Related papers: Deep learning algorithm for data-driven simulation…

An algorithm for a family of self-starting high-order implicit time integration schemes with controllable numerical dissipation is proposed for both linear and nonlinear transient problems. This work builds on the previous works of the…

System identification is of special interest in science and engineering. This article is concerned with a system identification problem arising in stochastic dynamic systems, where the aim is to estimate the parameters of a system along…

Modeling high-dimensional, nonlinear dynamic structural systems under natural hazards presents formidable computational challenges, especially when simultaneously accounting for uncertainties in external loads and structural parameters.…

Supervised deep-embedding methods project inputs of a domain to a representational space in which same-class instances lie near one another and different-class instances lie far apart. We propose a probabilistic method that treats…

A multifidelity method for the nonlinear propagation of uncertainties in the presence of stochastic accelerations is presented. The proposed algorithm treats the uncertainty propagation (UP) problem by separating the propagation of the…

Diffusion models have quickly become some of the most popular and powerful generative models for high-dimensional data. The key insight that enabled their development was the realization that access to the score -- the gradient of the…

We introduce DeRegiME -- Deep Regime Mixture of Experts -- a direct multi-horizon probabilistic forecaster that separates latent uncertainty regimes from the underlying signal and softly assigns each forecast location to learned recurring…

We consider the problem of minimizing a convex function that is evolving according to unknown and possibly stochastic dynamics, which may depend jointly on time and on the decision variable itself. Such problems abound in the machine…

Most real world phenomena such as sunlight distribution under a forest canopy, minerals concentration, stock valuation, exhibit nonstationary dynamics i.e. phenomenon variation changes depending on the locality. Nonstationary dynamics pose…

In this paper, we aim to solve the high dimensional stochastic optimal control problem from the view of the stochastic maximum principle via deep learning. By introducing the extended Hamiltonian system which is essentially an FBSDE with a…

We prove that stochastic gradient descent efficiently converges to the global optimizer of the maximum likelihood objective of an unknown linear time-invariant dynamical system from a sequence of noisy observations generated by the system.…

Despite advancements in vehicle security systems, over the last decade, auto-theft rates have increased, and cyber-security attacks on internet-connected and autonomous vehicles are becoming a new threat. In this paper, a deep learning…

We present a deep transformation model for probabilistic regression. Deep learning is known for outstandingly accurate predictions on complex data but in regression tasks, it is predominantly used to just predict a single number. This…

We analyze the statistical performance of identification of stochastic dynamical systems with non-linear measurement sensors. This includes stochastic Wiener systems, with linear dynamics, process noise and measured by a non-linear sensor…

Massive volumes of high-dimensional data that evolves over time is continuously collected by contemporary information processing systems, which brings up the problem of organizing this data into clusters, i.e. achieve the purpose of…

Increasing effort is put into the development of methods for learning mechanistic models from data. This task entails not only the accurate estimation of parameters but also a suitable model structure. Recent work on the discovery of…

The topic of deep learning has seen a surge of interest in recent years both within and outside of the field of Statistics. Deep models leverage both nonlinearity and interaction effects to provide superior predictions in many cases when…

We analyze the performance of Dynamic Mode Decomposition (DMD)-based approximations of the stochastic Koopman operator for random dynamical systems where either the dynamics or observables are affected by noise. For many DMD algorithms, the…

We consider the problem of making nonparametric inference in a class of multi-dimensional diffusions in divergence form, from low-frequency data. Statistical analysis in this setting is notoriously challenging due to the intractability of…

In this paper, a data-driven nonparametric approach is presented for forecasting the probability density evolution of stochastic dynamical systems. The method is based on stochastic Koopman operator and extended dynamic mode decomposition…