相关论文: Enhancing Symbolic Regression and Universal Physic…

Compact symbolic expressions have been shown to be more efficient than neural network models in terms of resource consumption and inference speed when implemented on custom hardware such as FPGAs, while maintaining comparable…

Representation learning has become an invaluable approach for learning from symbolic data such as text and graphs. However, while complex symbolic datasets often exhibit a latent hierarchical structure, state-of-the-art methods typically…

The curse-of-dimensionality taxes computational resources heavily with exponentially increasing computational cost as the dimension increases. This poses great challenges in solving high-dimensional PDEs, as Richard E. Bellman first pointed…

Symbolic regression aims to discover human-interpretable equations that explain observational data. However, existing approaches rely heavily on discrete structure search (e.g., genetic programming), which often leads to high computational…

We propose a dynamical scaling analysis improved by a deep learning approach. While Gaussian process regression has been widely employed for estimating scaling parameters, its computational cost for parameter optimization becomes a…

We present a probabilistic programmed deep kernel learning approach to personalized, predictive modeling of neurodegenerative diseases. Our analysis considers a spectrum of neural and symbolic machine learning approaches, which we assess…

Symbolic regression searches for analytic expressions that accurately describe studied phenomena. The main attraction of this approach is that it returns an interpretable model that can be insightful to users. Historically, the majority of…

Bayesian inverse problems use observed data to update a prior probability distribution for an unknown state or parameter of a scientific system to a posterior distribution conditioned on the data. In many applications, the unknown parameter…

Symbolic regression (SR) has emerged as a powerful method for uncovering interpretable mathematical relationships from data, offering a novel route to both scientific discovery and efficient empirical modelling. This article introduces the…

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…

In recent years there has been great progress in the use of machine learning algorithms to develop interatomic potential models. Machine-learned potential models are typically orders of magnitude faster than density functional theory but…

We demonstrate the efficacy of symbolic regression (SR) to probe models of particle physics Beyond the Standard Model (BSM), by considering the so-called Constrained Minimal Supersymmetric Standard Model (CMSSM). Like many incarnations of…

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,…

A new penalty-free neural network method, PFNN-2, is presented for solving partial differential equations, which is a subsequent improvement of our previously proposed PFNN method [1]. PFNN-2 inherits all advantages of PFNN in handling the…

We consider the problem of learning free-form symbolic expressions from raw data, such as that produced by an experiment in any scientific domain. Accurate and interpretable models of scientific phenomena are the cornerstone of scientific…

We describe a neural-based method for generating exact or approximate solutions to differential equations in the form of mathematical expressions. Unlike other neural methods, our system returns symbolic expressions that can be interpreted…

Symbolic Regression (SR) enables the discovery of interpretable mathematical relationships from experimental and simulation data. These relationships are often coined descriptors which are defined as a fundamental materials property that is…

The Symbolic Regression (SR) problem, where the goal is to find a regression function that does not have a pre-specified form but is any function that can be composed of a list of operators, is a hard problem in machine learning, both…

We present a novel approach to optimizing the reduction of Feynman integrals using integration-by-parts identities. By developing a priority function through the FunSearch algorithm, which combines large language models and genetic…

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…