Abstract In this work, a unified AI-framework named Hierarchical Deep Learning Neural Network (HiDeNN) is proposed to solve challenging computational science and engineering problems with little or no available physics as well as with extreme computational demand. The detailed construction and mathematical elements of HiDeNN are introduced and discussed to show the flexibility of the framework for diverse problems from disparate fields. Three example problems are solved to demonstrate the accuracy, efficiency, and versatility of the framework. The first example is designed to show that HiDeNN is capable of achieving better accuracy than conventional finite element method by learning the optimal nodal positions and capturing the stress concentration with a coarse mesh. The second example applies HiDeNN for multiscale analysis with sub-neural networks at each material point of macroscale. The final example demonstrates how HiDeNN can discover governing dimensionless parameters from experimental data so that a reduced set of input can be used to increase the learning efficiency. We further present a discussion and demonstration of the solution for advanced engineering problems that require state-of-the-art AI approaches and how a general and flexible system, such as HiDeNN-AI framework, can be applied to solve these problems.

中文翻译：

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分层深度学习神经网络 (HiDeNN)：用于计算科学和工程的人工智能 (AI) 框架

摘要 在这项工作中，提出了一个名为分层深度学习神经网络 (HiDeNN) 的统一 AI 框架，以解决具有挑战性的计算科学和工程问题，这些问题几乎没有或没有可用的物理学以及极端的计算需求。介绍和讨论了 HiDeNN 的详细构造和数学元素，以展示该框架对来自不同领域的各种问题的灵活性。解决了三个示例问题，以证明框架的准确性、效率和通用性。第一个示例旨在表明 HiDeNN 能够通过学习最佳节点位置并使用粗网格捕获应力集中来实现比传统有限元方法更高的精度。第二个示例应用 HiDeNN 进行多尺度分析，在每个宏观尺度的物质点使用子神经网络。最后一个例子展示了 HiDeNN 如何从实验数据中发现控制无量纲参数，以便可以使用减少的输入集来提高学习效率。我们进一步讨论和演示了需要最先进的 AI 方法的高级工程问题的解决方案，以及如何应用 HiDeNN-AI 框架等通用且灵活的系统来解决这些问题。