Related papers: Operator Feature Neural Network for Symbolic Regre…

Understanding and predicting the activity of oxide perovskite catalysts for the oxygen evolution reaction (OER) requires descriptors that are both accurate and physically interpretable. While symbolic regression (SR) offers a path to…

Discovering governing equations of complex network dynamics is a fundamental challenge in contemporary science with rich data, which can uncover the mysterious patterns and mechanisms of the formation and evolution of complex phenomena in…

Neural networks have emerged as a powerful tool for modeling physical systems, offering the ability to learn complex representations from limited data while integrating foundational scientific knowledge. In particular, neuro-symbolic…

Friction systems are mechanical systems wherein friction is used for force transmission (e.g. mechanical braking systems or automatic gearboxes). For finding optimal and safe design parameters, engineers have to predict friction system…

Since polynomial regression models are generally quite reliable for data with a linear trend, it is important to note that, in some cases, they may encounter overfitting issues during the training phase, which could result in negative…

We consider solving a probably ill-conditioned linear operator equation, where the operator is not modeled by physical laws but is specified via training pairs (consisting of images and data) of the input-output relation of the operator. We…

Traditional single image super-resolution (SISR) methods that focus on solving single and uniform degradation (i.e., bicubic down-sampling), typically suffer from poor performance when applied into real-world low-resolution (LR) images due…

Function regression/approximation is a fundamental application of machine learning. Neural networks (NNs) can be easily trained for function regression using a sufficient number of neurons and epochs. The forward-forward learning algorithm…

The idea of neural Ordinary Differential Equations (ODE) is to approximate the derivative of a function (data model) instead of the function itself. In residual networks, instead of having a discrete sequence of hidden layers, the…

Neural operators have emerged as a powerful, data-driven paradigm for learning solution operators of partial differential equations (PDEs). State-of-the-art architectures, such as the Fourier Neural Operator (FNO), have achieved remarkable…

Feature selection aims to identify the optimal feature subset for enhancing downstream models. Effective feature selection can remove redundant features, save computational resources, accelerate the model learning process, and improve the…

Neural networks adapt very well to distributed and continuous representations, but struggle to generalize from small amounts of data. Symbolic systems commonly achieve data efficient generalization by exploiting modularity to benefit from…

Symbolic regression, the task of extracting mathematical expressions from the observed data $\{ \vx_i, y_i \}$, plays a crucial role in scientific discovery. Despite the promising performance of existing methods, most of them conduct…

Symbolic has been long considered as a language of human intelligence while neural networks have advantages of robust computation and dealing with noisy data. The integration of neural-symbolic can offer better learning and reasoning while…

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…

Traditional machine learning models, particularly neural networks, are rooted in finite-dimensional parameter spaces and nonlinear function approximations. This report explores an alternative formulation where learning tasks are expressed…

The recent success of implicit neural scene representations has presented a viable new method for how we capture and store 3D scenes. Unlike conventional 3D representations, such as point clouds, which explicitly store scene properties in…

Deep Neural Networks are powerful models that attained remarkable results on a variety of tasks. These models are shown to be extremely efficient when training and test data are drawn from the same distribution. However, it is not clear how…

The goal of neuro-symbolic AI is to integrate symbolic and subsymbolic AI approaches, to overcome the limitations of either. Prominent systems include Logic Tensor Networks (LTN) or DeepProbLog, which offer neural predicates and end-to-end…

Spectral decomposition of linear operators plays a central role in many areas of machine learning and scientific computing. Recent work has explored training neural networks to approximate eigenfunctions of such operators, enabling scalable…