Related papers: Identification of Differential Equations by Dynami…
Recently a category of tracking methods based on "tracking-by-detection" is widely used in visual tracking problem. Most of these methods update the classifier online using the samples generated by the tracker to handle the appearance…
The objective function of a matrix factorization model usually aims to minimize the average of a regression error contributed by each element. However, given the existence of stochastic noises, the implicit deviations of sample data from…
The key difficulty to develop efficient high-order methods for integrating stochastic differential equations lies in the calculations of the multiple stochastic integrals. This letter suggests a scheme to compute the stochastic integrals…
Delay Differential Equations (DDEs) are a class of differential equations that can model diverse scientific phenomena. However, identifying the parameters, especially the time delay, that make a DDE's predictions match experimental results…
Predicting the response of nonlinear dynamical systems subject to random, broadband excitation is important across a range of scientific disciplines, such as structural dynamics and neuroscience. Building data-driven models requires…
Over the past few years, equation discovery has gained popularity in different fields of science and engineering. However, existing equation discovery algorithms rely on the availability of noisy measurements of the state variables (i.e.,…
In this paper is proposed the method of the identification of complex dynamic systems. Method can be used for the identification of linear and nonlinear complex dynamic systems for the determined or stochastic signals at the inputs and the…
Ordinary differential equations (ODEs) are foundational in modeling intricate dynamics across a gamut of scientific disciplines. Yet, a possibility to represent a single phenomenon through multiple ODE models, driven by different…
Many safety-critical scientific and engineering systems evolve according to differential-algebraic equations (DAEs), where dynamical behavior is constrained by physical laws and admissibility conditions. In practice, these systems operate…
Symbolic recovery of differential equations is the ambitious attempt at automating the derivation of governing equations with the use of machine learning techniques. In contrast to classical methods which assume the structure of the…
Complex systems in science and engineering sometimes exhibit behavior that changes across different regimes. Traditional global models struggle to capture the full range of this complex behavior, limiting their ability to accurately…
This work proposes a Stochastic Variational Deep Kernel Learning method for the data-driven discovery of low-dimensional dynamical models from high-dimensional noisy data. The framework is composed of an encoder that compresses…
In person re-identification (ReID) tasks, many works explore the learning of part features to improve the performance over global image features. Existing methods explicitly extract part features by either using a hand-designed image…
A main challenge in applying deep learning to music processing is the availability of training data. One potential solution is Multi-task Learning, in which the model also learns to solve related auxiliary tasks on additional datasets to…
Despite the advancements in learning governing differential equations from observations of dynamical systems, data-driven methods are often unaware of fundamental physical laws, such as frame invariance. As a result, these algorithms may…
Nonnegative matrix factorization (NMF) has been widely used to dimensionality reduction in machine learning. However, the traditional NMF does not properly handle outliers, so that it is sensitive to noise. In order to improve the…
We propose a detector of adversarial samples that is based on the view of neural networks as discrete dynamic systems. The detector tells clean inputs from abnormal ones by comparing the discrete vector fields they follow through the…
This note presents a unified analysis of the identification of dynamical systems with low-rank constraints under high-dimensional scaling. This identification problem for dynamic systems are challenging due to the intrinsic dependency of…
We study a stochastic differential equation driven by a gamma process, for which we give results on the existence of weak solutions under conditions on the volatility function. To that end we provide results on the density process between…
We address the weak numerical solution of stochastic differential equations driven by independent Brownian motions (SDEs for short). This paper develops a new methodology to design adaptive strategies for determining automatically the…