相关论文: Feature engineering and symbolic regression method…

We introduce Statistical Flow Matching (SFM), a novel and mathematically rigorous flow-matching framework on the manifold of parameterized probability measures inspired by the results from information geometry. We demonstrate the…

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…

A new approach for functional data description is proposed in this paper. It consists of a regression model with a discrete hidden logistic process which is adapted for modeling curves with abrupt or smooth regime changes. The model…

Data-driven discovery of governing equations is of great significance for helping us understand intrinsic mechanisms and build physical models. Recently, numerous highly innovative algorithms have emerged, aimed at inversely discovering the…

Symbolic regression is emerging as a promising machine learning method for learning succinct underlying interpretable mathematical expressions directly from data. Whereas it has been traditionally tackled with genetic programming, it has…

The process of discovering equations from data lies at the heart of physics and in many other areas of research, including mathematical ecology and epidemiology. Recently, machine learning methods known as symbolic regression emerged as a…

Complex, dynamic networks underlie many systems, and understanding these networks is the concern of a great span of important scientific and engineering problems. Quantitative description is crucial for this understanding yet, due to a…

This study develops invariance-embedded machine learning sub-grid-scale (SGS) stress models admitting turbulence kinetic energy (TKE) backscatter towards more accurate large eddy simulation (LES) of meso-scale turbulent hurricane boundary…

Computational fluid dynamics (CFD)-driven machine learning frameworks based on symbolic regression offer a promising pathway for turbulence model discovery, but are often hindered by numerical instability, residual stagnation, and…

To improve the physical understanding and the predictions of complex dynamic systems, such as ocean dynamics and weather predictions, it is of paramount interest to identify interpretable models from coarsely and off-grid sampled…

The study presents a general framework for discovering underlying Partial Differential Equations (PDEs) using measured spatiotemporal data. The method, called Sparse Spatiotemporal System Discovery ($\text{S}^3\text{d}$), decides which…

The challenges in feature selection, particularly in balancing model accuracy, interpretability, and computational efficiency, remain a critical issue in advancing machine learning methodologies. To address these complexities, this study…

In computational physics, machine learning has now emerged as a powerful complementary tool to explore efficiently candidate designs in engineering studies. Outputs in such supervised problems are signals defined on meshes, and a natural…

Symbolic regression refers to the task of finding a closed-form mathematical expression to fit a set of data points. Genetic programming based techniques are the most common algorithms used to tackle this problem, but recently,…

Feature engineering is a crucial step in the process of predictive modeling. It involves the transformation of given feature space, typically using mathematical functions, with the objective of reducing the modeling error for a given…

Hiding data using neural networks (i.e., neural steganography) has achieved remarkable success across both discriminative classifiers and generative adversarial networks. However, the potential of data hiding in diffusion models remains…

While there is currently a lot of enthusiasm about "big data", useful data is usually "small" and expensive to acquire. In this paper, we present a new paradigm of learning partial differential equations from {\em small} data. In…

Symbolic Regression (SR) is a machine learning approach that explores the space of mathematical expressions to identify those that best fit a given dataset, balancing both accuracy and simplicity. We apply SR to the study of Gray-Body…

The discovery of partial differential equations (PDEs) is a challenging task that involves both theoretical and empirical methods. Machine learning approaches have been developed and used to solve this problem; however, it is important to…

The redundant features existing in high dimensional datasets always affect the performance of learning and mining algorithms. How to detect and remove them is an important research topic in machine learning and data mining research. In this…