相关论文: Importance of equivariant and invariant symmetries…

Data-driven modeling of collective dynamics is a challenging problem because emergent phenomena in multi-agent systems are often shaped by long-range interactions among individuals. For example, in bird flocks and fish schools, long-range…

Normalizing flows are exact-likelihood generative neural networks which approximately transform samples from a simple prior distribution to samples of the probability distribution of interest. Recent work showed that such generative models…

Deep neural networks are being increasingly used for short-term traffic flow prediction, which can be generally categorized as convolutional (CNNs) or graph neural networks (GNNs). CNNs are preferable for region-wise traffic prediction by…

Equivariant Graph Neural Networks (GNNs) have demonstrated significant success across various applications. To achieve completeness -- that is, the universal approximation property over the space of equivariant functions -- the network must…

Exploiting symmetries and invariance in data is a powerful, yet not fully exploited, way to achieve better generalisation with more efficiency. In this paper, we introduce two graph network architectures that are equivariant to several…

Continuum mechanics simulators, numerically solving one or more partial differential equations, are essential tools in many areas of science and engineering, but their performance often limits application in practice. Recent modern machine…

Deep generative models are increasingly used for molecular discovery, with most recent approaches relying on equivariant graph neural networks (GNNs) under the assumption that explicit equivariance is essential for generating high-quality…

A novel hybrid deep neural network architecture is designed to capture the spatial-temporal features of unsteady flows around moving boundaries directly from high-dimensional unsteady flow fields data. The hybrid deep neural network is…

Numerical simulation is an essential tool in many areas of science and engineering, but its performance often limits application in practice or when used to explore large parameter spaces. On the other hand, surrogate deep learning models,…

State estimation from limited sensor measurements is ubiquitously found as a common challenge in a broad range of fields including mechanics, astronomy, and geophysics. Fluid mechanics is no exception -- state estimation of fluid flows is…

Deep generative models such as flow and diffusion models have proven to be effective in modeling high-dimensional and complex data types such as videos or proteins, and this has motivated their use in different data modalities, such as…

While deep learning has shown tremendous success in a wide range of domains, it remains a grand challenge to incorporate physical principles in a systematic manner to the design, training, and inference of such models. In this paper, we aim…

Embodied systems experience the world as 'a symphony of flows': a combination of many continuous streams of sensory input coupled to self-motion, interwoven with the dynamics of external objects. These streams obey smooth,…

The simulation of microcirculatory blood flow in realistic vascular architectures poses significant challenges due to the multiscale nature of the problem and the topological complexity of capillary networks. In this work, we propose a…

Quantum neural network architectures that have little-to-no inductive biases are known to face trainability and generalization issues. Inspired by a similar problem, recent breakthroughs in machine learning address this challenge by…

This work proposes a novel methodology for turbulence modeling in Large Eddy Simulation (LES) based on Graph Neural Networks (GNNs), which embeds the discrete rotational, reflectional and translational symmetries of the Navier-Stokes…

Convolutional neural networks (CNNs) have recently been applied to predict or model fluid dynamics. However, mechanisms of CNNs for learning fluid dynamics are still not well understood, while such understanding is highly necessary to…

In the recent years, the domain of fast flow field prediction has been vastly dominated by pixel-based convolutional neural networks. Yet, the recent advent of graph convolutional neural networks (GCNNs) have attracted a considerable…

We address the problem of improving the performance and in particular the sample complexity of deep neural networks by enforcing and guaranteeing invariances to symmetry transformations rather than learning them from data. Group-equivariant…

Learning and reasoning about 3D molecular structures with varying size is an emerging and important challenge in machine learning and especially in drug discovery. Equivariant Graph Neural Networks (GNNs) can simultaneously leverage the…