相关论文: Combining Neural Networks and Symbolic Regression …

Symbolic regression is a task aimed at identifying patterns in data and representing them through mathematical expressions, generally involving skeleton prediction and constant optimization. Many methods have achieved some success, however…

We study the modeling and prediction of dynamical systems based on conventional models derived from measurements. Such algorithms are highly desirable in situations where the underlying dynamics are hard to model from physical principles or…

Symbolic Regression is the study of algorithms that automate the search for analytic expressions that fit data. While recent advances in deep learning have generated renewed interest in such approaches, the development of symbolic…

The analysis of variance (ANOVA) decomposition offers a systematic method to understand the interaction effects that contribute to a specific decision output. In this paper we introduce Neural-ANOVA, an approach to decompose neural networks…

We showcase the potential of symbolic regression as an analytic method for use in materials research. First, we briefly describe the current state-of-the-art method, genetic programming-based symbolic regression (GPSR), and recent advances…

Training convolutional neural networks (CNNs) with back-propagation (BP) is time-consuming and resource-intensive particularly in view of the need to visit the dataset multiple times. In contrast, analytic learning attempts to obtain the…

Machine learning algorithms such as linear regression, SVM and neural network have played an increasingly important role in the process of scientific discovery. However, none of them is both interpretable and accurate on nonlinear datasets.…

Symbolic regression, the task of extracting mathematical expressions from the observed data $\{ \vx_i, y_i \}$, plays a crucial role in scientific discovery. Despite the promising performance of existing methods, most of them conduct…

Recurrent Neural Networks (RNN) are ubiquitous computing systems for sequences and multivariate time series data. While several robust architectures of RNN are known, it is unclear how to relate RNN initialization, architecture, and other…

Many recent studies focus on developing mechanisms to explain the black-box behaviors of neural networks (NNs). However, little work has been done to extract the potential hidden semantics (mathematical representation) of a neural network.…

We investigate the addition of constraints on the function image and its derivatives for the incorporation of prior knowledge in symbolic regression. The approach is called shape-constrained symbolic regression and allows us to enforce e.g.…

Symbolic regression (SR) is a powerful technique for discovering the underlying mathematical expressions from observed data. Inspired by the success of deep learning, recent deep generative SR methods have shown promising results. However,…

A fundamental but largely unaddressed obstacle in Symbolic regression (SR) is structural redundancy: every expression DAG with admits many distinct node-numbering schemes that all encode the same expression, each occupying a separate point…

Deep learning methods have been widely used in robotic applications, making learning-enabled control design for complex nonlinear systems a promising direction. Although deep reinforcement learning methods have demonstrated impressive…

The goal of neural-symbolic computation is to integrate the connectionist and symbolist paradigms. Prior methods learn the neural-symbolic models using reinforcement learning (RL) approaches, which ignore the error propagation in the…

Symbolic regression searches for analytic expressions that accurately describe studied phenomena. The main attraction of this approach is that it returns an interpretable model that can be insightful to users. Historically, the majority of…

Symbolic Regression aims to automatically identify compact and interpretable mathematical expressions that model the functional relationship between input and output variables. Most existing search-based symbolic regression methods…

We develop a versatile deep neural network architecture, called Lyapunov-Net, to approximate Lyapunov functions of dynamical systems in high dimensions. Lyapunov-Net guarantees positive definiteness, and thus it can be easily trained to…

[RETRACTED]Data increasingly abounds, but distilling their underlying relationships down to something interpretable remains challenging. One approach is genetic programming, which `symbolically regresses' a data set down into an equation.…

Symbolic regression corresponds to an ensemble of techniques that allow to uncover an analytical equation from data. Through a closed form formula, these techniques provide great advantages such as potential scientific discovery of new…