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We present a brief survey on the modern tensor numerical methods for multidimensional stationary and time-dependent partial differential equations (PDEs). The guiding principle of the tensor approach is the rank-structured separable…

Pre-training by numerous image data has become de-facto for robust 2D representations. In contrast, due to the expensive data acquisition and annotation, a paucity of large-scale 3D datasets severely hinders the learning for high-quality 3D…

Partial differential equations (PDEs) govern a wide range of physical systems, but solving them efficiently remains a major challenge. The idea of a scientific foundation model (SciFM) is emerging as a promising tool for learning…

Recent works have shown that the computational efficiency of video recognition can be significantly improved by reducing the spatial redundancy. As a representative work, the adaptive focus method (AdaFocus) has achieved a favorable…

This paper introduces a novel approach to position embeddings in transformer models, named "Exact Positional Embeddings" (ExPE). An absolute positional embedding method that can extrapolate to sequences of lengths longer than the ones it…

Deep neural networks (DNNs) exploit many layers and a large number of parameters to achieve excellent performance. The training process of DNN models generally handles large-scale input data with many sparse features, which incurs high…

Design and optimal control problems are among the fundamental, ubiquitous tasks we face in science and engineering. In both cases, we aim to represent and optimize an unknown (black-box) function that associates a performance/outcome to a…

This paper presents a novel topology-aware dimensionality reduction approach aiming at accurately visualizing the cyclic patterns present in high dimensional data. To that end, we build on the Topological Autoencoders (TopoAE) formulation.…

Pooling layers are essential building blocks of convolutional neural networks (CNNs), to reduce computational overhead and increase the receptive fields of proceeding convolutional operations. Their goal is to produce downsampled volumes…

Many problems in science and engineering can be represented by a set of partial differential equations (PDEs) through mathematical modeling. Mechanism-based computation following PDEs has long been an essential paradigm for studying topics…

Monocular 3D pose estimation is fundamentally ill-posed due to depth ambiguity and occlusions, thereby motivating probabilistic methods that generate multiple plausible 3D pose hypotheses. In particular, diffusion-based models have recently…

In certain practical engineering applications, there is an urgent need to perform repetitive solving of partial differential equations (PDEs) in a short period. This paper primarily considers three scenarios requiring extensive repetitive…

While recent continual learning methods largely alleviate the catastrophic problem on toy-sized datasets, some issues remain to be tackled to apply them to real-world problem domains. First, a continual learning model should effectively…

Applications in quantitative finance such as optimal trade execution, risk management of options, and optimal asset allocation involve the solution of high dimensional and nonlinear Partial Differential Equations (PDEs). The connection…

We present DeepFDM, a differentiable finite-difference framework for learning spatially varying coefficients in time-dependent partial differential equations (PDEs). By embedding a classical forward-Euler discretization into a convolutional…

Explainable machine learning significantly improves the transparency of deep neural networks. However, existing work is constrained to explaining the behavior of individual model predictions, and lacks the ability to transfer the…

Multi-task dense prediction, which aims to jointly solve tasks like semantic segmentation and depth estimation, is crucial for robotics applications but suffers from domain shift when deploying models in new environments. While unsupervised…

Solving parametric Partial Differential Equations (PDEs) for a broad range of parameters is a critical challenge in scientific computing. To this end, neural operators, which \textcolor{black}{predicts the PDE solution with variable PDE…

Modelling complex multiphysics systems governed by nonlinear and strongly coupled partial differential equations (PDEs) is a cornerstone in computational science and engineering. However, it remains a formidable challenge for traditional…

While analytical solutions of critical (phase) transitions in physical systems are abundant for simple nonlinear systems, such analysis remains intractable for real-life dynamical systems. A key example of such a physical system is…