Related papers: SINDy for delay-differential equations: applicatio…
We address the problem of using nonlinear models to design experiments to characterize the dynamics of cellular processes by using the approach of the Maximally Informative Next Experiment (MINE), which was introduced in [W. Dong, et al.…
Discontinuities and delayed terms are encountered in the governing equations of a large class of problems ranging from physics and engineering to medicine and economics. These systems cannot be properly modelled and simulated with standard…
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…
We report a method to determine the phase and amplitude of sinusoidally modulated event rates, binned into four bins per oscillation, based on data generated at the resonant neutron spin-echo spectrometer RESEDA. The presented algorithm…
Using the Poincar\'{e} section technique, we study in detail the dynamical behaviors of delay differential system and find a new type of solutions $S_i$ in short-time delay feedback. Our numerical results remind us to deny the opinion that…
In this paper, we propose a novel data-driven framework for discovering probabilistic laws underlying the Feynman-Kac formula. Specifically, we introduce the first stochastic SINDy method formulated under the risk-neutral probability…
Physics-informed neural networks (PINNs) have shown promising potential for solving partial differential equations (PDEs) using deep learning. However, PINNs face training difficulties for evolutionary PDEs, particularly for dynamical…
Disentangled representation learning aims to uncover latent variables underlying the observed data, and generally speaking, rather strong assumptions are needed to ensure identifiability. Some approaches rely on sufficient changes on the…
An online, adaptive method of time delay and magnitude estimation for sinusoidal signals is presented. The method is based on an adaptive gradient descent algorithm that directly determines the time delay and magnitudes of two noisy…
Hybrid modelling enhances the accuracy and predictive capability of dynamic models by integrating first principles with data-driven methods, effectively mitigating epistemic uncertainties inherent in mechanistic approaches. However, hybrid…
We have derived the governing equations for an SIR model with delay terms in both the infectivity and recovery of the disease. The equations are derived by modelling the dynamics as a continuous time random walk, where individuals move…
Mathematical modeling based on time-delay differential equations is an important tool to study the role of delay in biological systems and to evaluate its impact on the asymptotic behavior of their dynamics. Delays are indeed found in many…
Interacting particle system (IPS) models have proven to be highly successful for describing the spatial movement of organisms. However, it has proven challenging to infer the interaction rules directly from data. In the field of equation…
Distributed stochastic gradient descent (SGD) has attracted considerable recent attention due to its potential for scaling computational resources, reducing training time, and helping protect user privacy in machine learning. However, the…
Identifying unknown differential equations from a given set of discrete time dependent data is a challenging problem. A small amount of noise can make the recovery unstable, and nonlinearity and differential equations with varying…
Pretrained diffusion models are effective priors for Bayesian inverse problems, but posterior sampling with these priors is often costly because data-consistency guidance is applied throughout the full reverse trajectory. Existing methods…
In this work, we define a practical identifiability criterion, (e, q)-identifiability, based on a parameter e, reflecting the noise in observed variables, and a parameter q, reflecting the mean-square error of the parameter estimator. This…
This study proposes a novel framework for learning the underlying physics of phenomena with moving boundaries. The proposed approach combines Ensemble SINDy and Peridynamic Differential Operator (PDDO) and imposes an inductive bias assuming…
Utilizing the Sparse Identification of Nonlinear Dynamics algorithm (SINDy) and Long Short-Term Memory Recurrent Neural Networks (LSTM), the population of resident space objects, divided into Active, Derelict, and Debris, in LEO can be…
In differential equation discovery algorithms, numerical differentiation is usually a fixed preliminary step. Current methods improve robustness with data subsampling and sparsity but often ignore the variability from the differentiation…