Related papers: Introduction to Symbolic Regression in the Physica…
Symbolic regression has recently gained traction in AI-driven scientific discovery, aiming to recover explicit closed-form expressions from data that reveal underlying physical laws. Despite recent advances, existing methods remain…
This paper presents QDSR, an advanced symbolic Regression (SR) system that integrates genetic programming (GP), a quality-diversity (QD) algorithm, and a dimensional analysis (DA) engine. Our method focuses on exact symbolic recovery of…
The mathematical formula is the human language to describe nature and is the essence of scientific research. Finding mathematical formulas from observational data is a major demand of scientific research and a major challenge of artificial…
Symbolic regression is a powerful tool for discovering governing equations directly from data, but its sensitivity to noise hinders its broader application. This paper introduces a Sequential Monte Carlo (SMC) framework for Bayesian…
We study the addition of shape constraints (SC) and their consideration during the parameter identification step of symbolic regression (SR). SC serve as a means to introduce prior knowledge about the shape of the otherwise unknown model…
Turbulence modeling within the RANS equations' framework is essential in engineering due to its high efficiency. Field inversion and machine learning (FIML) techniques have improved RANS models' predictive capabilities for separated flows.…
Solutions of symbolic regression problems are expressions that are composed of input variables and operators from a finite set of function symbols. One measure for evaluating symbolic regression algorithms is their ability to recover…
Symbolic Regression tries to find a mathematical expression that describes the relationship of a set of explanatory variables to a measured variable. The main objective is to find a model that minimizes the error and, optionally, that also…
Symbolic Regression (SR) is a powerful technique for automatically discovering mathematical expressions from input data. Mainstream SR algorithms search for the optimal symbolic tree in a vast function space, but the increasing complexity…
Discovering governing equations of complex network dynamics is a fundamental challenge in contemporary science with rich data, which can uncover the mysterious patterns and mechanisms of the formation and evolution of complex phenomena in…
Symbolic regression (SR) poses a significant challenge for randomized search heuristics due to its reliance on the synthesis of expressions for input-output mappings. Although traditional genetic programming (GP) algorithms have achieved…
We propose SatelliteFormula, a novel symbolic regression framework that derives physically interpretable expressions directly from multi-spectral remote sensing imagery. Unlike traditional empirical indices or black-box learning models,…
The typical methods for symbolic regression produce rather abrupt changes in solution candidates. In this work, we have tried to transform symbolic regression from an optimization problem, with a landscape that is so rugged that typical…
Reinforcement learning (RL) is concerned with how intelligence agents take actions in a given environment to maximize the cumulative reward they receive. In healthcare, applying RL algorithms could assist patients in improving their health…
We present a Machine Learning approach based on Symbolic Regression to derive, from either numerically generated or experimentally measured spectral data, closed-form expressions that model the optical properties of biological materials. To…
In social science, formal and quantitative models, such as ones describing economic growth and collective action, are used to formulate mechanistic explanations, provide predictions, and uncover questions about observed phenomena. Here, we…
Despite successful seminal works on passive systems in the literature, learning free-form physical laws for controlled dynamical systems given experimental data is still an open problem. For decades, symbolic mathematical equations and…
Symbolic regression (SR) is the process of discovering hidden relationships from data with mathematical expressions, which is considered an effective way to reach interpretable machine learning (ML). Genetic programming (GP) has been the…
Physics-informed Neural Networks (PINNs) have been widely used to obtain accurate neural surrogates for a system of Partial Differential Equations (PDE). One of the major limitations of PINNs is that the neural solutions are challenging to…
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…