Related papers: Space-time multiscale model reduction for transpor…
In the recent paper [C. Lehrenfeld, A. Reusken, SIAM J. Num. Anal., 51 (2013)] a new finite element discretization method for a class of two-phase mass transport problems is presented and analyzed. The transport problem describes mass…
Accurate crop mapping fundamentally relies on modeling multi-scale spatiotemporal patterns, where spatial scales range from individual field textures to landscape-level context, and temporal scales capture both short-term phenological…
Understanding city-scale vehicular mobility and trip patterns is essential to addressing many problems, from transportation and pollution to public safety, among others. Using spatio-temporal analysis of vehicular mobility, promising…
Inverse problems with spatiotemporal observations are ubiquitous in scientific studies and engineering applications. In these spatiotemporal inverse problems, observed multivariate time series are used to infer parameters of physical or…
We develop couplings of a recent space-time first-order system least-squares (FOSLS) method for parabolic problems and space-time boundary element methods (BEM) for the heat equation to numerically solve a parabolic transmission problem on…
Multivariate functional data can be intrinsically multivariate like movement trajectories in 2D or complementary like precipitation, temperature, and wind speeds over time at a given weather station. We propose a multivariate functional…
In this paper, we develop the constraint energy minimizing generalized multiscale finite element method (CEM-GMsFEM) for convection-diffusion equations with inhomogeneous Dirichlet, Neumann and Robin boundary conditions, along with…
We propose a unified, few-step generative modeling framework based on \emph{cumulative flow maps} for long-range transport in probability space, inspired by flow-map techniques for physical transport and dynamics. At its core is a…
Gaussian Process state-space models capture complex temporal dependencies in a principled manner by placing a Gaussian Process prior on the transition function. These models have a natural interpretation as discretized stochastic…
This work presents an abstract framework for the design, implementation, and analysis of the multiscale spectral generalized finite element method (MS-GFEM), a particular numerical multiscale method originally proposed in [I. Babuska and R.…
Mode-based model-reduction is used to reduce the degrees of freedom of high dimensional systems, often by describing the system state by a linear combination of spatial modes. Transport dominated phenomena, ubiquitous in technical and…
In this paper, we study the least-squares finite element methods (LSFEM) for the linear hyperbolic transport equations. The linear transport equation naturally allows discontinuous solutions and discontinuous inflow conditions, while the…
This study addresses a large-scale multimodal transit network design problem, with Shared Autonomous Mobility Services (SAMS) as both transit feeders and an origin-to-destination mode. The framework captures spatial demand and modal…
Traditional vision-based autonomous driving systems often face difficulties in navigating complex environments when relying solely on single-image inputs. To overcome this limitation, incorporating temporal data such as past image frames or…
Accurate spatiotemporal pattern analysis is critical in fields such as urban traffic, meteorology, and public health monitoring. However, existing methods face performance bottlenecks, typically yielding only incremental gains and often…
Motivated by the computational difficulties incurred by popular deep learning algorithms for the generative modeling of temporal densities, we propose a cheap alternative which requires minimal hyperparameter tuning and scales favorably to…
Accurately forecasting traffic flows is critically important to many real applications including public safety and intelligent transportation systems. The challenges of this problem include both the dynamic mobility patterns of the people…
Including terrain in atmospheric models gives rise to mesh distortions near the lower boundary that can degrade accuracy and challenge the stability of transport schemes. Multidimensional transport schemes avoid splitting errors on…
Notably, current intelligent transportation systems rely heavily on accurate traffic forecasting and swift inference provision to make timely decisions. While Graph Convolutional Networks (GCNs) have shown benefits in modeling complex…
This work proposes a novel variational approximation of partial differential equations on moving geometries determined by explicit boundary representations. The benefits of the proposed formulation are the ability to handle large…