亲属转换加快了一个单维的整合问题的物理信息的神经网络的训练
Luis Mandl1, André Mielke1, Seyed Morteza Seyedpour1,2
1Institute of Structural Mechanics and Dynamics in Aerospace Engineering, Faculty of Aerospace Engineering and Geodesy, University of Stuttgart, Pfaffenwaldring 27, 70569, Stuttgart, Germany.
Scientific reports
|September 20, 2023
概括
有关物理信息的神经网络 (AfPINNs) 改善了对复杂微分方程的训练. 这种方法加快了趋同,提高了解决多孔介质整合问题的准确性.
科学领域:
- 计算物理学的计算物理.
- 应用数学 应用数学 应用数学
- 机器学习是机器学习.
背景情况:
- 基于物理学的神经网络 (PINNs) 为解决微分方程提供了一种新的数据驱动方法.
- PINNs将物理定律直接集成到神经网络架构中.
- 在将PINNs应用于合偏微分方程时,仍然存在挑战,特别是在收和初始条件方面.
研究的目的:
- 提高PINNs的训练效率和解决方案准确性,用于合微分方程.
- 在PINN优化中解决边界条件和底层方程之间的关键冲突.
- 在特定的物理领域引入一种新的架构,以提高PINN性能.
主要方法:
- 在标准神经网络架构的输出层中引入同源转换,创建同源物理信息的神经网络 (AfPINNs).
- 基于Biot的理论,应用AfPINNs来解决多孔介质中的一维整合问题.
- 对AfPINNs与传统PINNs的实证评估,重点关注融合速度和解决方案准确性.
主要成果:
- 在PINN培训中,AfPINNs显著减轻了与不良初始条件相关的问题.
- 拟议的AfPINN架构加速了复杂问题的培训过程.
- 对于一维整合问题,AfPINNs的准确性得到了提高,相对误差平均减少了[公式:参见文本].
结论:
- 亲属转换为PINN架构提供了有效的增强,用于解决具有挑战性的微分方程.
- 通过AfPINNs,可以生成准确而非碎的场解决方案,即使是在具有广泛大小的参数空间中.
- 这种方法对推进物理信息的神经网络在诸如多孔的介质力学等领域的应用有希望.
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