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Inferring parameters of high-dimensional partial differential equations (PDEs) poses significant computational and inferential challenges, primarily due to the curse of dimensionality and the inherent limitations of traditional numerical…

Traditional machine learning models, particularly neural networks, are rooted in finite-dimensional parameter spaces and nonlinear function approximations. This report explores an alternative formulation where learning tasks are expressed…

Learning dynamical systems through operator-theoretic representations provides a powerful framework for analyzing complex dynamics, as spectral quantities such as eigenvalues and invariant structures encode characteristic time scales and…

The majority of Multi-Object Tracking (MOT) algorithms based on the tracking-by-detection scheme do not use higher order dependencies among objects or tracklets, which makes them less effective in handling complex scenarios. In this work,…

We propose a metric learning framework for the construction of invariant geometric functions of planar curves for the Eucledian and Similarity group of transformations. We leverage on the representational power of convolutional neural…

In this paper we propose a novel variable selection method for two-view settings, or for vector-valued supervised learning problems. Our framework is able to handle extremely large scale selection tasks, where number of data samples could…

Extending the success of 2D Large Kernel to 3D perception is challenging due to: 1. the cubically-increasing overhead in processing 3D data; 2. the optimization difficulties from data scarcity and sparsity. Previous work has taken the first…

We propose a novel sparse dictionary learning method for planar shapes in the sense of Kendall, namely configurations of landmarks in the plane considered up to similitudes. Our shape dictionary method provides a good trade-off between…

Occupancy prediction plays a pivotal role in autonomous driving (AD) due to the fine-grained geometric perception and general object recognition capabilities. However, existing methods often incur high computational costs, which contradicts…

The probabilistic velocity obstacle (PVO) extends the concept of velocity obstacle (VO) to work in uncertain dynamic environments. In this paper, we show how a robust model predictive control (MPC) with PVO constraints under non-parametric…

The scientific computation methods development in conjunction with artificial intelligence technologies remains a hot research topic. Finding a balance between lightweight and accurate computations is a solid foundation for this direction.…

In this paper, we study discrete-time absorbing Markov Decision Processes (MDP) with measurable state space and Borel action space with a given initial distribution. For such models, solutions to the characteristic equation that are not…

This paper develops a data-driven learning framework for approximating the feasible region and invariant set of a nonlinear system under the nonlinear Model Predictive Control (MPC) scheme. The developed approach is based on the feasibility…

We present a unified theoretical and computational framework for constructing reproducing kernels tailored to transport equations and adapted to Koopman eigenfunctions of nonlinear dynamical systems. These eigenfunctions satisfy a…

Monocular Semantic Occupancy Prediction aims to infer the complete 3D geometry and semantic information of scenes from only 2D images. It has garnered significant attention, particularly due to its potential to enhance the 3D perception of…

This article presents a general framework for the transport of probability measures towards minimum divergence generative modeling and sampling using ordinary differential equations (ODEs) and Reproducing Kernel Hilbert Spaces (RKHSs),…

We present a new scientific machine learning method that learns from data a computationally inexpensive surrogate model for predicting the evolution of a system governed by a time-dependent nonlinear partial differential equation (PDE), an…

Multi-objective combinatorial optimization problems (MOCOPs), one type of complex optimization problems, widely exist in various real applications. Although meta-heuristics have been successfully applied to address MOCOPs, the calculation…

The shapes and morphology of the organs and tissues are important prior knowledge in medical imaging recognition and segmentation. The morphological operation is a well-known method for morphological feature extraction. As the morphological…

Despite the remarkable capabilities of deep neural networks in image recognition, the dependence on activation functions remains a largely unexplored area and has yet to be eliminated. On the other hand, Polynomial Networks is a class of…