Related papers: Inferring temporal dynamics from cross-sectional d…

One of the pivotal tasks in scientific machine learning is to represent underlying dynamical systems from time series data. Many methods for such dynamics learning explicitly require the derivatives of state data, which are not directly…

We present a numerical method to produce stochastic dynamics according to the generalized Langevin equation with a non-stationary memory kernel. This type of dynamics occurs when a microscopic system with an explicitly time-dependent…

The generation of non-separable, physically motivated covariance functions is a theme of ongoing research interest, given that only a few classes of such functions are available. We construct a non-separable space-time covariance function…

We present a Bayesian approach for modeling multivariate, dependent functional data. To account for the three dominant structural features in the data--functional, time dependent, and multivariate components--we extend hierarchical dynamic…

Dynamics simulations of constrained particles can greatly aid in understanding the temporal and spatial evolution of biological processes such as lateral transport along membranes and self-assembly of viruses. Most theoretical efforts in…

Many of the biological, social and man-made networks around us are inherently dynamic, with their links switching on and off over time. The evolution of these networks is often non-Markovian, and the dynamics of their links correlated.…

Diffusion studies of adsorbates moving on a surface are often analyzed using 2D Langevin simulations. These simulations are computationally cheap and offer valuable insight into the dynamics, however, they simplify the complex interactions…

A methodology for high dimensional causal inference in a time series context is introduced. It is assumed that there is a monotonic transformation of the data such that the dynamics of the transformed variables are described by a Gaussian…

Longitudinal analysis is important in many disciplines, such as the study of behavioral transitions in social science. Only very recently, feature selection has drawn adequate attention in the context of longitudinal modeling. Standard…

Fourier acceleration has been successfully applied to the simulation of lattice field theories for more than a decade. In this paper, we extend the method to the dynamics of discrete particles moving in continuum. Although our method is…

Wild animals are commonly fitted with trackers that record their position through time, and statistical models for tracking data broadly fall into two categories: models focused on small-scale movement decisions, and models for large-scale…

Detecting anomalies and discovering driving signals is an essential component of scientific research and industrial practice. Often the underlying mechanism is highly complex, involving hidden evolving nonlinear dynamics and noise…

The problem of mass diffusion in layered systems has relevance to applications in different scientific disciplines, e.g., chemistry, material science, soil science, and biomedical engineering. The mathematical challenge in these type of…

Anticipating bifurcation-induced transitions in dynamical systems has gained relevance in various fields of the natural, social, and economic sciences. Before the annihilation of a system's equilibrium point by means of a bifurcation, the…

We experimentally study a piezoelectric energy harvester driven by broadband random vibrations. We show that a linear model, consisting of an underdamped Langevin equation for the dynamics of the tip mass, electromechanically coupled with a…

Deep learning methods achieve remarkable predictive performance in modeling complex, large-scale data. However, assessing the quality of derived models has become increasingly challenging, as more classical statistical assumptions may no…

We propose a solution for linear inverse problems based on higher-order Langevin diffusion. More precisely, we propose pre-conditioned second-order and third-order Langevin dynamics that provably sample from the posterior distribution of…

Bayesian neural learning feature a rigorous approach to estimation and uncertainty quantification via the posterior distribution of weights that represent knowledge of the neural network. This not only provides point estimates of optimal…

Data-driven, model-free analytics are natural choices for discovery and forecasting of complex, nonlinear systems. Methods that operate in the system state-space require either an explicit multidimensional state-space, or, one approximated…

A key task in Bayesian statistics is sampling from distributions that are only specified up to a partition function (i.e., constant of proportionality). However, without any assumptions, sampling (even approximately) can be #P-hard, and few…