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While complex simulations of physical systems have been widely used in engineering and scientific computing, lowering their often prohibitive computational requirements has only recently been tackled by deep learning approaches. In this…
Improving both accuracy and computational performance of numerical tools is a major challenge for seismic imaging and generally requires specialized implementations to make full use of modern parallel architectures. We present a…
Learning in deep neural networks (DNNs) is implemented through minimizing a highly non-convex loss function, typically by a stochastic gradient descent (SGD) method. This learning process can effectively find good wide minima without being…
Diffusion generative models have emerged as a powerful framework for addressing problems in structural biology and structure-based drug design. These models operate directly on 3D molecular structures. Due to the unfavorable scaling of…
Graph neural networks (GNNs) are naturally distributed architectures for learning representations from network data. This renders them suitable candidates for decentralized tasks. In these scenarios, the underlying graph often changes with…
Deep generative models (DGM) are neural networks with many hidden layers trained to approximate complicated, high-dimensional probability distributions using a large number of samples. When trained successfully, we can use the DGMs to…
Large-scale or high-resolution geologic models usually comprise a huge number of grid blocks, which can be computationally demanding and time-consuming to solve with numerical simulators. Therefore, it is advantageous to upscale geologic…
Dynamic Graph Neural Networks (DGNNs) have been broadly applied in various real-life applications, such as link prediction and pandemic forecast, to capture both static structural information and temporal characteristics from dynamic…
Plasmonic nanostructures significantly improve the performance of photoconductive devices (PCDs) in generating terahertz radiation. However, they are geometrically intricate and result in complicated electromagnetic (EM) field and carrier…
This work deals with Direct Numerical Simulations (DNS) and Large Eddy Simulations (LES) of turbulent gravity currents, performed by means of a Discontinuous Galerkin (DG) Finite Element method. In particular, a DG-LES approach in which the…
Dynamic Mode Decomposition (DMD) is a powerful tool for extracting spatial and temporal patterns from multi-dimensional time series, and it has been used successfully in a wide range of fields, including fluid mechanics, robotics, and…
A nonlocal subgrid-scale stress (SGS) model is developed based on the convolution neural network (CNN), a powerful supervised data-driven approach. The CNN is an ideal approach to naturally consider nonlocal spatial information in…
Functional brain dynamics is supported by parallel and overlapping functional network modes that are associated with specific neural circuits. Decomposing these network modes from fMRI data and finding their temporal characteristics is…
We present novel empirical observations regarding how stochastic gradient descent (SGD) navigates the loss landscape of over-parametrized deep neural networks (DNNs). These observations expose the qualitatively different roles of learning…
Graph neural networks (GNNs) are a popular class of machine learning models whose major advantage is their ability to incorporate a sparse and discrete dependency structure between data points. Unfortunately, GNNs can only be used when such…
We present diffusion-convolutional neural networks (DCNNs), a new model for graph-structured data. Through the introduction of a diffusion-convolution operation, we show how diffusion-based representations can be learned from…
Dynamic scene reconstruction from monocular video is essential for real-world applications. We introduce DGNS, a hybrid framework integrating \underline{D}eformable \underline{G}aussian Splatting and Dynamic \underline{N}eural…
Forecasting future stock trends remains challenging for academia and industry due to stochastic inter-stock dynamics and hierarchical intra-stock dynamics influencing stock prices. In recent years, graph neural networks have achieved…
Molecular dynamics (MD) simulation predicts the trajectory of atoms by solving Newton's equation of motion with a numeric integrator. Due to physical constraints, the time step of the integrator need to be small to maintain sufficient…
Dynamic scenes rendering is an intriguing yet challenging problem. Although current methods based on NeRF have achieved satisfactory performance, they still can not reach real-time levels. Recently, 3D Gaussian Splatting (3DGS) has garnered…