Related papers: AutoKE: An automatic knowledge embedding framework…

Machine learning on graph-structured data has recently become a major topic in industry and research, finding many exciting applications such as recommender systems and automated theorem proving. We propose an energy-based graph embedding…

Incorporating a priori physics knowledge into machine learning leads to more robust and interpretable algorithms. In this work, we combine deep learning techniques and classic numerical methods for differential equations to address two…

We present an unsupervised approach for discovering semantic representations of mathematical equations. Equations are challenging to analyze because each is unique, or nearly unique. Our method, which we call equation embeddings, finds good…

Learning data representations that capture task-related features, but are invariant to nuisance variations remains a key challenge in machine learning. We introduce an automated Bayesian inference framework, called AutoBayes, that explores…

The high-pressure transportation process of pipeline necessitates an accurate hydraulic transient simulation tool to prevent slack line flow and over-pressure, which can endanger pipeline operations. However, current numerical solution…

Recently, neural network based methods have shown their power in learning more expressive features on the task of knowledge graph embedding (KGE). However, the performance of deep methods often falls behind the shallow ones on simple…

When learning dynamical systems from data, embedding physical structure can constrain the solution space and improve generalization, but many physics-informed models assume access to the full system state. This limits their use in partially…

Modeling complex systems using standard neural ordinary differential equations (NODEs) often faces some essential challenges, including high computational costs and susceptibility to local optima. To address these challenges, we propose a…

Analyzing large-scale data from simulations of turbulent flows is memory intensive, requiring significant resources. This major challenge highlights the need for data compression techniques. In this study, we apply a physics-informed Deep…

The primary goal of motion planning is to generate safe and efficient trajectories for vehicles. Traditionally, motion planning models are trained using imitation learning to mimic the behavior of human experts. However, these models often…

Integrating large language models (LLMs) and knowledge graphs (KGs) holds great promise for revolutionizing intelligent education, but challenges remain in achieving personalization, interactivity, and explainability. We propose FOKE, a…

Partial differential equations (PDEs) govern nearly every physical process in science and engineering, yet solving them at scale remains prohibitively expensive. Generative AI has transformed language, vision, and protein science, but…

Knowledge graph embedding (KGE) is a technique that enhances knowledge graphs by addressing incompleteness and improving knowledge retrieval. A limitation of the existing KGE models is their underutilization of ontologies, specifically the…

A cardinal obstacle to performing quantum-mechanical simulations of strongly-correlated matter is that, with the theoretical tools presently available, sufficiently-accurate computations are often too expensive to be ever feasible. Here we…

Although optimal control problems of dynamical systems can be formulated within the framework of variational calculus, their solution for complex systems is often analytically and computationally intractable. In this Letter we present a…

Estimating fluid dynamics is classically done through the simulation and integration of numerical models solving the Navier-Stokes equations, which is computationally complex and time-consuming even on high-end hardware. This is a…

Partial Differential Equations (PDE) are fundamental to model different phenomena in science and engineering mathematically. Solving them is a crucial step towards a precise knowledge of the behaviour of natural and engineered systems. In…

Reasoning is essential for the development of large knowledge graphs, especially for completion, which aims to infer new triples based on existing ones. Both rules and embeddings can be used for knowledge graph reasoning and they have their…

Harnessing data to discover the underlying governing laws or equations that describe the behavior of complex physical systems can significantly advance our modeling, simulation and understanding of such systems in various science and…

Physics-informed neural networks (PINNs) have shown promise for solving partial differential equations (PDEs) by directly embedding them into the loss function. Despite their notable success, existing PINNs often exhibit training…