相关论文: StruSR: Structure-Aware Symbolic Regression with P…

Physics-informed neural networks (PINNs) have shown promising potential for solving partial differential equations (PDEs) using deep learning. However, PINNs face training difficulties for evolutionary PDEs, particularly for dynamical…

Implicit Neural Spatial Representation (INSR) has emerged as an effective representation of spatially-dependent vector fields. This work explores solving time-dependent PDEs with INSR. Classical PDE solvers introduce both temporal and…

Symbolic Regression (SR) is a powerful technique for automatically discovering mathematical expressions from input data. Mainstream SR algorithms search for the optimal symbolic tree in a vast function space, but the increasing complexity…

Implicit neural representation (INR) has become the standard approach for arbitrary-scale image super-resolution (ASSR). To date, no empirical study has systematically examined the effectiveness of existing methods, nor investigated the…

Current learning models often struggle with human-like systematic generalization, particularly in learning compositional rules from limited data and extrapolating them to novel combinations. We introduce the Neural-Symbolic Recursive…

The current paper presents a novel recurrent neural network model, the predictive multiple spatio-temporal scales RNN (P-MSTRNN), which can generate as well as recognize dynamic visual patterns in the predictive coding framework. The model…

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…

Symbolic discovery of governing equations is a long-standing goal in scientific machine learning, yet a fundamental trade-off persists between interpretability and scalable learning. Classical symbolic regression methods yield explicit…

Evolutionary symbolic regression approaches are powerful tools that can approximate an explicit mapping between input features and observation for various problems. However, ensuring that explored expressions maintain consistency with…

Symbolic Regression (SR) tries to reveal the hidden equations behind observed data. However, most methods search within a discrete equation space, where the structural modifications of equations rarely align with their numerical behavior,…

Supervised learning of time series data has been extensively studied for the case of a categorical target variable. In some application domains, e.g., energy, environment and health monitoring, it occurs that the target variable is…

Medical decision-making makes frequent use of algorithms that combine risk equations with rules, providing clear and standardized treatment pathways. Symbolic regression (SR) traditionally limits its search space to continuous function…

Symbolic regression (SR) uncovers mathematical models from data. Several benchmarks have been proposed to compare the performance of SR algorithms. However, existing ground-truth rediscovery benchmarks overemphasize the recovery of "the…

This tutorial paper provides a general overview of symbolic regression (SR) with specific focus on standards of interpretability. We posit that interpretable modeling, although its definition is still disputed in the literature, is a…

Protein representation learning methods have shown great potential to yield useful representation for many downstream tasks, especially on protein classification. Moreover, a few recent studies have shown great promise in addressing…

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 introduce Structure Informed Neural Networks (SINNs), a novel method for solving boundary observation problems involving PDEs. The SINN methodology is a data-driven framework for creating approximate solutions to internal variables on…

The accurate modelling of structural dynamics is crucial across numerous engineering applications, such as Structural Health Monitoring (SHM), seismic analysis, and vibration control. Often, these models originate from physics-based…

This work presents a multi-resolution physics-informed recurrent neural network (MR PI-RNN), for simultaneous prediction of musculoskeletal (MSK) motion and parameter identification of the MSK systems. The MSK application was selected as…

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.…