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Learning dynamics governed by differential equations is crucial for predicting and controlling the systems in science and engineering. Neural Ordinary Differential Equation (NODE), a deep learning model integrated with differential…
We present compact semi-implicit finite difference schemes on structured grids for numerical solutions of the advection by an external velocity and by a speed in normal direction that are applicable in level set methods. The most involved…
In coupled learning rules for PCA (principal component analysis) and SVD (singular value decomposition), the update of the estimates of eigenvectors or singular vectors is influenced by the estimates of eigenvalues or singular values,…
This paper presents novel hybrid architectures that combine grid- and point-based processing to improve the detection performance and orientation estimation of radar-based object detection networks. Purely grid-based detection models…
Atmospheric correction is a fundamental task in remote sensing because observations are taken either of the atmosphere or looking through the atmosphere. Atmospheric correction errors can significantly alter the spectral signature of the…
Estimating motion from spatiotemporal geoscientific data is a fundamental component of many environmental modeling and forecasting tasks. In this work, we propose a physics-informed deep learning framework for estimating altitude-wise…
This study used a multigrid-based convolutional neural network architecture known as MgNet in operator learning to solve numerical partial differential equations (PDEs). Given the property of smoothing iterations in multigrid methods where…
In the rapidly advancing field of deep learning, optimising deep neural networks is paramount. This paper introduces a novel method, Enhanced Velocity Estimation (EVE), which innovatively applies different learning rates to distinct…
Surface parameterization is a fundamental geometry processing problem with rich downstream applications. Traditional approaches are designed to operate on well-behaved mesh models with high-quality triangulations that are laboriously…
We introduce a generative learning framework to model high-dimensional parametric systems using gradient guidance and virtual observations. We consider systems described by Partial Differential Equations (PDEs) discretized with structured…
In this study, we address the challenge of 3D scene structure recovery from monocular depth estimation. While traditional depth estimation methods leverage labeled datasets to directly predict absolute depth, recent advancements advocate…
Automated pavement crack image segmentation is challenging because of inherent irregular patterns, lighting conditions, and noise in images. Conventional approaches require a substantial amount of feature engineering to differentiate crack…
Recent years have witnessed a growth in mathematics for deep learning--which seeks a deeper understanding of the concepts of deep learning with mathematics and explores how to make it more robust--and deep learning for mathematics, where…
Wavelet-based grid adaptation methods use multiresolution analysis for error estimation, offering a mathematically rigorous approach to adaptive grid refinement when solving Partial Differential Equations (PDEs). However, applying these…
To improve the physical understanding and the predictions of complex dynamic systems, such as ocean dynamics and weather predictions, it is of paramount interest to identify interpretable models from coarsely and off-grid sampled…
In this paper, we consider the use of structure learning methods for probabilistic graphical models to identify statistical dependencies in high-dimensional physical processes. Such processes are often synthetically characterized using PDEs…
Neural ordinary differential equations (NODEs) are an effective approach for data-driven modeling of dynamical systems arising from simulations and experiments. One of the major shortcomings of NODEs, especially when coupled with explicit…
The demand for substantial increases in the spatial resolution of global weather- and climate- prediction models makes it necessary to use numerically efficient and highly scalable algorithms to solve the equations of large scale…
Operational weather forecasting models have advanced for decades on both the explicit numerical solvers and the empirical physical parameterization schemes. However, the involved high computational costs and uncertainties in these existing…
Measurement and analysis of high energetic particles for scientific, medical or industrial applications is a complex procedure, requiring the design of sophisticated detector and data processing systems. The development of adaptive and…