Related papers: A Graph-Based Framework for Exploring Mathematical…
Graph neural networks (GNNs) excel at predictive tasks on graph-structured data but often lack the ability to incorporate symbolic domain knowledge and perform general reasoning. Relational Bayesian Networks (RBNs), in contrast, enable…
Understanding and interacting with everyday physical scenes requires rich knowledge about the structure of the world, represented either implicitly in a value or policy function, or explicitly in a transition model. Here we introduce a new…
The recent developments and growing interest in neural-symbolic models has shown that hybrid approaches can offer richer models for Artificial Intelligence. The integration of effective relational learning and reasoning methods is one of…
Graphs and networks provide a canonical representation of relational data, with massive network data sets becoming increasingly prevalent across a variety of scientific fields. Although tools from mathematics and computer science have been…
The challenge of answering graph queries over incomplete knowledge graphs is gaining significant attention in the machine learning community. Neuro-symbolic models have emerged as a promising approach, combining good performance with high…
Mathematical models and algorithms are an essential part of mathematical research data, as they are epistemically grounding numerical data. In order to represent models and algorithms as well as their relationship semantically to make this…
Neurosymbolic AI is an increasingly active area of research that combines symbolic reasoning methods with deep learning to leverage their complementary benefits. As knowledge graphs are becoming a popular way to represent heterogeneous and…
Leveraging generative Artificial Intelligence (AI), we have transformed a dataset comprising 1,000 scientific papers into an ontological knowledge graph. Through an in-depth structural analysis, we have calculated node degrees, identified…
We present a novel methodology to jointly perform multi-task learning and infer intrinsic relationship among tasks by an interpretable and sparse graph. Unlike existing multi-task learning methodologies, the graph structure is not assumed…
Constitutive models are fundamental to solid mechanics and materials science, underpinning the quantitative description and prediction of material responses under diverse loading conditions. Traditional phenomenological models, which are…
A graph theoretic perspective is taken for a range of phenomena in continuum physics in order to develop representations for analysis of large scale, high-fidelity solutions to these problems. Of interest are phenomena described by partial…
Graphs serve as generic tools to encode the underlying relational structure of data. Often this graph is not given, and so the task of inferring it from nodal observations becomes important. Traditional approaches formulate a convex inverse…
Graphs are fundamental data structures which concisely capture the relational structure in many important real-world domains, such as knowledge graphs, physical and social interactions, language, and chemistry. Here we introduce a powerful…
Particle physics is a branch of science aiming at discovering the fundamental laws of matter and forces. Graph neural networks are trainable functions which operate on graphs---sets of elements and their pairwise relations---and are a…
Network theory has proven to be a powerful tool in describing and analyzing systems by modelling the relations between their constituent objects. In recent years great progress has been made by augmenting `traditional' network theory.…
The pursuit of automated scientific discovery has fueled progress from symbolic logic to modern AI, forging new frontiers in reasoning and pattern recognition. Transformers function as potential systems, where every possible relationship…
Graph Neural Networks (GNNs) have become essential in interpreting relational data across various domains, yet, they often struggle to generalize to unseen graph data that differs markedly from training instances. In this paper, we…
We introduce a framework for generating, organizing, and reasoning with computational knowledge. It is motivated by the observation that most problems in Computational Sciences and Engineering (CSE) can be formulated as that of completing…
In this work, we propose an end-to-end graph network that learns forward and inverse models of particle-based physics using interpretable inductive biases. Physics-informed neural networks are often engineered to solve specific problems…
The ability to discover meaningful, accurate, and concise mathematical equations that describe datasets is valuable across various domains. Equations offer explicit relationships between variables, enabling deeper insights into underlying…