Related papers: Combining Neural Networks and Symbolic Regression …
Symbolic regression is a powerful technique that can discover analytical equations that describe data, which can lead to explainable models and generalizability outside of the training data set. In contrast, neural networks have achieved…
Learning the underlying equation from data is a fundamental problem in many disciplines. Recent advances rely on Neural Networks (NNs) but do not provide theoretical guarantees in obtaining the exact equations owing to the non-convexity of…
We explore the use of symbolic regression to derive compact analytical expressions for angular observables relevant to electroweak boson production at the Large Hadron Collider (LHC). Focusing on the angular coefficients that govern the…
We introduce a novel symbolic regression framework, namely KAN-SR, built on Kolmogorov Arnold Networks (KANs) which follows a divide-and-conquer approach. Symbolic regression searches for mathematical equations that best fit a given dataset…
Identifying governing equations for a dynamical system is a topic of critical interest across an array of disciplines, from mathematics to engineering to biology. Machine learning -- specifically deep learning -- techniques have shown their…
Symbolic discovery of governing equations is a long-standing goal in scientific machine learning, yet a fundamental trade-off persists between interpretability and scalable learning. Classical symbolic regression methods yield explicit…
Symbolic regression (SR) is a powerful technique for discovering the analytical mathematical expression from data, finding various applications in natural sciences due to its good interpretability of results. However, existing methods face…
Symbolic regression is a technique that can automatically derive analytic models from data. Traditionally, symbolic regression has been implemented primarily through genetic programming that evolves populations of candidate solutions…
Symbolic regression is a machine learning technique that can learn the governing formulas of data and thus has the potential to transform scientific discovery. However, symbolic regression is still limited in the complexity and…
Using representations of functional data can be more convenient and beneficial in subsequent statistical models than direct observations. These representations, in a lower-dimensional space, extract and compress information from individual…
In this paper, we show how convolutional neural networks (CNN) can be used in regression and classification learning problems of noisy and non-noisy functional data. The main idea is to transform the functional data into a 28 by 28 image.…
In a regression task, a function is learned from labeled data to predict the labels at new data points. The goal is to achieve small prediction errors. In symbolic regression, the goal is more ambitious, namely, to learn an interpretable…
Symbolic regression is a type of discrete optimization problem that involves searching expressions that fit given data points. In many cases, other mathematical constraints about the unknown expression not only provide more information…
Complex networks describe important structures in nature and society, composed of nodes and the edges that connect them. The evolution of these networks is typically described by dynamics, which are labor-intensive and require expert…
Despite advances in learning-based methods, finding valid Lyapunov functions for nonlinear dynamical systems remains challenging. Current neural network approaches face two main issues: challenges in scalable verification and limited…
We present a novel approach to symbolic regression using vision-capable large language models (LLMs) and the ideas behind Google DeepMind's Funsearch. The LLM is given a plot of a univariate function and tasked with proposing an ansatz for…
We propose neural-symbolic integration for abstract concept explanation and interactive learning. Neural-symbolic integration and explanation allow users and domain-experts to learn about the data-driven decision making process of large…
Computational fluid dynamics (CFD) analysis is widely used in engineering. Although CFD calculations are accurate, the computational cost associated with complex systems makes it difficult to obtain empirical equations between system…
Inferring latent interaction structures from observed dynamics is a fundamental inverse problem in many-body interacting systems. Most neural approaches rely on black-box surrogates over trainable graphs, achieving accuracy at the expense…
Automated scientific discovery aims to improve scientific understanding through machine learning. A central approach in this field is symbolic regression, which uses genetic programming or sparse regression to learn interpretable…