相关论文: Rethinking Symbolic Regression Datasets and Benchm…

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…

Symbolic data analysis (SDA) is an emerging area of statistics concerned with understanding and modelling data that takes distributional form (i.e. symbols), such as random lists, intervals and histograms. It was developed under the premise…

Data-driven discovery of partial differential equations (PDEs) offers a promising paradigm for uncovering governing physical laws from observational data. However, in practical scenarios, measurements are often contaminated by noise and…

For non-randomized studies, the regression discontinuity design (RDD) can be used to identify and estimate causal effects from a "locally-randomized" subgroup of subjects, under relatively mild conditions. However, current models focus…

Thousands of person-years have been invested in searches for New Physics (NP), the majority of them motivated by theoretical considerations. Yet, no evidence of beyond the Standard Model (BSM) physics has been found. This suggests that…

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…

In this paper we provide a broad benchmarking of recent genetic programming approaches to symbolic regression in the context of state of the art machine learning approaches. We use a set of nearly 100 regression benchmark problems culled…

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…

We propose SYRAN, an unsupervised anomaly detection method based on symbolic regression. Instead of encoding normal patterns in an opaque, high-dimensional model, our method learns an ensemble of human-readable equations that describe…

Discovering interpretable physical laws from high-dimensional data is a fundamental challenge in scientific research. Traditional methods, such as symbolic regression, often produce complex, unphysical formulas when searching a vast space…

Digital twins (DTs), serving as the core enablers for real-time monitoring and predictive maintenance of complex cyber-physical systems, impose critical requirements on their virtual models: high predictive accuracy, strong…

Neural-guided equation discovery systems use a data set as prompt and predict an equation that describes the data set without extensive search. However, if the equation does not meet the user's expectations, there are few options for…

Discrete probability laws underpin statistical modeling, yet the catalog of interpretable distributions has expanded only gradually through centuries of case-by-case mathematical derivations. We introduce symbolic density estimation (SDE),…

Ensuring the reliability of autonomous driving perception systems requires extensive environment-based testing, yet real-world execution is often impractical. Synthetic datasets have therefore emerged as a promising alternative, offering…

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…

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 (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 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…

Conventional neural network elastoplasticity models are often perceived as lacking interpretability. This paper introduces a two-step machine learning approach that returns mathematical models interpretable by human experts. In particular,…

Neuro-encoded expression programming(NEEP) that aims to offer a novel continuous representation of combinatorial encoding for genetic programming methods is proposed in this paper. Genetic programming with linear representation uses…