自扩展的Tanh (Stan):用于物理信息的神经网络的多尺度解决方案.
IEEE transactions on pattern analysis and machine intelligence
|August 23, 2023
概括
基于物理学的神经网络 (PINNs) 为微分方程提供无网格的解决方案. 一个新的自我可扩展的tanh (Stan) 激活功能改善了复杂物理系统的PINN训练和预测准确性.
科学领域:
- 计算数学 计算数学 计算数学
- 深度学习应用程序
- 科学计算科学计算
背景情况:
- 微分方程对于在各种领域建模物理系统至关重要.
- 传统的数值方法近似解决方案,面临复杂系统的局限性.
- 基于物理学的神经网络 (PINNs) 成为解决微分方程和反向问题的强大无网格替代方案.
研究的目的:
- 为了解决由常规激活函数引起的物理信息神经网络 (PINNs) 的训练限制.
- 引入一个新的,可扩展的激活功能,旨在增强PINNs的学习过程.
- 提高使用PINNs解决微分方程的准确性和效率.
主要方法:
- 为PINNs开发了一种新的自扩展的tanh (Stan) 激活功能.
- 斯坦函数是光滑的,不和的,并包含一个可训练的参数,用于自适应缩放.
- 通过前问题 (解决微分方程) 和反向问题 (参数识别) 进行评估.
主要成果:
- 拟议的Stan激活功能在训练期间促进了更顺的梯度流和系统的输入-输出映射调整.
- 与PINNs中现有的激活功能相比,证明了卓越的训练性能和预测准确性.
- 成功应用于解决复杂的微分方程和识别系统参数.
结论:
- 斯坦激活功能代表了基于物理学的神经网络的重大进步.
- 它增强了PINNs能够准确有效地模拟由微分方程控制的物理系统的能力.
- 斯坦函数为未来的物理信息机器学习研究提供了一个有希望的方向.
更多相关视频
07:52Multiscale Investigations of Cortical Processing by Integrating Laminar Polytrodes and Optogenetics with Micro Electrocorticography in Rodents
Published on: May 23, 2025
245
12:27Large-scale Reconstructions and Independent, Unbiased Clustering Based on Morphological Metrics to Classify Neurons in Selective Populations
Published on: February 15, 2017
7.0K
相关概念视频
Ampere-Maxwell's Law: Problem-Solving
667
A parallel-plate capacitor with capacitance C, whose plates have area A and separation distance d, is connected to a resistor R and a battery of voltage V. The current starts to flow at t = 0. What is the displacement current between the capacitor plates at time t? From the properties of the capacitor, what is the corresponding real current?
To solve the problem, we can use the equations from the analysis of an RC circuit and Maxwell's version of Ampère's law.
For the first part of...
To solve the problem, we can use the equations from the analysis of an RC circuit and Maxwell's version of Ampère's law.
For the first part of...
667
Maxwell-Boltzmann Distribution: Problem Solving
1.6K
Individual molecules in a gas move in random directions, but a gas containing numerous molecules has a predictable distribution of molecular speeds, which is known as the Maxwell-Boltzmann distribution, f(v).
This distribution function f(v) is defined by saying that the expected number N (v1,v2) of particles with speeds between v1 and v2 is given by
This distribution function f(v) is defined by saying that the expected number N (v1,v2) of particles with speeds between v1 and v2 is given by
1.6K
Collisions in Multiple Dimensions: Problem Solving
4.3K
In multiple dimensions, the conservation of momentum applies in each direction independently. Hence, to solve collisions in multiple dimensions, we should write down the momentum conservation in each direction separately. To help understand collisions in multiple dimensions, consider an example.
A small car of mass 1,200 kg traveling east at 60 km/h collides at an intersection with a truck of mass 3,000 kg traveling due north at 40 km/h. The two vehicles are locked together. What is the...
A small car of mass 1,200 kg traveling east at 60 km/h collides at an intersection with a truck of mass 3,000 kg traveling due north at 40 km/h. The two vehicles are locked together. What is the...
4.3K
Solving Problems in Physics
5.9K
Problem-solving is the ability to apply general physical principles to specific situations, usually expressed by equations. It is an essential skill in physics, and can also be useful for applying physics in everyday life as well. Analytical skills and problem-solving abilities can be applied to new situations, compared to a list of facts, which can never be extensive enough to include every possible circumstance. To solve physics problems, a certain amount of creativity and insight is...
5.9K
Neural Circuits
1.3K
Neural circuits and neuronal pools are two of the main structures found in the nervous system. Neural circuits are networks of neurons that work together to carry out a specific task or process. They consist of interconnected neurons and glial cells, which provide structural and metabolic support.
Neuronal pools are collections of nerve cells with similar functions and interact through chemical and electrical signals. These pools include both interneurons (the central neural circuit nodes that...
Neuronal pools are collections of nerve cells with similar functions and interact through chemical and electrical signals. These pools include both interneurons (the central neural circuit nodes that...
1.3K
Two-Dimensional Force System: Problem Solving
615
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...
615
