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Recent advances in stochastic differential equations (SDEs) have enabled robust modeling of real-world dynamical processes across diverse domains, such as finance, health, and systems biology. However, parameter estimation for SDEs…
An important class of spatio-temporal models is constructed by leveraging the hierarchical structure of dynamical (or, state-space) models. This paper proposes a new statistical dynamical model for spatio-temporal processes motivated by…
This study examines the challenges of modeling complex and noisy data related to socioeconomic factors over time, with a focus on data from various districts in Odisha, India. Traditional time-series models struggle to capture both trends…
Learning unknown stochastic differential equations (SDEs) from observed data is a significant and challenging task with applications in various fields. Current approaches often use neural networks to represent drift and diffusion functions,…
This paper focuses on a stochastic system identification problem: given time series observations of a stochastic differential equation (SDE) driven by L\'{e}vy $\alpha$-stable noise, estimate the SDE's drift field. For $\alpha$ in the…
Stochastic differential equations (SDEs) are well suited to modelling noisy and irregularly sampled time series found in finance, physics, and machine learning. Traditional approaches require costly numerical solvers to sample between…
The ubiquity of missing data in urban intelligence systems, attributable to adverse environmental conditions and equipment failures, poses a significant challenge to the efficacy of downstream applications, notably in the realms of traffic…
Visual Odometry (VO) and SLAM are fundamental components for spatial perception in mobile robots. Despite enormous progress in the field, current VO/SLAM systems are limited by their sensors' capability. Event cameras are novel visual…
Low-fidelity analytical models of turbine wakes have traditionally been used for wind farm planning, performance evaluation, and demonstrating the utility of advanced control algorithms in increasing the annual energy production. In…
This work improves upon our previously introduced explicit dynamic modal filter (DEMF) within the framework of the discontinuous Galerkin spectral element method (DGSEM) by introducing a mechanism for self-tuning of the model parameters.…
We present a novel generative modeling method called diffusion normalizing flow based on stochastic differential equations (SDEs). The algorithm consists of two neural SDEs: a forward SDE that gradually adds noise to the data to transform…
Foundation-model-based monocular depth estimation offers a viable alternative to active sensors for robot perception, yet its computational cost often prohibits deployment on edge platforms. Existing methods perform independent per-frame…
Generative models have achieved remarkable progress with the emergence of flow matching (FM). It has demonstrated strong generative capabilities and attracted significant attention as a simulation-free flow-based framework capable of…
Stochastic Differential Equations (SDEs) serve as a powerful modeling tool in various scientific domains, including systems science, engineering, and ecological science. While the specific form of SDEs is typically known for a given…
This paper presents a Long Short-Term Memory network-based Fluid Experiment Data-Driven model (FED-LSTM) for predicting unsteady, nonlinear hydrodynamic forces on the underwater quadruped robot we constructed. Trained on experimental data…
Patient-specific modeling of cardiovascular flows with high-fidelity is challenging due to its dependence on accurately estimated velocity boundary profiles, which are essential for precise simulations and directly influence wall shear…
Inverse problems describe the process of estimating the causal factors from a set of measurements or data. Mapping of often incomplete or degraded data to parameters is ill-posed, thus data-driven iterative solutions are required, for…
Stochastic dynamical systems with slow or metastable behavior evolve, on long time scales, on an unknown low-dimensional manifold in high-dimensional ambient space. Building a reduced simulator from short-burst ambient ensembles is a…
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…
Stochastic differential equations (SDEs) are established tools to model physical phenomena whose dynamics are affected by random noise. By estimating parameters of an SDE intrinsic randomness of a system around its drift can be identified…