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Found 14 papers, 3 papers with code
Graph Convolutions Enrich the Self-Attention in Transformers!
Transformers, renowned for their self-attention mechanism, have achieved state-of-the-art performance across various tasks in natural language processing, computer vision, time-series modeling, etc.
Causal disentanglement of multimodal data
Causal representation learning algorithms discover lower-dimensional representations of data that admit a decipherable interpretation of cause and effect; as achieving such interpretable representations is challenging, many causal learning algorithms utilize elements indicating prior information, such as (linear) structural causal models, interventional data, or weak supervision.
Reversible and irreversible bracket-based dynamics for deep graph neural networks
Recent works have shown that physics-inspired architectures allow the training of deep graph neural networks (GNNs) without oversmoothing.
Probabilistic partition of unity networks for high-dimensional regression problems
We explore the probabilistic partition of unity network (PPOU-Net) model in the context of high-dimensional regression problems and propose a general framework focusing on adaptive dimensionality reduction.
Parameter-varying neural ordinary differential equations with partition-of-unity networks
In this study, we propose parameter-varying neural ordinary differential equations (NODEs) where the evolution of model parameters is represented by partition-of-unity networks (POUNets), a mixture of experts architecture.
Scalable algorithms for physics-informed neural and graph networks
For more complex systems or systems of systems and unstructured data, graph neural networks (GNNs) present some distinct advantages, and here we review how physics-informed learning can be accomplished with GNNs based on graph exterior calculus to construct differential operators; we refer to these architectures as physics-informed graph networks (PIGNs).
BIG-bench Machine Learning
Physics-informed machine learning
Unsupervised physics-informed disentanglement of multimodal data for high-throughput scientific discovery
We introduce physics-informed multimodal autoencoders (PIMA) - a variational inference framework for discovering shared information in multimodal scientific datasets representative of high-throughput testing.
Polynomial-Spline Neural Networks with Exact Integrals
Using neural networks to solve variational problems, and other scientific machine learning tasks, has been limited by a lack of consistency and an inability to exactly integrate expressions involving neural network architectures.
Structure-preserving Sparse Identification of Nonlinear Dynamics for Data-driven Modeling
Discovery of dynamical systems from data forms the foundation for data-driven modeling and recently, structure-preserving geometric perspectives have been shown to provide improved forecasting, stability, and physical realizability guarantees.
An asymptotically compatible treatment of traction loading in linearly elastic peridynamic fracture
In the absence of fracture, when a corresponding classical continuum mechanics model exists, our improvements provide asymptotically compatible convergence to corresponding local solutions, eliminating surface effects and issues with traction loading which have historically plagued peridynamic discretizations.
Numerical Analysis Computational Engineering, Finance, and Science Numerical Analysis Analysis of PDEs
Enforcing exact physics in scientific machine learning: a data-driven exterior calculus on graphs
To enforce physics strongly, we turn to the exterior calculus framework underpinning combinatorial Hodge theory and physics-compatible discretization of partial differential equations (PDEs).
Numerical Analysis Numerical Analysis Mathematical Physics Mathematical Physics
Data-driven learning of robust nonlocal physics from high-fidelity synthetic data
A key challenge to nonlocal models is the analytical complexity of deriving them from first principles, and frequently their use is justified a posteriori.
GMLS-Nets: A framework for learning from unstructured data
Data fields sampled on irregularly spaced points arise in many applications in the sciences and engineering.
Constrained particle-mesh projections in a hybridized discontinuous Galerkin framework with applications to advection-dominated flows
By combining concepts from particle-in-cell (PIC) and hybridized discontinuous Galerkin (HDG) methods, we present a particle-mesh scheme which allows for diffusion-free advection, satisfies mass and momentum conservation principles in a local sense, and allows the extension to high-order spatial accuracy.
Numerical Analysis
