将有限元素与深度神经运算符连接起来,以快速多尺度建模力学问题
Minglang Yin1,2, Enrui Zhang3, Yue Yu4
1Center for Biomedical Engineering, Brown University, Providence, RI, United States of America.
Computer methods in applied mechanics and engineering
|June 29, 2023
概括
本研究介绍了一种机器学习方法,使用DeepONet创建高效的多尺度模型. 这种方法显著降低了复杂模拟的计算成本,使多物理系统的预测速度更快.
科学领域:
- 计算科学 计算科学
- 应用数学 应用数学 应用数学
- 机器学习 机器学习
背景情况:
- 多尺度建模对于具有不同尺度的多物理系统至关重要,但高保真模拟在计算上是昂贵的.
- 现有的方法难以应对详细模拟的高成本,特别是对于时间依赖的问题.
- 桥梁不同的模型分辨率 (例如,连续和粒子方法) 提出了重要的计算挑战.
研究的目的:
- 利用机器学习开发一个高效的多尺度建模框架,以降低计算成本.
- 雇佣DeepONet,一个神经操作员,作为昂贵的高保真解决方案的替代品.
- 证明框架能够在新条件下准确预测系统响应的能力.
主要方法:
- 在线训练DeepONet,使用来自精细分辨率解决器的数据来学习精细规模的动态.
- 将训练有素的DeepONet与标准的PDE解决方案相结合,用于实时预测.
- 通过使用静态和时间依赖的基准来验证方法,包括将有限元方法 (FEM) 与神经操作员替代物用于光滑粒子水力学 (SPH) 的合.
主要成果:
- 基于DeepONet的多尺度建模框架显著降低了计算成本.
- DeepONet准确地捕捉了微小规模的动态,并为新的预测做出了很好的概括.
- 证明了连续 (FEM) 和基于粒子 (SPH代理) 的模型的成功合,用于材料响应预测.
结论:
- 机器学习,特别是DeepONet,在多尺度建模中为高保真度解决器提供了一个高效的替代品.
- 拟议的框架可为复杂的多物理问题提供具有成本效益和准确的预测.
- 这种方法促进了各种建模技术和接口条件的整合.
相关概念视频
01:29Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving
81
Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
81
01:30Three-Dimensional Force System:Problem Solving
695
A three-dimensional force system refers to a scenario in which three forces act simultaneously in three different directions. This type of problem is commonly encountered in physics and engineering, where it is necessary to calculate the resultant force on the system, which can then be used to predict or analyze the behavior of the object or structure under consideration.
To solve a three-dimensional force system, first resolve each force into its respective scalar components. Do this using...
To solve a three-dimensional force system, first resolve each force into its respective scalar components. Do this using...
695
01:30Three-Dimensional Force System
2.1K
In mechanical engineering, a three-dimensional force system is a system of forces acting in three dimensions, with forces applied along the x, y, and z coordinate axes. The three-dimensional force system is an important concept in mechanical engineering, as it allows engineers to understand and analyze the behavior of objects and structures in three dimensions. By understanding the forces acting on a system, engineers can design more efficient and effective mechanical systems that can withstand...
2.1K
01:30Typical Model Studies
385
Fluid mechanics model studies often utilize scaled-down systems to predict fluid behavior in full-scale environments, such as river flows, dam spillways, and structures interacting with open surfaces. Maintaining Froude number similarity in river models is crucial, as it replicates surface flow features like wave patterns and velocities.
385
01:29Two-Dimensional Force System: Problem Solving
619
Solving problems related to two-dimensional force systems is an essential aspect of mechanics and engineering. By applying the principles of vector analysis and force equilibrium, one can determine the effect of multiple forces acting on an object in a two-dimensional space.
The first step to solving a two-dimensional force system problem is to draw a free-body diagram of the object under consideration. This diagram helps identify all the external forces acting on the object, including their...
The first step to solving a two-dimensional force system problem is to draw a free-body diagram of the object under consideration. This diagram helps identify all the external forces acting on the object, including their...
619