We consider the commonly encountered situation (e.g., in weather forecasting) where the goal is to predict the time evolution of a large, spatiotemporally chaotic dynamical system when we have access to both time series data of previous system states and an imperfect model of the full system dynamics. Specifically, we attempt to utilize machine learning as the essential tool for integrating the use of past data into predictions. In order to facilitate scalability to the common scenario of interest where the spatiotemporally chaotic system is very large and complex, we propose combining two approaches:(i) a parallel machine learning prediction scheme; and (ii) a hybrid technique, for a composite prediction system composed of a knowledge-based component and a machine-learning-based component. We demonstrate that not only can this method combining (i) and (ii) be scaled to give excellent performance for very large systems, but also that the length of time series data needed to train our multiple, parallel machine learning components is dramatically less than that necessary without parallelization. Furthermore, considering cases where computational realization of the knowledge-based component does not resolve subgrid-scale processes, our scheme is able to use training data to incorporate the effect of the unresolved short-scale dynamics upon the resolved longer-scale dynamics ("subgrid-scale closure").
An Analytical and AI-discovered Stable, Accurate, and Generalizable Subgrid-scale Closure for Geophysical Turbulence
Department of Geophysical Sciences, University of Chicago（芝加哥大学地球科学系）；Department of Mechanical Engineering, Rice University（里士满大学机械工程系）；Department of Mechanical Engineering, Union College（联合学院机械工程系）；Department of Geophysical Sciences（地球科学系）；Committee on Computational and Applied Mathematics, University of Chicago（芝加哥大学计算与应用数学委员会）
Stanford University（斯坦福大学）；SLAC National Accelerator Laboratory（SLAC国家加速器实验室）
Many practical combustion systems such as those in rockets, gas turbines, and internal combustion engines operate under high pressures that surpass the thermodynamic critical limit of fuel-oxidizer mixtures. These conditions require the consideration of complex fluid behaviors that pose challenges for numerical simulations, casting doubts on the validity of existing subgrid-scale (SGS) models in large-eddy simulations of these systems. While data-driven methods have shown high accuracy as closure models in simulations of turbulent flames, these models are often criticized for lack of physical …
Oklahoma State University（俄克拉荷马州立大学）；Norwegian University of Science and Technology（挪威科技大学）；SINTEF Digital（SINTEF数字研究所）
A central challenge in the computational modeling and simulation of a multitude of science applications is to achieve robust and accurate closures for their coarse-grained representations due to underlying highly nonlinear multiscale interactions. These closure models are common in many nonlinear spatiotemporal systems to account for losses due to reduced order representations, including many transport phenomena in fluids. Previous data-driven closure modeling efforts have mostly focused on supervised learning approaches using high fidelity simulation data. On the other hand, reinforcement lea…
Coarse Graining with Neural Operators for Simulating Chaotic Systems
Department of Computing and Mathematical Sciences, California Institute of Technology（计算与数学科学系，加利福尼亚理工学院）；NVIDIA Research（NVIDIA研究）；Graduate Aerospace Laboratories, California Institute of Technology（航空航天实验室，加利福尼亚理工学院）
Turbulence is still one of the main challenges for accurately predicting reactive flows. Therefore, the development of new turbulence closures which can be applied to combustion problems is essential. Data-driven modeling has become very popular in many fields over the last years as large, often extensively labeled, datasets became available and training of large neural networks became possible on GPUs speeding up the learning process tremendously. However, the successful application of deep neural networks in fluid dynamics, for example for subgrid modeling in the context of large-eddy simula…
ETH Zürich（苏黎世联邦理工学院）；Harvard University（哈佛大学）；Massachusetts Institute of Technology（麻省理工学院）
