| RelaxNet: A structure-preserving neural network to approximate the Boltzmann collision operator | |
| Xiao TB(肖天白); Frank, Martin | |
| Source Publication | JOURNAL OF COMPUTATIONAL PHYSICS
 |
| 2023-10-01 | |
| Volume | 490Pages:112317 |
| ISSN | 0021-9991 |
| Abstract | The extremely high dimensionality and nonlinearity in the Boltzmann equation bring tremendous difficulties to the study of rarefied gas dynamics. This paper addresses a neural network-based surrogate model that provides a structure-preserving approximation for the fivefold collision integral. The notion originates from the similarity in structure between the BGK-type relaxation model and residual neural network (ResNet) when a particle distribution function is treated as the input to the neural network function. Therefore, we extend the ResNet architecture and construct what we call the relaxation neural network (RelaxNet). Specifically, two feed-forward neural networks with physics informed connections and activations are introduced as building blocks in RelaxNet, which provide bounded and physically realizable approximations of the equilibrium distribution and velocity-dependent relaxation time respectively. The evaluation of the collision term is thus significantly accelerated due to the fact that the convolution in the fivefold integral is replaced by tensor multiplication in the neural network. We fuse the mechanical advection operator and the RelaxNet-based collision operator into a unified model named the universal Boltzmann equation (UBE). We prove that UBE preserves the key structural properties in a many-particle system, i.e., positivity, conservation, invariance, H-theorem, and correct fluid dynamic limit. These properties promise that RelaxNet is superior to strategies that naively approximate the right-hand side of the Boltzmann equation using a machine learning model. A novel sampling strategy based on closure hierarchies of the moment system of the Boltzmann equation is developed to generate reliable and unbiased sampling for the supervised learning. The construction of the RelaxNet-based UBE and its solution algorithm are demonstrated in detail. Several numerical experiments, where the ground-truth datasets are produced by the Shakhov model, velocity-dependent & nu;-BGK model, and the full Boltzmann equation, are investigated. The capability of the current approach for simulating non-equilibrium flow physics is validated through satisfactory in and out-of-distribution performance. The open-source codes to reproduce the numerical results are available under the MIT license [1].& COPY; 2023 Elsevier Inc. All rights reserved. |
| Keyword | Kinetic theory Computational fluid dynamics Scientific machine learning Artificial neural network |
| DOI | 10.1016/j.jcp.2023.112317 |
| Indexed By | SCI ; EI |
| Language | 英语 |
| WOS ID | WOS:001029759700001 |
| WOS Research Area | Computer Science ; Physics |
| WOS Subject | Computer Science, Interdisciplinary Applications ; Physics, Mathematical |
| Funding Organization | German Research Foundation [SPP 2298, 441826958] |
| Classification | 一类/力学重要期刊 |
| Ranking | 1 |
| Contributor | Xiao, TB (corresponding author), Chinese Acad Sci, Inst Mech, State Key Lab High Temp Gas Dynam, Beijing, Peoples R China. |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://dspace.imech.ac.cn/handle/311007/92556 |
| Collection | 高温气体动力学国家重点实验室 |
| Affiliation | 1.{Xiao, Tianbai} Chinese Acad Sci, Inst Mech, State Key Lab High Temp Gas Dynam, Beijing, Peoples R China 2.{Frank, Martin} Karlsruhe Inst Technol, Steinbuch Ctr Comp, Karlsruhe, Germany |
| Recommended Citation GB/T 7714 | Xiao TB,Frank, Martin. RelaxNet: A structure-preserving neural network to approximate the Boltzmann collision operator[J]. JOURNAL OF COMPUTATIONAL PHYSICS,2023,490:112317.Rp_Au:Xiao, TB (corresponding author), Chinese Acad Sci, Inst Mech, State Key Lab High Temp Gas Dynam, Beijing, Peoples R China. |
| APA | 肖天白,&Frank, Martin.(2023).RelaxNet: A structure-preserving neural network to approximate the Boltzmann collision operator.JOURNAL OF COMPUTATIONAL PHYSICS,490,112317. |
| MLA | 肖天白,et al."RelaxNet: A structure-preserving neural network to approximate the Boltzmann collision operator".JOURNAL OF COMPUTATIONAL PHYSICS 490(2023):112317. |
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| Jp2023A224.pdf（5203KB） | 期刊论文 | 出版稿 | 开放获取 | CC BY-NC-SA | View Download | |
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