相关论文: Flow-driven spectral chaos (FSC) method for simula…
We propose a systematic training-free method to transform the probability flow of a "linear" stochastic process characterized by the equation X_{t}=a_{t}X_{0}+\sigma_{t}X_{1} into a straight constant-speed (SC) flow, reminiscent of…
Conformal prediction provides a distribution-free framework for uncertainty quantification via prediction sets with exact finite-sample coverage. In low dimensions these sets are easy to interpret, but in high-dimensional or structured…
We present gPC-SCP: Generalized Polynomial Chaos-based Sequential Convex Programming to compute a sub-optimal solution for a continuous-time chance-constrained stochastic nonlinear optimal control (SNOC) problem. The approach enables motion…
Polynomial chaos is a powerful technique for propagating uncertainty through ordinary and partial differential equations. Random variables are expanded in terms of orthogonal polynomials and differential equations are derived for the…
We present an approach to the simulation of quantum systems driven by classical stochastic processes that is based on the polynomial chaos expansion, a well-known technique in the field of uncertainty quantification. The polynomial chaos…
We present an alternative "encapsulated" formulation of the Selective Frequency Damping method for finding unstable equilibria of dynamical systems, which is particularly useful when analysing the stability of fluid flows. The formulation…
Fractional calculus provides a rigorous mathematical framework to describe anomalous stochastic processes by generalizing the notion of classical differential equations to their fractional-order counterparts. By introducing the fractional…
A stochastic optimal control problem for incompressible Newtonian channel flow past a circular cylinder is used as a prototype optimal control problem for the stochastic Navier-Stokes equations. The inlet flow and the rotation speed of the…
Generating high-quality time series data has emerged as a critical research topic due to its broad utility in supporting downstream time series mining tasks. A major challenge lies in modeling the intrinsic stochasticity of temporal…
The probability distributions, as well as the mean values of stochastic currents and fluxes, associated with a driven Langevin process, provide a good and topologically protected measure of how far a stochastic system is driven out of…
The effective management of stochastic characteristics of renewable power generations is vital for ensuring the stable and secure operation of power systems. This paper addresses the task of optimizing the chance-constrained…
Model predictive control is an advanced control approach for multivariable systems with constraints, which is reliant on an accurate dynamic model. Most real dynamic models are however affected by uncertainties, which can lead to…
A Gaussian process (GP)-based methodology is proposed to emulate complex dynamical computer models (or simulators). The method relies on emulating the numerical flow map of the system over an initial (short) time step, where the flow map is…
This paper presents a spectral scheme for the numerical solution of nonlinear conservation laws in non-periodic domains under arbitrary boundary conditions. The approach relies on the use of the Fourier Continuation (FC) method for spectral…
The uncertainty of multiple power loads and renewable energy generations (PLREG) in power systems increases the complexity of power flow analysis for decision-makers. The chance-constrained method can be applied to model the optimization…
Stochastic spectral methods are efficient techniques for uncertainty quantification. Recently they have shown excellent performance in the statistical analysis of integrated circuits. In stochastic spectral methods, one needs to determine a…
In this paper, we develop and analyze a stochastic algorithm for solving space-time fractional diffusion models, which are widely used to describe anomalous diffusion dynamics. These models pose substantial numerical challenges due to the…
Polynomial Chaos Expansions represent a powerful tool to simulate stochastic models of dynamical systems. Yet, deriving the expansion's coefficients for complex systems might require a significant and non-trivial manipulation of the model,…
We introduce Statistical Flow Matching (SFM), a novel and mathematically rigorous flow-matching framework on the manifold of parameterized probability measures inspired by the results from information geometry. We demonstrate the…
Stochastic model-predictive control (SMPC) has evolved to a powerful framework for the control of stochastic dynamical systems. SMPC utilizes a probabilistic uncertainty description to provide a systematic trade-off between the control…