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The Sparse Identification of Nonlinear Dynamics (SINDy) algorithm can be applied to stochastic differential equations to estimate the drift and the diffusion function using data from a realization of the SDE. The SINDy algorithm requires…
We study the small deviation probabilities of a family of very smooth self-similar Gaussian processes. The canonical process from the family has the same scaling property as standard Brownian motion and plays an important role in the study…
We propose a new approach, called as functional deep neural network (FDNN), for classifying multi-dimensional functional data. Specifically, a deep neural network is trained based on the principle components of the training data which shall…
We study the minimization of a convex function $f(X)$ over the set of $n\times n$ positive semi-definite matrices, but when the problem is recast as $\min_U g(U) := f(UU^\top)$, with $U \in \mathbb{R}^{n \times r}$ and $r \leq n$. We study…
We propose a drone signal out-of-distribution (OOD) detection algorithm based on discriminability-driven spatial-channel selection with a gradient norm. Time-frequency image features are adaptively weighted along both spatial and channel…
A variant of consensus based distributed gradient descent (\textbf{DGD}) is studied for finite sums of smooth but possibly non-convex functions. In particular, the local gradient term in the fixed step-size iteration of each agent is…
Sampling a probability distribution with an unknown normalization constant is a fundamental problem in computational science and engineering. This task may be cast as an optimization problem over all probability measures, and an initial…
Deep learning techniques with neural networks have been used effectively in computational fluid dynamics (CFD) to obtain solutions to nonlinear differential equations. This paper presents a physics-informed neural network (PINN) approach to…
Anomaly detection is important for industrial automation and part quality assurance, and while humans can easily detect anomalies in components given a few examples, designing a generic automated system that can perform at human or above…
Anomaly detection (AD) in images, identifying significant deviations from normality, is a critical issue in computer vision. This paper introduces a novel approach to dimensionality reduction for AD using pre-trained convolutional neural…
We present a novel method for estimation of the fiber orientation distribution (FOD) function based on diffusion-weighted Magnetic Resonance Imaging (D-MRI) data. We formulate the problem of FOD estimation as a regression problem through…
Deep neural networks have attained remarkable performance when applied to data that comes from the same distribution as that of the training set, but can significantly degrade otherwise. Therefore, detecting whether an example is…
Boundary discontinuity and its inconsistency to the final detection metric have been the bottleneck for rotating detection regression loss design. In this paper, we propose a novel regression loss based on Gaussian Wasserstein distance as a…
Instance-level change detection in 3D scenes presents significant challenges, particularly in uncontrolled environments lacking labeled image pairs, consistent camera poses, or uniform lighting conditions. This paper addresses these…
Computational fluid dynamics (CFD) simulations are crucial in automotive, aerospace, maritime and medical applications, but are limited by the complexity, cost and computational requirements of directly calculating the flow, often taking…
Flatness of the loss landscape has been widely studied as an important perspective for understanding the behavior and generalization of deep learning algorithms. Motivated by this view, we propose Flatness-Aware Stochastic Gradient Langevin…
In this paper, we develop a 2D and 3D segmentation pipelines for fully automated cardiac MR image segmentation using Deep Convolutional Neural Networks (CNN). Our models are trained end-to-end from scratch using the ACD Challenge 2017…
Computational Fluid Dynamics (CFD) simulations are used for many air flow simulations including road vehicle aerodynamics. Numerical diffusion occurs when local flow direction is not aligned with the mesh lines and when there is a non-zero…
We consider the fundamental problem of learning linear predictors (i.e., separable datasets with zero margin) using neural networks with gradient flow or gradient descent. Under the assumption of spherically symmetric data distribution, we…
Inspired by graph-based methodologies, we introduce a novel graph-spanning algorithm designed to identify changes in both offline and online data across low to high dimensions. This versatile approach is applicable to Euclidean and…