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We introduce Prob-GParareal, a probabilistic extension of the GParareal algorithm designed to provide uncertainty quantification for the Parallel-in-Time (PinT) solution of (ordinary and partial) differential equations (ODEs, PDEs). The…
Training with sparse annotations is known to reduce the performance of object detectors. Previous methods have focused on proxies for missing ground truth annotations in the form of pseudo-labels for unlabeled boxes. We observe that…
Learning the solution of partial differential equations (PDEs) with a neural network is an attractive alternative to traditional solvers due to its elegance, greater flexibility and the ease of incorporating observed data. However, training…
We introduce a soft computing approach for automatically selecting and combining indices from remote sensing multispectral images that can be used for classification tasks. The proposed approach is based on a Genetic-Programming (GP)…
Gradient Descent (GD) and Conjugate Gradient (CG) methods are among the most effective iterative algorithms for solving unconstrained optimization problems, particularly in machine learning and statistical modeling, where they are employed…
Generalized linear models (GLMs) such as logistic regression are among the most widely used arms in data analyst's repertoire and often used on sensitive datasets. A large body of prior works that investigate GLMs under differential privacy…
The paper proposes a deep learning method specifically dealing with the forward and inverse problem of variable coefficient partial differential equations -- Variable Coefficient Physical Information Neural Network (VC-PINN). The shortcut…
The explicit governing equation is one of the simplest and most intuitive forms for characterizing physical laws. However, directly discovering partial differential equations (PDEs) from data poses significant challenges, primarily in…
This paper develops interior penalty discontinuous Galerkin (IP-DG) methods to approximate $W^{2,p}$ strong solutions of second order linear elliptic partial differential equations (PDEs) in non-divergence form with continuous coefficients.…
We propose a fast probabilistic framework for identifying differential equations governing the dynamics of observed data. We recast the SINDy method within a Bayesian framework and use Gaussian approximations for the prior and likelihood to…
Physics-informed neural networks (PINNs) have shown promising potential for solving partial differential equations (PDEs) using deep learning. However, PINNs face training difficulties for evolutionary PDEs, particularly for dynamical…
Several complex physical systems are governed by multi-scale partial differential equations (PDEs) that exhibit both smooth low-frequency components and localized high-frequency structures. Existing physics-informed neural network (PINN)…
This paper proposes a probabilistic Bayesian formulation for system identification (ID) and estimation of nonseparable Hamiltonian systems using stochastic dynamic models. Nonseparable Hamiltonian systems arise in models from diverse…
This article concerns the predictive modeling for spatio-temporal data as well as model interpretation using data information in space and time. We develop a novel approach based on supervised dimension reduction for such data in order to…
Pattern discovery is a machine learning technique that aims to find sets of items, subsequences, or substructures that are present in a dataset with a higher frequency value than a manually set threshold. This process helps to identify…
A parametric adaptive physics-informed greedy Latent Space Dynamics Identification (gLaSDI) method is proposed for accurate, efficient, and robust data-driven reduced-order modeling of high-dimensional nonlinear dynamical systems. In the…
Solving partial differential equations (PDEs) has been indispensable in scientific and engineering applications. Recently, deep learning methods have been widely used to solve high-dimensional problems, one of which is the physics-informed…
We study the problem of searching for and tracking a collection of moving targets using a robot with a limited Field-Of-View (FOV) sensor. The actual number of targets present in the environment is not known a priori. We propose a search…
We introduce a generative learning framework to model high-dimensional parametric systems using gradient guidance and virtual observations. We consider systems described by Partial Differential Equations (PDEs) discretized with structured…
3D anomaly detection has recently become a significant focus in computer vision. Several advanced methods have achieved satisfying anomaly detection performance. However, they typically concentrate on the external structure of 3D samples…