Related papers: Efficient Spectral Differentiation in Grid-Based C…
Power grids must modernize to meet climate goals while maintaining reliable and stable operating conditions. Yet progress is hindered by a limited understanding of the stochastic processes underlying grid frequency and phase-angle…
Ordinary Differential Equations are a simple but powerful framework for modeling complex systems. Parameter estimation from times series can be done by Nonlinear Least Squares (or other classical approaches), but this can give…
We propose a fixed-point-based numerical framework for computing stationary states of nonlocal Fokker-Planck-type equations. Instead of discretising the differential operators directly, we reformulate the stationary problem as a nonlinear…
It is an established fact that a finite difference operator approximates a derivative with a fixed algebraic rate of convergence. Nevertheless, we exhibit a new finite difference operator and prove it has spectral accuracy. Its rate of…
Spectral methods, thanks to the high accuracy and the possibility of using fast algorithms, represent an effective way to approximate collisional kinetic equations in kinetic theory. On the other hand, the loss of some local invariants can…
Stochastic differential equations (SDEs) are of utmost importance in various scientific and industrial areas. They are the natural description of dynamical processes whose precise equations of motion are either not known or too expensive to…
Welch's method provides an estimator of the power spectral density that is statistically consistent. This is achieved by averaging over periodograms calculated from overlapping segments of a time series. For a finite length time series,…
We propose a method to obtain phase portraits for stochastic systems. Starting from the Fokker-Planck equation, we separate the dynamics into a convective and a diffusive part. We show that stable and unstable fixed points of the convective…
We study a two-grid strategy for decoupling the time-dependent Poisson-Nernst-Planck equations describing the mass concentration of ions and the electrostatic potential. The computational system is decoupled to smaller systems by using…
In a mixed generalized linear model, the goal is to learn multiple signals from unlabeled observations: each sample comes from exactly one signal, but it is not known which one. We consider the prototypical problem of estimating two…
High dimensional random dynamical systems are ubiquitous, including -- but not limited to -- cyber-physical systems, daily return on different stocks of S&P 1500 and velocity profile of interacting particle systems around McKeanVlasov…
We develop a new continuous-time stochastic gradient descent method for optimizing over the stationary distribution of stochastic differential equation (SDE) models. The algorithm continuously updates the SDE model's parameters using an…
Multi-object state estimation is a fundamental problem for robotic applications where a robot must interact with other moving objects. Typically, other objects' relevant state features are not directly observable, and must instead be…
Stochastic sampling methods are arguably the most direct and least intrusive means of incorporating parametric uncertainty into numerical simulations of partial differential equations with random inputs. However, to achieve an overall error…
We consider the problem of estimating a consensus community structure by combining information from multiple layers of a multi-layer network using methods based on the spectral clustering or a low-rank matrix factorization. As a general…
Stochastic gradient (SG) methods are fundamental to system identification and machine learning, enabling online parameter estimation in large-scale and streaming-data settings. As a classical identification method, the SG algorithm has been…
Multivariate global polynomial approximations - such as polynomial chaos or stochastic collocation methods - are now in widespread use for sensitivity analysis and uncertainty quantification. The pseudospectral variety of these methods uses…
Gradient matching with Gaussian processes is a promising tool for learning parameters of ordinary differential equations (ODE's). The essence of gradient matching is to model the prior over state variables as a Gaussian process which…
This paper deals with the state estimation of stochastic systems and examines the possible employment of tensor decompositions in grid-based filtering routines, in particular, the tensor-train decomposition. The aim is to show that these…
Stochastic filtering refers to estimating the probability distribution of the latent stochastic process conditioned on the observed measurements in time. In this paper, we introduce a new class of convergent filters that represent the…