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We demonstrate a smart laser-diffraction analysis technique for particle mixture identification. We retrieve information about the size, geometry, and ratio concentration of two-component heterogeneous particle mixtures with an efficiency…

Instance segmentation is a fundamental research in computer vision, especially in autonomous driving. However, manual mask annotation for instance segmentation is quite time-consuming and costly. To address this problem, some prior works…

Stochastic differential equations (SDEs) are of utmost importance in various scientific and industrial areas. They are the natural description of dynamical processes whose precise equations of motion are either not known or too expensive to…

The electron density is a key parameter to characterize any plasma. Most of the plasma applications and research in the area of low-temperature plasmas (LTPs) are based on the accurate estimations of plasma density and plasma temperature.…

Deep neural networks (DNN) have been used to model nonlinear relations between physical quantities. Those DNNs are embedded in physical systems described by partial differential equations (PDE) and trained by minimizing a loss function that…

We propose a framework for the joint inference of network topology, multi-type interaction kernels, and latent type assignments in heterogeneous interacting particle systems from multi-trajectory data. This learning task is a challenging…

Focusing on identification, this paper develops techniques to reconstruct zero and nonzero elements of a sparse parameter vector of a stochastic dynamic system under feedback control, for which the current input may depend on the past…

This paper presents a novel approach for learning instance segmentation with image-level class labels as supervision. Our approach generates pseudo instance segmentation labels of training images, which are used to train a fully supervised…

We present a novel approach to system identification (SI) using deep learning techniques. Focusing on parametric system identification (PSI), we use a supervised learning approach for estimating the parameters of discrete and…

In this paper, we construct a type of interacting particle systems to approximate a class of stochastic different equations whose coefficients depend on the conditional probability distributions of the processes given partial observations.…

We propose a novel data-driven method called QENDy (Quadratic Embedding of Nonlinear Dynamics) that not only allows us to learn quadratic representations of highly nonlinear dynamical systems, but also to identify the governing equations.…

The sparse identification of nonlinear dynamics (SINDy) approach can discover the governing equations of dynamical systems based on measurement data, where the dynamical model is identified as the sparse linear combination of the given…

This paper proposes a sparse regression strategy for discovery of ordinary differential equations from incomplete and noisy data. Inference is performed over both equation parameters and state variables using a statistically motivated…

We study two interacting particle systems, both modeled as a system of $N$ stochastic differential equations driven by Brownian motions with singular kernels and moderate interaction. We show a quantitative result where the convergence rate…

Discovering governing Partial Differential Equations (PDEs) from sparse and noisy data is a challenging issue in data-driven scientific computing. Conventional sparse regression methods often suffer from two major limitations: (i) the…

We introduce Weak-PDE-LEARN, a Partial Differential Equation (PDE) discovery algorithm that can identify non-linear PDEs from noisy, limited measurements of their solutions. Weak-PDE-LEARN uses an adaptive loss function based on weak forms…

We compare the efficiency and ease-of-use of the Sparse Identification of Nonlinear Dynamics (SINDy) algorithm and Sparse Physics-Informed Discovery of Empirical Relations (SPIDER) framework in recovering the relevant governing equations…

The discovery of underlying surface partial differential equation (PDE) from observational data has significant implications across various fields, bridging the gap between theory and observation, enhancing our understanding of complex…

The moment quantities associated with the nonlinear Schrodinger equation offer important insights towards the evolution dynamics of such dispersive wave partial differential equation (PDE) models. The effective dynamics of the moment…

Integration against a probability distribution given its unnormalized density is a central task in Bayesian inference and other fields. We introduce new methods for approximating such expectations with a small set of weighted samples --…