A5021740847- Advanced Graph Neural Networks
- Fluid Dynamics and Turbulent Flows
- Natural Language Processing Techniques
- Plant Water Relations and Carbon Dynamics
- Semantic Web and Ontologies
- Recommender Systems and Techniques
- Magnetic and Electromagnetic Effects
- Geophysics and Gravity Measurements
- Phase Equilibria and Thermodynamics
- Graph Theory and Algorithms
- Topic Modeling
- Meteorological Phenomena and Simulations
- Complex Network Analysis Techniques
- Geomagnetism and Paleomagnetism Studies
- Image Processing and 3D Reconstruction
- Fluid Dynamics and Vibration Analysis
- Computational Physics and Python Applications
- Model-Driven Software Engineering Techniques
- Historical Geography and Cartography
- Advanced Fluorescence Microscopy Techniques
- Big Data and Digital Economy
- Biomedical Text Mining and Ontologies
- Advanced Software Engineering Methodologies
- Scientific Computing and Data Management
- Caching and Content Delivery
Google (United States)
2023-2024
Google (United Kingdom)
2020
Georgia Institute of Technology
2008-2009
Motivated by recent experimental and numerical studies of coherent structures in wall-bounded shear flows, we initiate a systematic exploration the hierarchy unstable invariant solutions Navier-Stokes equations. We construct dynamical, 10^5-dimensional state-space representation plane Couette flow at Re = 400 small, periodic cell offer new method visualizing manifolds embedded such high dimensions. compute equilibrium solution leading eigenvalues eigenfunctions known equilibria this Reynolds...
We present ten new equilibrium solutions to plane Couette flow in small periodic cells at low Reynolds number (Re) and two traveling-wave solutions. The are continued under changes of Re spanwise period. provide a partial classification the isotropy groups show which kinds allowed by each group. find complementary visualizations particularly revealing. Suitably chosen sections their 3D-physical space velocity fields helpful developing physical intuition about coherent structures observed...
Plane Couette flow transitions to turbulence at Re ≈ 325 even though the laminar solution with a linear profile is linearly stable for all (Reynolds number). One starting point understanding this subcritical transition existence of invariant sets in state space Navier–Stokes equation, such as upper and lower branch equilibria periodic relative solutions, that are distinct from solution. This article reports several heteroclinic connections between objects briefly describes numerical method...
Graphs are a powerful tool for representing and analyzing complex relationships in real-world applications such as social networks, recommender systems, computational finance. Reasoning on graphs is essential drawing inferences about the between entities system, to identify hidden patterns trends. Despite remarkable progress automated reasoning with natural text, large language models (LLMs) remains an understudied problem. In this work, we perform first comprehensive study of encoding...
TensorFlow-GNN (TF-GNN) is a scalable library for Graph Neural Networks in TensorFlow. It designed from the bottom up to support kinds of rich heterogeneous graph data that occurs today's information ecosystems. In addition enabling machine learning researchers and advanced developers, TF-GNN offers low-code solutions empower broader developer community learning. Many production models at Google use TF-GNN, it has been recently released as an open source project. this paper we describe...
How can we find the right graph for semi-supervised learning? In real world applications, choice of which edges to use computation is first step in any learning process. Interestingly, there are often many types similarity available choose as between nodes, and drastically affect performance downstream systems. However, despite importance design, most literature assumes that static.
How can we best encode structured data into sequential form for use in large language models (LLMs)? In this work, introduce a parameter-efficient method to explicitly represent LLMs. Our method, GraphToken, learns an encoding function extend prompts with explicit information. Unlike other work which focuses on limited domains (e.g. knowledge graph representation), our is the first effort focused general of be used various reasoning tasks. We show that representing structure allows...
Graphs are a powerful tool for representing and analyzing complex relationships in real-world applications. Large Language Models (LLMs) have demonstrated impressive capabilities by advancing state-of-the-art on many language-based benchmarks. Their ability to process understand natural language open exciting possibilities various domains. Despite the remarkable progress automated reasoning with text, graphs LLMs remains an understudied problem that has recently gained more attention.This...
Which transformer scaling regimes are able to perfectly solve different classes of algorithmic problems? While tremendous empirical advances have been attained by transformer-based neural networks, a theoretical understanding their reasoning capabilities in realistic parameter is lacking. We investigate this question terms the network's depth, width, and number extra tokens for algorithm execution. Our novel representational hierarchy separates 9 problems into solvable transformers regimes....
Large language models (LLMs) have showcased remarkable reasoning capabilities, yet they remain susceptible to errors, particularly in temporal tasks involving complex logic. Existing research has explored LLM performance on using diverse datasets and benchmarks. However, these studies often rely real-world data that LLMs may encountered during pre-training or employ anonymization techniques can inadvertently introduce factual inconsistencies. In this work, we address limitations by...
Lagrangian tracer particle trajectories for invariant solutions of the Navier-Stokes equations confined to three-dimensional geometry plane Couette flow are studied. Treating Eulerian velocity field an solution as a dynamical system, transport these passive scalars along reveals rich repertoire different types motion that can occur, including stagnation points, which there is no fluid movement, and tori, obstruct chaotic mixing across full volume minimal cell. We determine stability with...
A fundamental procedure in the analysis of massive datasets is construction similarity graphs. Such graphs play a key role for many downstream tasks, including clustering, classification, graph learning, and nearest neighbor search. For these it critical to build which are sparse yet still representative underlying data. The benefits sparsity twofold: firstly, constructing dense infeasible practice large datasets, secondly, runtime tasks directly influenced by graph. In this work, we present...
Graphs are a representation of structured data that captures the relationships between sets objects. With ubiquity available network data, there is increasing industrial and academic need to quickly analyze graphs with billions nodes trillions edges. A common first step for understanding Graph Embedding, process creating continuous in graph. often more amenable, especially at scale, solving downstream machine learning tasks such as classification, link prediction, clustering....
Graph neural networks (GNNs) demonstrate outstanding performance in a broad range of applications. While the majority GNN applications assume that graph structure is given, some recent methods substantially expanded applicability GNNs by showing they may be effective even when no explicitly provided. The parameters and are jointly learned. Previous studies adopt different experimentation setups, making it difficult to compare their merits. In this paper, we propose benchmarking strategy for...