Related papers: Using machine learning to find exact analytic solu…
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…
Symbolic regression (SR) methods have been extensively investigated to explore explicit algebraic Reynolds stress models (EARSM) for turbulence closure of Reynolds-averaged Navier-Stokes (RANS) equations. The deduced EARSM can be readily…
Symbolic Regression (SR) allows for the discovery of scientific equations from data. To limit the large search space of possible equations, prior knowledge has been expressed in terms of formal grammars that characterize subsets of…
The application of machine learning to physics problems is widely found in the scientific literature. Both regression and classification problems are addressed by a large array of techniques that involve learning algorithms. Unfortunately,…
Symbolic Regression (SR) aims to discover interpretable equations from observational data, with the potential to reveal underlying principles behind natural phenomena. However, existing approaches often fall into the Pseudo-Equation Trap:…
Symbolic regression (SR), the automated discovery of mathematical expressions from data, is a cornerstone of scientific inquiry. However, it is often hindered by the combinatorial explosion of the search space and a tendency to overfit.…
Symbolic Regression (SR) holds great potential for uncovering underlying mathematical and physical relationships from observed data. However, the vast combinatorial space of possible expressions poses significant challenges for both online…
Symbolic Regression (SR) holds great potential for uncovering underlying mathematical and physical relationships from observed data. However, the vast combinatorial space of possible expressions poses significant challenges for both online…
In science, we are interested not only in forecasting but also in understanding how predictions are made, specifically what the interpretable underlying model looks like. Data-driven machine learning technology can significantly streamline…
Cylindrical Algebraic Decomposition (CAD) is a key tool in computational algebraic geometry, best known as a procedure to enable Quantifier Elimination over real-closed fields. However, it has a worst case complexity doubly exponential in…
Neural-symbolic methods have demonstrated efficiency in enhancing the reasoning abilities of large language models (LLMs). However, existing methods mainly rely on syntactically mapping natural languages to complete formal languages like…
Symbolic regression (SR) is a challenging task in machine learning that involves finding a mathematical expression for a function based on its values. Recent advancements in SR have demonstrated the effectiveness of pre-trained…
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…
We introduce an Invertible Symbolic Regression (ISR) method. It is a machine learning technique that generates analytical relationships between inputs and outputs of a given dataset via invertible maps (or architectures). The proposed ISR…
Stochastic rounding (SR) is a probabilistic rounding mode that mitigates errors in large-scale numerical computations, especially when prone to stagnation effects. Beyond numerical analysis, SR has shown significant benefits in practical…
Machine learning models have become firmly established across all scientific fields. Extracting features from data and making inferences based on them with neural network models often yields high accuracy; however, this approach has several…
In nature, the behaviors of many complex systems can be described by parsimonious math equations. Automatically distilling these equations from limited data is cast as a symbolic regression process which hitherto remains a grand challenge.…
Symbolic regression seeks to uncover physical laws from experimental data by searching for closed-form expressions, which is an important task in AI-driven scientific discovery. Yet the exponential growth of the search space of expression…
Motivated by the remarkable success of artificial intelligence (AI) across diverse fields, the application of AI to solve scientific problems, often formulated as partial differential equations (PDEs), has garnered increasing attention.…
Any representation of data involves arbitrary investigator choices. Because those choices are external to the data-generating process, each choice leads to an exact symmetry, corresponding to the group of transformations that takes one…