this gap, we introduce PARAGON, a parallel architecture-aware graph partition refinement algorithm, which mitigates the mismatch by modifying a given decomposition according to the nonuniform network communication costs and the contentiousness of the underlying hardware topology. To further reduce the overhead of the refinement, we also make PARAGON itself architecture-aware. Our experiments with a diverse collection of datasets showed that on average PARAGON improved the quality of graph decompositions computed by the de-facto standard (hashing partitioning) and two state-of-the-art streaming graph partitioning heuristics (deterministic greedy and linear deterministic greedy) by 43%, 17%, and 36%, respectively. Furthermore, our experiments with an MPI implementation of Breadth First Search and Single Source Shortest Path showed that, in comparison to the state-of-the-art streaming and multi-level graph (re)partitioners, PARAGON achieved up to 5.9x speedups. Finally, we demonstrated the scalability of PARAGON by scaling it up to a graph with 3.6 billion edges using only 3 machines (60 physical cores).