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Deep Learning research is advancing at a fantastic rate, and there is much to gain from transferring this knowledge to older fields like Computational Fluid Dynamics in practical engineering contexts. This work compares state-of-the-art…
Rectified flow (Liu et al., 2022; Liu, 2022; Wu et al., 2023) is a method for defining a transport map between two distributions, and enjoys popularity in machine learning, although theoretical results supporting the validity of these…
Accurate spatial-temporal prediction of network-based travelers' requests is crucial for the effective policy design of ridesharing platforms. Having knowledge of the total demand between various locations in the upcoming time slots enables…
Optical flow estimation is an essential step for many real-world computer vision tasks. Existing deep networks have achieved satisfactory results by mostly employing a pyramidal coarse-to-fine paradigm, where a key process is to adopt…
The Inverse Problem for the estimation of a point-wise approximation error occurring at the discretization and solving of the system of partial differential equations is addressed. The set of the differences between the numerical solutions…
Transportation networks are unprecedentedly complex with heterogeneous vehicular flow. Conventionally, vehicle classes are considered by vehicle classifications (such as standard passenger cars and trucks). However, vehicle flow…
This paper proposes a new mathematical formulation for flow measurement based on the inverse source problem for wave equations with partial boundary measurement. Inspired by the design of acoustic Doppler current profilers (ADCPs), we…
We consider statistical methods for reduction of multivariate dimensionality that have invariance and/or commutativity properties under the affine group of transformations (origin translations plus linear combinations of coordinates along…
We present a novel data-driven approach of learning traffic flow patterns of a transportation network given that many instances of origin to destination (OD) travel demand and link flows of the network are available. Instead of estimating…
Optimal transport (OT) and unbalanced optimal transport (UOT) are central in many machine learning, statistics and engineering applications. 1D OT is easily solved, with complexity O(n log n), but no efficient algorithm was known for 1D…
Deep learning approaches have achieved great success in addressing the problem of optical flow estimation. The keys to success lie in the use of cost volume and coarse-to-fine flow inference. However, the matching problem becomes ill-posed…
Inverse optimal transport (OT) refers to the problem of learning the cost function for OT from observed transport plan or its samples. In this paper, we derive an unconstrained convex optimization formulation of the inverse OT problem,…
Commuting flow prediction is an essential task for municipal operations in the real world. Previous studies have revealed that it is feasible to estimate the commuting origin-destination (OD) demand within a city using multiple auxiliary…
Public transport in sub-Saharan Africa (SSA) often operates in overcrowded conditions where existing automated systems fail to capture reliable passenger flow data. Leveraging onboard CCTV already deployed for security, we present a…
Deep neural networks (DNNs) often produce overconfident predictions on out-of-distribution (OOD) inputs, undermining their reliability in open-world environments. Singularities in semi-discrete optimal transport (OT) mark regions of…
We present a novel data- and first-principles-driven method for inferring the shape of a solid obstacle and its flow field in three-dimensional steady-state supersonic flows. The method combines the Optimizing a Discrete Loss (ODIL)…
Using the intuition that out-of-distribution data have lower likelihoods, a common approach for out-of-distribution detection involves estimating the underlying data distribution. Normalizing flows are likelihood-based generative models…
In the backbone of large-scale networks, origin-to-destination (OD) traffic flows experience abrupt unusual changes known as traffic volume anomalies, which can result in congestion and limit the extent to which end-user quality of service…
Inverse problems are crucial for many applications in science, engineering and medicine that involve data assimilation, design, and imaging. Their solution infers the parameters or latent states of a complex system from noisy data and…
Detecting out-of-distribution (OOD) samples is essential for ensuring the reliability of deep neural networks (DNNs) in real-world scenarios. While previous research has predominantly investigated the disparity between in-distribution (ID)…