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A well-established approach for inferring full displacement and stress fields from possibly sparse data is to calibrate the parameter of a given constitutive model using a Bayesian update. After calibration, a (stochastic) forward…
This paper considers filtering, parameter estimation, and testing for potentially dynamically misspecified state-space models. When dynamics are misspecified, filtered values of state variables often do not satisfy model restrictions,…
3D particle tracking velocimetry (PTV) is a key technique for analyzing turbulent flow, one of the most challenging computational problems of our century. At the core of 3D PTV is the dual-frame fluid motion estimation algorithm, which…
Unmanned aerial vehicle (UAV) photogrammetry allows for the creation of orthophotos and digital surface models (DSMs) of a terrain. However, DSMs of water bodies mapped with this technique reveal water surface distortions, preventing the…
Distribution system state estimation (DSSE) is paramount for effective state monitoring and control. However, stochastic outputs of renewables and asynchronous streaming of multi-rate measurements in practical systems largely degrade the…
Data-space inversion (DSI) and related procedures represent a family of methods applicable for data assimilation in subsurface flow settings. These methods differ from model-based techniques in that they provide only posterior predictions…
This work proposes convolutional-sparse-coded dynamic mode decomposition (CSC-DMD) by unifying extended dynamic mode decomposition (EDMD) and convolutional sparse coding. EDMD is a data driven analysis method for describing a nonlinear…
We propose the Diffusion-Inversion-Net (DIN) framework for inverse modeling of groundwater flow and solute transport processes. DIN utilizes an offline-trained Denoising Diffusion Probabilistic Model (DDPM) as a powerful prior leaner, which…
The reconstruction and prediction of full-state flows from sparse data are of great scientific and engineering significance yet remain challenging, especially in applications where data are sparse and/or subjected to noise. To this end,…
Dimensional synthesis of planar four-bar mechanisms is a challenging inverse problem in kinematics, requiring the determination of mechanism dimensions from desired motion specifications. We propose a data-driven framework that bypasses…
Multi-agent trajectory prediction is crucial for various practical applications, spurring the construction of many large-scale trajectory datasets, including vehicles and pedestrians. However, discrepancies exist among datasets due to…
We investigated the feature map inside deep neural networks (DNNs) by tracking the transport map. We are interested in the role of depth (why do DNNs perform better than shallow models?) and the interpretation of DNNs (what do intermediate…
Unsteady fluid systems are nonlinear high-dimensional dynamical systems that may exhibit multiple complex phenomena both in time and space. Reduced Order Modeling (ROM) of fluid flows has been an active research topic in the recent decade…
The fractional advection-dispersion equation (FADE) has attracted increased attention from researchers as it provides an accurate description for challenging phenomenas with long-range time memory and spatial interactions, such as the…
Systems comprising a turbulent channel flow overlaying a permeable bed can be found in a variety of industrial and natural applications (e.g. urban planning, fracking, submerged vegetation). One important realization of this system is at…
This study presents a novel integrated framework for dynamic origin-destination demand estimation (DODE) in multi-class mesoscopic network models, incorporating high-resolution satellite imagery together with conventional traffic data from…
Flow Matching (FM) models achieve remarkable results in generative tasks. Building upon diffusion models, FM's simulation-free training paradigm enables simplicity and efficiency but introduces a train-inference gap: model outputs cannot be…
We study uncertainty in the dynamics of time-dependent flows by identifying barriers and enhancers to stochastic transport. This topological segmentation is closely related to the theory of Lagrangian coherent structures and is based on a…
Many real-world systems modeled using partial differential equations (PDEs) involve unknown parameters that must be estimated from limited, noisy system observations. While typically assumed to be constants, some of these unobserved…
Fast and reliable prediction of riverine flow velocities is important in many applications, including flood risk management. The shallow water equations (SWEs) are commonly used for prediction of the flow velocities. However, accurate and…