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Training a neural network with the gradient descent algorithm gives rise to a discrete-time nonlinear dynamical system. Consequently, behaviors that are typically observed in these systems emerge during training, such as convergence to an…

Understanding the dynamics of neural network parameters during training is one of the key challenges in building a theoretical foundation for deep learning. A central obstacle is that the motion of a network in high-dimensional parameter…

While deep learning is successful in a number of applications, it is not yet well understood theoretically. A satisfactory theoretical characterization of deep learning however, is beginning to emerge. It covers the following questions: 1)…

The recent surge in Deep Learning (DL) research of the past decade has successfully provided solutions to many difficult problems. The field of quantitative analysis has been slowly adapting the new methods to its problems, but due to…

Changes, planned or unexpected, are common during the execution of real-life processes. Detecting these changes is a must for optimizing the performance of organizations running such processes. Most of the algorithms present in the…

In this work, a data-driven modeling framework of switched dynamical systems under time-dependent switching is proposed. The learning technique utilized to model system dynamics is Extreme Learning Machine (ELM). First, a method is…

This work proposes a machine-learning framework for modeling the error incurred by approximate solutions to parameterized dynamical systems. In particular, we extend the machine-learning error models (MLEM) framework proposed in Ref. 15 to…

Soft error, namely silent corruption of signal or datum in a computer system, cannot be caverlierly ignored as compute and communication density grow exponentially. Soft error detection has been studied in the context of enterprise…

In stochastic systems, numerically sampling the relevant trajectories for the estimation of the large deviation statistics of time-extensive observables requires overcoming their exponential (in space and time) scarcity. The optimal way to…

This paper focuses on the identification of dynamical systems with tailor-made model structures, where neural networks are used to approximate uncertain components and domain knowledge is retained, if available. These model structures are…

This paper presents a deep relational metric learning (DRML) framework for image clustering and retrieval. Most existing deep metric learning methods learn an embedding space with a general objective of increasing interclass distances and…

Data-driven modeling of human motions is ubiquitous in computer graphics and computer vision applications, such as synthesizing realistic motions or recognizing actions. Recent research has shown that such problems can be approached by…

Modeling the evolution of system with time-series data is a challenging and critical task in a wide range of fields, especially when the time-series data is regularly sampled and partially observable. Some methods have been proposed to…

Dynamic networks consist of a sequence of time-varying networks, and it is of great importance to detect the network change points. Most existing methods focus on detecting abrupt change points, necessitating the assumption that the…

Neural networks are known to be effective function approximators. Recently, deep neural networks have proven to be very effective in pattern recognition, classification tasks and human-level control to model highly nonlinear realworld…

Dynamic networks are interconnected dynamic systems with measured node signals and dynamic modules reflecting the links between the nodes. We address the problem of \red{identifying a dynamic network with known topology, on the basis of…

In order to identify a system (module) embedded in a dynamic network, one has to formulate a multiple-input estimation problem that necessitates certain nodes to be measured and included as predictor inputs. However, some of these nodes may…

The combination of numerical integration and deep learning, i.e., ODE-net, has been successfully employed in a variety of applications. In this work, we introduce inverse modified differential equations (IMDE) to contribute to the behaviour…

One of the most influential results in neural network theory is the universal approximation theorem [1, 2, 3] which states that continuous functions can be approximated to within arbitrary accuracy by single-hidden-layer feedforward neural…

Model precision in a classification task is highly dependent on the feature space that is used to train the model. Moreover, whether the features are sequential or static will dictate which classification method can be applied as most of…