Related papers: A Novel Statistical Method Based on Dynamic Models…
Ordinary differential equations (ODE) have been widely used for modeling dynamical complex systems. For high-dimensional ODE models where the number of differential equations is large, it remains challenging to estimate the ODE parameters…
Causal discovery is a data-driven paradigm for analyzing complex systems, while physics-based models, such as ordinary differential equations (ODEs), provide mechanistic structure for real-world dynamical processes. Integrating these…
The hazard function represents one of the main quantities of interest in the analysis of survival data. We propose a general approach for parametrically modelling the dynamics of the hazard function using systems of autonomous ordinary…
Deformable image registration (DIR) is crucial in medical image analysis, enabling the exploration of biological dynamics such as organ motions and longitudinal changes in imaging. Leveraging Neural Ordinary Differential Equations (ODE) for…
Ordinary differential equations (ODEs) can provide mechanistic models of temporally local changes of processes, where parameters are often informed by external knowledge. While ODEs are popular in systems modeling, they are less established…
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…
The data-driven discovery of interpretable models approximating the underlying dynamics of a physical system has gained attraction in the past decade. Current approaches employ pre-specified functional forms or basis functions and often…
Portable, Wearable and Wireless electrocardiogram (ECG) Systems have the potential to be used as point-of-care for cardiovascular disease diagnostic systems. Such wearable and wireless ECG systems require automatic detection of…
Neural ODEs (NODEs) have emerged as powerful tools for modeling time series data, offering the flexibility to adapt to varying input scales and capture complex dynamics. However, they face significant challenges: first, their reliance on…
Fractional Differential Equations (FDEs) are essential tools for modelling complex systems in science and engineering. They extend the traditional concepts of differentiation and integration to non-integer orders, enabling a more precise…
End-to-end learning of dynamical systems with black-box models, such as neural ordinary differential equations (ODEs), provides a flexible framework for learning dynamics from data without prescribing a mathematical model for the dynamics.…
Effectively modeling phenomena present in highly nonlinear dynamical systems whilst also accurately quantifying uncertainty is a challenging task, which often requires problem-specific techniques. We present a novel, domain-agnostic…
Hazard functions play a central role in survival analysis, providing insight into the underlying risk dynamics of time-to-event data, with broad applications in medicine, epidemiology, and related fields. First-order ordinary differential…
The understanding and modeling of complex physical phenomena through dynamical systems has historically driven scientific progress, as it provides the tools for predicting the behavior of different systems under diverse conditions through…
In our previous paper [N. Tsutsumi, K. Nakai and Y. Saiki, Chaos 32, 091101 (2022)], we proposed a method for constructing a system of differential equations of chaotic behavior from only observable deterministic time series, which we call…
Given an autonomous system of ordinary differential equations (ODE), we consider developing practical models for the deterministic, slow/coarse behavior of the ODE system. Two types of coarse variables are considered. The first type…
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…
A variety of complex biological, natural and man-made systems exhibit non-Markovian dynamics that can be modeled through fractional order differential equations, yet, we lack sample comlexity aware system identification strategies. Towards…
Ordinary differential equation (ODE) is widely used in modeling biological and physical processes in science. In this article, we propose a new reproducing kernel-based approach for estimation and inference of ODE given noisy observations.…
Dynamical systems appear in nearly every aspect of the physical world. As such, understanding the properties of dynamical systems is of great importance. Typically, a dynamical system is described by a system of ordinary differential…