Predictive simulations of complex systems are essential for applications ranging from weather forecasting to drug design. The veracity of these predictions hinges on their capacity to capture the effective system dynamics. Massively parallel simulations predict the system dynamics by resolving all spatiotemporal scales, often at a cost that prevents experimentation while their findings may not allow for generalisation. On the other hand reduced order models are fast but limited by the frequently adopted linearization of the system dynamics and/or the utilization of heuristic closures. Here we …
Complex dynamical systems are used for predictions in many domains. Because of computational costs, models are truncated, coarsened, or aggregated. As the neglected and unresolved terms become important, the utility of model predictions diminishes. We develop a novel, versatile, and rigorous methodology to learn non-Markovian closure parameterizations for known-physics/low-fidelity models using data from high-fidelity simulations. The new "neural closure models" augment low-fidelity models with neural delay differential equations (nDDEs), motivated by the Mori-Zwanzig formulation and the inher…
Deep Learning of Solver-Aware Turbulence Closures from Nudged LES Dynamics
School of Mechanical Engineering（机械工程学院）；Purdue University（普渡大学）；College of Information Sciences and Technology（信息科学与技术学院）；Pennsylvania State University（宾夕法尼亚州立大学）
Generalizable data-driven turbulence closure modeling on unstructured grids with differentiable physics
School of Mechanical Engineering, Purdue University, West Lafayette, 47907, IN, USA（机械工程学院，普渡大学）；Mechanical Engineering Department, Carnegie Mellon University, Pittsburgh, 15213, PA, USA（机械工程系，卡内基梅隆大学）；Department of Aerospace Engineering, University of Michigan, Ann Arbor, 48109, MI, USA（航空航天工程系，密歇根大学）；College of Information Sciences and Technology, Pennsylvania State University, University Park, 16802, PA, USA（信息科学与技术学院，宾夕法尼亚州立大学）；Computer Science Division, Argonne National Laboratory, Lemont, 60439, IL, USA（计算机科学 division，阿贡国家实验室）
Oklahoma State University（俄克拉荷马州立大学）；The University of Tulsa（塔尔萨大学）；Norwegian University of Science and Technology（挪威科技大学）
Complex natural or engineered systems comprise multiple characteristic scales, multiple spatiotemporal domains, and even multiple physical closure laws. To address such challenges, we introduce an interface learning paradigm and put forth a data-driven closure approach based on memory embedding to provide physically correct boundary conditions at the interface. To enable the interface learning for hyperbolic systems by considering the domain of influence and wave structures into account, we put forth the concept of upwind learning towards a physics-informed domain decomposition. The promise of…
Latent Representation Learning of Multi-scale Thermophysics: Application to Dynamics in Shocked Porous Energetic Material
School of Data Science, University of Virginia, United States（数据科学学院，弗吉尼亚大学）；Department of Mechanical Engineering, University of Iowa, United States（机械工程系，爱荷华大学）；Department of Mechanical and Aerospace Engineering, University of Virginia, United States（机械与航空航天工程系，弗吉尼亚大学）
Statistical (machine learning) tools for equation discovery require large amounts of data that are typically computer generated rather than experimentally observed. Multiscale modeling and stochastic simulations are two areas where learning on simulated data can lead to such discovery. In both, the data are generated with a reliable but impractical model, e.g., molecular dynamics simulations, while a model on the scale of interest is uncertain, requiring phenomenological constitutive relations and ad-hoc approximations. We replace the human discovery of such models, which typically involves sp…
Johns Hopkins University（约翰斯·霍普金斯大学）；Princeton University（普林斯顿大学）；University of Rostock（罗斯托克大学）；Universitá degli Studi di Napoli Federico II（那不勒斯费德里科二世大学）
Complex spatiotemporal dynamics of physicochemical processes are often modeled at a microscopic level (through e.g. atomistic, agent-based or lattice models) based on first principles. Some of these processes can also be successfully modeled at the macroscopic level using e.g. partial differential equations (PDEs) describing the evolution of the right few macroscopic observables (e.g. concentration and momentum fields). Deriving good macroscopic descriptions (the so-called "closure problem") is often a time-consuming process requiring deep understanding/intuition about the system of interest. …
