Related papers: A Novel Statistical Method Based on Dynamic Models…
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 existing Neural ODE formulation relies on an explicit knowledge of the termination time. We extend Neural ODEs to implicitly defined termination criteria modeled by neural event functions, which can be chained together and…
Mathematical modeling with Ordinary Differential Equations (ODEs) has proven to be extremely successful in a variety of fields, including biology. However, these models are completely deterministic given a certain set of initial conditions.…
Accurate aircraft trajectory prediction is critical for air traffic management, airline operations, and environmental assessment. This paper introduces NODE-FDM, a Neural Ordinary Differential Equations-based Flight Dynamics Model trained…
Ordinary differential equations (ODEs) are widely used to describe the time evolution of natural phenomena across various scientific fields. Estimating the parameters of these systems from data is a challenging task, particularly when…
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 identification of a mathematical dynamics model is a crucial step in the designing process of a controller. However, it is often very difficult to identify the system's governing equations, especially in complex environments that…
Recently, Neural Ordinary Differential Equations has emerged as a powerful framework for modeling physical simulations without explicitly defining the ODEs governing the system, but instead learning them via machine learning. However, the…
Modern graph representation learning works mostly under the assumption of dealing with regularly sampled temporal graph snapshots, which is far from realistic, e.g., social networks and physical systems are characterized by continuous…
The hazard function is central to the formulation of commonly used survival regression models such as the proportional hazards and accelerated failure time models. However, these models rely on a shared baseline hazard, which, when…
Order statistics play a fundamental role in statistical procedures such as risk estimation, outlier detection, and multiple hypothesis testing as well as in the analyses of mechanism design, queues, load balancing, and various other…
Data outside the problem domain poses significant threats to the security of AI-based intelligent systems. Aiming to investigate the data domain and out-of-distribution (OOD) data in AI quality management (AIQM) study, this paper proposes…
This paper proposes a novel fault detection and isolation (FDI) scheme for distributed parameter systems modeled by a class of parabolic partial differential equations (PDEs) with nonlinear uncertain dynamics. A key feature of the proposed…
In conventional ODE modelling coefficients of an equation driving the system state forward in time are estimated. However, for many complex systems it is practically impossible to determine the equations or interactions governing the…
The axiomatic theory of ordinary differential equations, owing to its simplicity, can provide a useful framework to describe various generalizations of dynamical systems. In this study, we consider how dynamical properties can be…
Ordinary differential equations (ODE's) are widespread models in physics, chemistry and biology. In particular, this mathematical formalism is used for describing the evolution of complex systems and it might consist of high-dimensional…
In the era of AI, neural networks have become increasingly popular for modeling, inference, and prediction, largely due to their potential for universal approximation. With the proliferation of such deep learning models, a question arises:…
This paper presents a data-integrated framework for learning the dynamics of fractional-order nonlinear systems in both discrete-time and continuous-time settings. The proposed framework consists of two main steps. In the first step,…
Discovering the underlying dynamics of complex systems from data is an important practical topic. Constrained optimization algorithms are widely utilized and lead to many successes. Yet, such purely data-driven methods may bring about…
Inspired by the ubiquitous use of differential equations to model continuous dynamics across diverse scientific and engineering domains, we propose a novel and intuitive approach to continuous sequence modeling. Our method interprets…