Related papers: Enhancing Symbolic Regression and Universal Physic…

Fast Function Extraction (FFX) is a deterministic algorithm for solving symbolic regression problems. We improve the accuracy of FFX by adding parameters to the arguments of nonlinear functions. Instead of only optimizing linear parameters,…

Rapid delineation of flash flood extents is critical to mobilize emergency resources and to manage evacuations, thereby saving lives and property. Machine learning (ML) approaches enable rapid flood delineation with reduced computational…

In unsupervised learning, dimensionality reduction is an important tool for data exploration and visualization. Because these aims are typically open-ended, it can be useful to frame the problem as looking for patterns that are enriched in…

Symbolic regression is the task of identifying a mathematical expression that best fits a provided dataset of input and output values. Due to the richness of the space of mathematical expressions, symbolic regression is generally a…

We elucidate the vector space (twisted relative cohomology) that is Poincar\'e dual to the vector space of Feynman integrals (twisted cohomology) in general spacetime dimension. The pairing between these spaces - an algebraic invariant…

We propose CoNSAL (Combining Neural networks and Symbolic regression for Analytical Lyapunov function) to construct analytical Lyapunov functions for nonlinear dynamic systems. This framework contains a neural Lyapunov function and a…

In symbolic regression, the goal is to find an analytical expression that accurately fits experimental data with the minimal use of mathematical symbols such as operators, variables, and constants. However, the combinatorial space of…

Dimensionality reduction techniques are fundamental for analyzing and visualizing high-dimensional data. With established methods like t-SNE and PCA presenting a trade-off between representational power and interpretability. This paper…

A pseudo independent (PI) model is a probabilistic domain model (PDM) where proper subsets of a set of collectively dependent variables display marginal independence. PI models cannot be learned correctly by many algorithms that rely on a…

We introduce the so called DeepParticle method to learn and generate invariant measures of stochastic dynamical systems with physical parameters based on data computed from an interacting particle method (IPM). We utilize the expressiveness…

Symbolic Regression (SR) searches for mathematical expressions which best describe numerical datasets. This allows to circumvent interpretation issues inherent to artificial neural networks, but SR algorithms are often computationally…

Phase retrieval, the problem of recovering lost phase information from measured intensity alone, is an inverse problem that is widely faced in various imaging modalities ranging from astronomy to nanoscale imaging. The current process of…

The recently proposed fully-connected tensor network (FCTN) decomposition has demonstrated significant advantages in correlation characterization and transpositional invariance, and has achieved notable achievements in multi-dimensional…

The working mechanisms of complex natural systems tend to abide by concise and profound partial differential equations (PDEs). Methods that directly mine equations from data are called PDE discovery, which reveals consistent physical laws…

The real-life data have a complex and non-linear structure due to their nature. These non-linearities and the large number of features can usually cause problems such as the empty-space phenomenon and the well-known curse of dimensionality.…

Automated facial expression analysis has a variety of applications in human-computer interaction. Traditional methods mainly analyze prototypical facial expressions of no more than eight discrete emotions as a classification task. However,…

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 (SR) models complex systems by discovering mathematical expressions that capture underlying relationships in observed data. However, most SR methods prioritize minimizing prediction error over identifying the governing…

Interpretability is crucial for machine learning in many scenarios such as quantitative finance, banking, healthcare, etc. Symbolic regression (SR) is a classic interpretable machine learning method by bridging X and Y using mathematical…

The length and time scales of atomistic simulations are limited by the computational cost of the methods used to predict material properties. In recent years there has been great progress in the use of machine learning algorithms to develop…