Related papers: Solving multiscale dynamical systems by deep learn…
Data-driven modeling of dynamical systems is a crucial area of machine learning. In many scenarios, a thorough understanding of the model's behavior becomes essential for practical applications. For instance, understanding the behavior of a…
Modeling dynamical systems is crucial across the science and engineering fields for accurate prediction, control, and decision-making. Recently, machine learning (ML) approaches, particularly neural ordinary differential equations (NODEs),…
Predicting outcomes and planning interactions with the physical world are long-standing goals for machine learning. A variety of such tasks involves continuous physical systems, which can be described by partial differential equations…
Data-enabled predictive control (DeePC) for linear systems utilizes data matrices of recorded trajectories to directly predict new system trajectories, which is very appealing for real-life applications. In this paper we leverage the…
Real-world time series are often governed by complex nonlinear dynamics. Understanding these underlying dynamics is crucial for precise future prediction. While deep learning has achieved major success in time series forecasting, many…
Annotating the right data for training deep neural networks is an important challenge. Active learning using uncertainty estimates from Bayesian Neural Networks (BNNs) could provide an effective solution to this. Despite being theoretically…
The process of transforming observed data into predictive mathematical models of the physical world has always been paramount in science and engineering. Although data is currently being collected at an ever-increasing pace, devising…
Neural ODEs (NODEs) are continuous-time neural networks (NNs) that can process data without the limitation of time intervals. They have advantages in learning and understanding the evolution of complex real dynamics. Many previous works…
We develop a methodology that utilizes deep learning to simultaneously solve and estimate canonical continuous-time general equilibrium models in financial economics. We illustrate our method in two examples: (1) industrial dynamics of…
We propose a new approach to learning the subgrid-scale model when simulating partial differential equations (PDEs) solved by the method of lines and their representation in chaotic ordinary differential equations, based on neural ordinary…
Differential equations in general and neural ODEs in particular are an essential technique in continuous-time system identification. While many deterministic learning algorithms have been designed based on numerical integration via the…
Obtaining dynamics models is essential for robotics to achieve accurate model-based controllers and simulators for planning. The dynamics models are typically obtained using model specification of the manufacturer or simple numerical…
We propose a multiscale approach for predicting quantities in dynamical systems which is explicitly structured to extract information in both fine-to-coarse and coarse-to-fine directions. We envision this method being generally applicable…
This paper presents a novel deep learning framework for solving multiple optimal stopping problems in high dimensions. While deep learning has recently shown promise for single stopping problems, the multiple exercise case involves complex…
This paper presents Mechanistic Neural Networks, a neural network design for machine learning applications in the sciences. It incorporates a new Mechanistic Block in standard architectures to explicitly learn governing differential…
Complex dynamic systems are typically either modeled using expert knowledge in the form of differential equations or via data-driven universal approximation models such as artificial neural networks (ANN). While the first approach has…
Deep neural networks (DNNs) recently emerged as a promising tool for analyzing and solving complex differential equations arising in science and engineering applications. Alternative to traditional numerical schemes, learning-based solvers…
The deep neural network has attained significant efficiency in image recognition. However, it has vulnerable recognition robustness under extensive data uncertainty in practical applications. The uncertainty is attributed to the inevitable…
To derive the hidden dynamics from observed data is one of the fundamental but also challenging problems in many different fields. In this study, we propose a new type of interpretable network called the ordinary differential equation…
The intersection of machine learning and dynamical systems has generated considerable interest recently. Neural Ordinary Differential Equations (NODEs) represent a rich overlap between these fields. In this paper, we develop a continuous…