Related papers: Continuous Simplicial Neural Networks
Stochastic differential equations (SDEs) are used to describe a wide variety of complex stochastic dynamical systems. Learning the hidden physics within SDEs is crucial for unraveling fundamental understanding of these systems' stochastic…
Following the great success of Machine Learning (ML), especially Deep Neural Networks (DNNs), in many research domains in 2010s, several ML-based approaches were proposed for detection in large inverse linear problems, e.g., massive MIMO…
Although very successfully used in conventional machine learning, convolution based neural network architectures -- believed to be inconsistent in function space -- have been largely ignored in the context of learning solution operators of…
Randomized Smoothing (RS) is a promising technique for certified robustness, and recently in RS the ensemble of multiple Deep Neural Networks (DNNs) has shown state-of-the-art performances due to its variance reduction effect over Gaussian…
Numerical simulation is dominant in solving partial difference equations (PDEs), but balancing fine-grained grids with low computational costs is challenging. Recently, solving PDEs with neural networks (NNs) has gained interest, yet…
Oversmoothing in Graph Neural Networks (GNNs) poses a significant challenge as network depth increases, leading to homogenized node representations and a loss of expressiveness. In this work, we approach the oversmoothing problem from a…
In this article, we present an efficient deep learning method called coupled deep neural networks (CDNNs) for coupled physical problems. Our method compiles the interface conditions of the coupled PDEs into the networks properly and can be…
The infinite-depth paradigm pioneered by Neural ODEs has launched a renaissance in the search for novel dynamical system-inspired deep learning primitives; however, their utilization in problems of non-trivial size has often proved…
Learning complex trajectories from demonstrations in robotic tasks has been effectively addressed through the utilization of Dynamical Systems (DS). State-of-the-art DS learning methods ensure stability of the generated trajectories;…
The deep network model, with the majority built on neural networks, has been proved to be a powerful framework to represent complex data for high performance machine learning. In recent years, more and more studies turn to nonneural network…
Stochastic partial differential equations (SPDEs) are significant tools for modeling dynamics in many areas including atmospheric sciences and physics. Neural Operators, generations of neural networks with capability of learning maps…
Linearized Graph Neural Networks (GNNs) have attracted great attention in recent years for graph representation learning. Compared with nonlinear Graph Neural Network (GNN) models, linearized GNNs are much more time-efficient and can…
We introduce the framework of continuous-depth graph neural networks (GNNs). Neural graph differential equations (Neural GDEs) are formalized as the counterpart to GNNs where the input-output relationship is determined by a continuum of GNN…
Neural operators have achieved strong performance in learning solution operators of partial differential equations (PDEs), but their inherently continuous representations struggle to capture discontinuities and sharp transitions. Existing…
Neural Ordinary Differential Equation (Neural ODE) has been proposed as a continuous approximation to the ResNet architecture. Some commonly used regularization mechanisms in discrete neural networks (e.g. dropout, Gaussian noise) are…
Deep neural networks exhibit a simplicity bias, a well-documented tendency to favor simple functions over complex ones. In this work, we cast new light on this phenomenon through the lens of the Minimum Description Length principle,…
As a fundamental mathmatical tool in many engineering disciplines, coupled differential equation groups are being widely used to model complex structures containing multiple physical quantities. Engineers constantly adjust structural…
As neural interfaces become more advanced, there has been an increase in the volume and complexity of neural data recordings. These interfaces capture rich information about neural dynamics that call for efficient, real-time processing…
Partial differential equations (PDEs) are indispensable for modeling many physical phenomena and also commonly used for solving image processing tasks. In the latter area, PDE-based approaches interpret image data as discretizations of…
Neural networks have shown significant potential in solving partial differential equations (PDEs). While deep networks are capable of approximating complex functions, direct one-shot training often faces limitations in both accuracy and…