通过神经网络进行符号回归
N Boddupalli1, T Matchen1, J Moehlis1
1Department of Mechanical Engineering, University of California, Santa Barbara, Santa Barbara, California 93106, USA.
Chaos (Woodbury, N.Y.)
|December 7, 2023
概括
这项研究引入了一种新的深度学习模型,该模型为管理方程生成符号表达式. 这种方法将深度学习的准确性与用于动态系统分析的符号解决方案实用性相结合.
科学领域:
- 动态系统 动态系统
- 机器学习 机器学习
- 科学计算科学计算
背景情况:
- 识别治理方程在科学和工程领域至关重要.
- 传统的深度学习对动态系统缺乏可解释性.
- 现有的符号方法往往需要领域专业知识或与过度配合作斗争.
研究的目的:
- 开发一种新的方法,将深度学习的灵活性与象征性解决方案的实用性相结合.
- 创建一个深层神经网络,能够生成用于管理方程的符号表达式.
- 在各种古典动态系统中证明这种新方法的准确性.
主要方法:
- 提出了一个新的深度神经网络架构.
- 该模型旨在输出代表管理方程的符号表达式.
- 该方法将深度学习的数据近似能力与符号回归相结合.
主要成果:
- 发达的深度神经网络准确地生成用于管理方程的符号表达式.
- 该算法在一系列经典动态系统中表现出高精度.
- 该方法通过提供可解释的符号解决方案,提供了超越数值预测的洞察力.
结论:
- 这种新的深度学习方法成功地弥合了准确的动态系统预测和可解释的符号模型之间的差距.
- 该方法通过提供明确的管理方程来增强机器学习在科学发现中的实用性.
- 未来的工作可以探索复杂系统中的应用,其中可解释性至关重要.
相关概念视频
Neural Regulation
39.5K
Digestion begins with a cephalic phase that prepares the digestive system to receive food. When our brain processes visual or olfactory information about food, it triggers impulses in the cranial nerves innervating the salivary glands and stomach to prepare for food.
39.5K
Regression Toward the Mean
6.3K
Regression toward the mean (“RTM”) is a phenomenon in which extremely high or low values—for example, and individual’s blood pressure at a particular moment—appear closer to a group’s average upon remeasuring. Although this statistical peculiarity is the result of random error and chance, it has been problematic across various medical, scientific, financial and psychological applications. In particular, RTM, if not taken into account, can interfere when...
6.3K
Regression Analysis
5.7K
Regression analysis is a statistical tool that describes a mathematical relationship between a dependent variable and one or more independent variables.
In regression analysis, a regression equation is determined based on the line of best fit– a line that best fits the data points plotted in a graph. This line is also called the regression line. The algebraic equation for the regression line is called the regression equation. It is represented as:
In regression analysis, a regression equation is determined based on the line of best fit– a line that best fits the data points plotted in a graph. This line is also called the regression line. The algebraic equation for the regression line is called the regression equation. It is represented as:
5.7K
Multiple Regression
3.0K
Multiple regression assesses a linear relationship between one response or dependent variable and two or more independent variables. It has many practical applications.
Farmers can use multiple regression to determine the crop yield based on more than one factor, such as water availability, fertilizer, soil properties, etc. Here, the crop yield is the response or dependent variable as it depends on the other independent variables. The analysis requires the construction of a scatter plot...
Farmers can use multiple regression to determine the crop yield based on more than one factor, such as water availability, fertilizer, soil properties, etc. Here, the crop yield is the response or dependent variable as it depends on the other independent variables. The analysis requires the construction of a scatter plot...
3.0K
Correlation and Regression
1.3K
In statistics, correlation describes the degree of association between two variables. In the subfield of linear regression, correlation is mathematically expressed by the correlation coefficient, which describes the strength and direction of the relationship between two variables. The coefficient is symbolically represented by 'r' and ranges from -1 to +1. A positive value indicates a positive correlation where the two variables move in the same direction. A negative value suggests a...
1.3K
Neural Regulation of Blood Pressure
2.8K
The neural regulation of blood pressure involves intricate interactions between the autonomic nervous system (ANS) and cardiovascular system, ensuring adequate perfusion of tissues. This regulation primarily occurs through baroreceptor and chemoreceptor reflexes, involving both short-term and long-term mechanisms.
Baroreceptor Reflex
Baroreceptors, located in the carotid sinuses and aortic arch, detect changes in blood pressure. When blood pressure rises, these stretch-sensitive receptors...
Baroreceptor Reflex
Baroreceptors, located in the carotid sinuses and aortic arch, detect changes in blood pressure. When blood pressure rises, these stretch-sensitive receptors...
2.8K


