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Identifying from observation data the governing differential equations of a physical dynamics is a key challenge in machine learning. Although approaches based on SINDy have shown great promise in this area, they still fail to address a…

In this paper, the estimation problem for sparse reduced rank regression (SRRR) model is considered. The SRRR model is widely used for dimension reduction and variable selection with applications in signal processing, econometrics, etc. The…

Deep reinforcement learning (DRL) has shown significant promise for uncovering sophisticated control policies that interact in complex environments, such as stabilizing a tokamak fusion reactor or minimizing the drag force on an object in a…

Identifying governing equations in physical and biological systems from datasets remains a long-standing challenge across various scientific disciplines, providing mechanistic insights into complex system evolution. Common methods like…

Deep reinforcement learning (DRL) agents are trained through trial-and-error interactions with the environment. This leads to a long training time for dense neural networks to achieve good performance. Hence, prohibitive computation and…

We present a novel deep learning approach to approximate the solution of large, sparse, symmetric, positive-definite linear systems of equations. These systems arise from many problems in applied science, e.g., in numerical methods for…

We propose a data-driven framework for learning reduced-order moment dynamics from PDE-governed systems using Neural ODEs. In contrast to derivative-based methods like SINDy, which necessitate densely sampled data and are sensitive to…

The problem of reconstructing nonlinear and complex dynamical systems from measured data or time series is central to many scientific disciplines including physical, biological, computer, and social sciences, as well as engineering and…

In distributed optimization, the practical problem-solving performance is essentially sensitive to algorithm selection, parameter setting, problem type and data pattern. Thus, it is often laborious to acquire a highly efficient method for a…

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 consider the problem of tracking the minimum of a time-varying convex optimization problem over a dynamic graph. Motivated by target tracking and parameter estimation problems in intermittently connected robotic and sensor networks, the…

Sparse system identification is the data-driven process of obtaining parsimonious differential equations that describe the evolution of a dynamical system, balancing model complexity and accuracy. There has been rapid innovation in system…

Over-parameterization of deep neural networks (DNNs) has shown high prediction accuracy for many applications. Although effective, the large number of parameters hinders its popularity on resource-limited devices and has an outsize…

In response to the continuously changing feedstock supply and market demand for products with different specifications, the processes need to be operated at time-varying operating conditions and targets (e.g., setpoints) to improve the…

Inspired by recent advances in deep learning, we propose a framework for reconstructing dynamic sequences of 2D cardiac magnetic resonance (MR) images from undersampled data using a deep cascade of convolutional neural networks (CNNs) to…

When optimizing over-parameterized models, such as deep neural networks, a large set of parameters can achieve zero training error. In such cases, the choice of the optimization algorithm and its respective hyper-parameters introduces…

The problem of reconstructing and identifying intracellular protein signaling and biochemical networks is of critical importance in biology today. We sought to develop a mathematical approach to this problem using, as a test case, one of…

In complex physical systems, conventional differential equations often fall short in capturing non-local and memory effects, as they are limited to local dynamics and integer-order interactions. This study introduces a stepwise data-driven…

Chemical reaction networks are widely used to model stochastic dynamics in chemical kinetics, systems biology and epidemiology. Solving the chemical master equation that governs these systems poses a significant challenge due to the large…

Reaction networks are commonly used to model the evolution of populations of species subject to transformations following an imposed stoichiometry. This paper focuses on the efficient characterisation of dynamical properties of Discrete…