Scientific Machine Learning (SciML) has advanced recently across many
different areas in computational science and engineering. The objective is to
integrate data and physics seamlessly without the need of employing elaborate
and computationally taxing data assimilation schemes. However, preprocessing,
problem formulation, code generation, postprocessing and analysis are still
time consuming and may prevent SciML from wide applicability in industrial
applications and in digital twin frameworks. Here, we integrate the various
stages of SciML under the umbrella of ChatGPT, to formulate CrunchGPT, which
plays the role of a conductor orchestrating the entire workflow of SciML based
on simple prompts by the user. Specifically, we present two examples that
demonstrate the potential use of CrunchGPT in optimizing airfoils in
aerodynamics, and in obtaining flow fields in various geometries in interactive
mode, with emphasis on the validation stage. To demonstrate the flow of the
CrunchGPT, and create an infrastructure that can facilitate a broader vision,
we built a webapp based guided user interface, that includes options for a
comprehensive summary report. The overall objective is to extend CrunchGPT to
handle diverse problems in computational mechanics, design, optimization and
controls, and general scientific computing tasks involved in SciML, hence using
it as a research assistant tool but also as an educational tool. While here the
examples focus in fluid mechanics, future versions will target solid mechanics
and materials science, geophysics, systems biology and bioinformatics.

本研究介绍了 CrunchGPT，这是一个基于 ChatGPT 的统一框架，可以在用户的简单提示下编排 SciML 的整个工作流程。研究还展示了两个案例，以演示 CrunchGPT 在气动优化和流场操作中的应用，重点是演示了 CrunchGPT 的流程，并创建了一个基于 Web 应用程序的用户界面，以促进更广泛的视野。未来版本将针对固体力学和材料科学，地球物理学，系统生物学和生物信息学。

CrunchGPT: 一种辅助科学机器学习的 ChatGPT 框架

CrunchGPT: A chatGPT assisted framework for scientific machine learning

Deep neural operators, such as DeepONets, have changed the paradigm in
high-dimensional nonlinear regression from function regression to
(differential) operator regression, paving the way for significant changes in
computational engineering applications. Here, we investigate the use of
DeepONets to infer flow fields around unseen airfoils with the aim of shape
optimization, an important design problem in aerodynamics that typically taxes
computational resources heavily. We present results which display little to no
degradation in prediction accuracy, while reducing the online optimization cost
by orders of magnitude. We consider NACA airfoils as a test case for our
proposed approach, as their shape can be easily defined by the four-digit
parametrization. We successfully optimize the constrained NACA four-digit
problem with respect to maximizing the lift-to-drag ratio and validate all
results by comparing them to a high-order CFD solver. We find that DeepONets
have low generalization error, making them ideal for generating solutions of
unseen shapes. Specifically, pressure, density, and velocity fields are
accurately inferred at a fraction of a second, hence enabling the use of
general objective functions beyond the maximization of the lift-to-drag ratio
considered in the current work.

本研究探索使用 DeepONets 方法推断未知气动翼型的流场并优化其形状，结果表明 DeepONets 非常适合生成未知形状的高准确度解决方案，可以在毫秒级时间内准确推断压强、密度和速度场等信息，为气动设计提供了极大的便利。

深度神经运算符可作为准确的形状优化替代方法：以翼型为例的案例研究

Deep neural operators can serve as accurate surrogates for shape optimization: A case study for airfoils

Simple aerodynamic configurations under even modest conditions can exhibit
complex flows with a wide range of temporal and spatial features. It has become
common practice in the analysis of these flows to look for and extract
physically important features, or modes, as a first step in the analysis. This
step typically starts with a modal decomposition of an experimental or
numerical dataset of the flow field, or of an operator relevant to the system.
We describe herein some of the dominant techniques for accomplishing these
modal decompositions and analyses that have seen a surge of activity in recent
decades. For a non-expert, keeping track of recent developments can be
daunting, and the intent of this document is to provide an introduction to
modal analysis that is accessible to the larger fluid dynamics community. In
particular, we present a brief overview of several of the well-established
techniques and clearly lay the framework of these methods using familiar linear
algebra. The modal analysis techniques covered in this paper include the proper
orthogonal decomposition (POD), balanced proper orthogonal decomposition
(Balanced POD), dynamic mode decomposition (DMD), Koopman analysis, global
linear stability analysis, and resolvent analysis.

本研究论文介绍实现流体动力学中基于模态分解的分析方法，其中包括 Proper Orthogonal Decomposition（POD）和 Dynamic Mode Decomposition (DMD) 等关键词。