Related papers: Nonlinear Evolution via Spatially-Dependent Linear…

Irregularly sampled time series with missing values are often observed in multiple real-world applications such as healthcare, climate and astronomy. They pose a significant challenge to standard deep learning models that operate only on…

Predicting the evolution of systems that exhibit spatio-temporal dynamics in response to external stimuli is a key enabling technology fostering scientific innovation. Traditional equations-based approaches leverage first principles to…

Learning nonlinear dynamics from diffusion data is a challenging problem since the individuals observed may be different at different time points, generally following an aggregate behaviour. Existing work cannot handle the tasks well since…

We present a framework designed to learn the underlying dynamics between two images observed at consecutive time steps. The complex nature of image data and the lack of temporal information pose significant challenges in capturing the…

We propose a thermodynamics-based learning strategy for non-equilibrium evolution equations based on Onsager's variational principle, which allows to write such PDEs in terms of two potentials: the free energy and the dissipation potential.…

Sparse identification of nonlinear dynamical systems is a topic of continuously increasing significance in the dynamical systems community. Here we explore it at the level of lattice nonlinear dynamical systems of many degrees of freedom.…

Modal methods are a long-standing approach to physical modelling synthesis. Extensions to nonlinear problems are possible, leading to coupled nonlinear systems of ordinary differential equations. Recent work in scalar auxiliary variable…

This paper focuses on developing a method to obtain an uncertain linear fractional transformation (LFT) system that adequately captures the dynamics of a nonlinear time-invariant system over some desired envelope. First, the nonlinear…

This work aims to provide an effective deep learning framework to predict the vector-soliton solutions of the coupled nonlinear equations and their interactions. The method we propose here is a physics-informed neural network (PINN)…

Due to the over-smoothing issue, most existing graph neural networks can only capture limited dependencies with their inherently finite aggregation layers. To overcome this limitation, we propose a new kind of graph convolution, called…

Seeking high-quality representations with latent variable models (LVMs) to reveal the intrinsic correlation between neural activity and behavior or sensory stimuli has attracted much interest. In the study of the biological visual system,…

Many physical datasets are generated by collections of instruments that make measurements at regular time intervals. For such regular monitoring data, we extend the framework of half-spectral covariance functions to the case of…

Physics-informed neural networks (PINNs) [31] use automatic differentiation to solve partial differential equations (PDEs) by penalizing the PDE in the loss function at a random set of points in the domain of interest. Here, we develop a…

Deep learning can accurately represent sub-grid-scale convective processes in climate models, learning from high resolution simulations. However, deep learning methods usually lack interpretability due to large internal dimensionality,…

Physics-Informed Neural Networks (PINNs) frequently encounter difficulties in accurately resolving shock waves within high-speed compressible flows, a failure largely attributed to the "gradient pathology" arising from extreme stiffness at…

The use of machine learning to predict wave dynamics is a topic of growing interest, but commonly-used deep learning approaches suffer from a lack of interpretability of the trained models. Here we present an interpretable machine learning…

A modified physics-informed neural network is used to predict the dynamics of optical pulses including one-soliton, two-soliton, and rogue wave based on the coupled nonlinear Schr\"odinger equation in birefringent fibers. At the same time,…

Modeling the time-dependent evolution of electron density is essential for understanding quantum mechanical behaviors of condensed matter and enabling predictive simulations in spectroscopy, photochemistry, and ultrafast science. Yet, while…

The Sparse Identification of Nonlinear Dynamics (SINDy) is a method for discovering nonlinear dynamical system models from data. Quantifying uncertainty in SINDy models is essential for assessing their reliability, particularly in…

We propose a novel data-driven method called QENDy (Quadratic Embedding of Nonlinear Dynamics) that not only allows us to learn quadratic representations of highly nonlinear dynamical systems, but also to identify the governing equations.…