Related papers: PROSE: Predicting Operators and Symbolic Expressio…

One of the major challenges in machine learning nowadays is to provide predictions with not only high accuracy but also user-friendly explanations. Although in recent years we have witnessed increasingly popular use of deep neural networks…

A new data-driven method for operator learning of stochastic differential equations(SDE) is proposed in this paper. The central goal is to solve forward and inverse stochastic problems more effectively using limited data. Deep operator…

Modeling dynamical systems is crucial across the science and engineering fields for accurate prediction, control, and decision-making. Recently, machine learning (ML) approaches, particularly neural ordinary differential equations (NODEs),…

We introduce the concept of a \textbf{neuro-symbolic pair} -- neural and symbolic approaches that are linked through a common knowledge representation. Next, we present \textbf{taxonomic networks}, a type of discrimination network in which…

In recent years, Artificial Intelligence has become a powerful partner for complex tasks such as data analysis, prediction, and problem-solving, yet its lack of transparency raises concerns about its reliability. In sensitive domains such…

Learning underlying dynamics from data is important and challenging in many real-world scenarios. Incorporating differential equations (DEs) to design continuous networks has drawn much attention recently, however, most prior works make…

Neural operator learning models have emerged as very effective surrogates in data-driven methods for partial differential equations (PDEs) across different applications from computational science and engineering. Such operator learning…

We consider the general class of time-homogeneous stochastic dynamical systems, both discrete and continuous, and study the problem of learning a representation of the state that faithfully captures its dynamics. This is instrumental to…

Thermal plasma properties play a critical role in plasma simulations and plasma-related applications. However, their strong nonlinear dependence on temperature, pressure, and gas composition makes accurate and efficient evaluation…

Latent representation learned from multi-layered neural networks via hierarchical feature abstraction enables recent success of deep learning. Under the deep learning framework, generalization performance highly depends on the learned…

Symbolic regression aims to derive interpretable symbolic expressions from data in order to better understand and interpret data. %which plays an important role in knowledge discovery and interpretable machine learning. In this study, a…

Measurement noise is an integral part while collecting data of a physical process. Thus, noise removal is necessary to draw conclusions from these data, and it often becomes essential to construct dynamical models using these data. We…

In this work, we aim to leverage prior symbolic knowledge to improve the performance of deep models. We propose a graph embedding network that projects propositional formulae (and assignments) onto a manifold via an augmented Graph…

Many physical processes such as weather phenomena or fluid mechanics are governed by partial differential equations (PDEs). Modelling such dynamical systems using Neural Networks is an active research field. However, current methods are…

Deep Symbolic Optimization (DSO) is a novel computational framework that enables symbolic optimization for scientific discovery, particularly in applications involving the search for intricate symbolic structures. One notable example is…

We propose and study a method for learning interpretable representations for the task of regression. Features are represented as networks of multi-type expression trees comprised of activation functions common in neural networks in addition…

Despite the success of neural models in solving reasoning tasks, their compositional generalization capabilities remain unclear. In this work, we propose a new setting of the structured explanation generation task to facilitate…

Many real-world systems can be described by mathematical models that are human-comprehensible, easy to analyze and help explain the system's behavior. Symbolic regression is a method that can automatically generate such models from data.…

Symbolic regression is a task aimed at identifying patterns in data and representing them through mathematical expressions, generally involving skeleton prediction and constant optimization. Many methods have achieved some success, however…

The joint prediction of continuous fields and statistical estimation of the underlying discrete parameters is a common problem for many physical systems, governed by PDEs. Hitherto, it has been separately addressed by employing operator…