Polynomial Chaos
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Related Articles from SNS
On Improved Statistical Accuracy of Low-Order Polynomial Chaos Approximations
arXiv:2606.07912v1 Announce Type: new Abstract: Polynomial chaos expansions provide surrogate models for stochastic systems, with coefficients typically derived using Galerkin projection, stochastic collocation, or least squares approximation. These traditional approaches often fail to accurately capture statistical moments without resorting to high-order approximations. We propose a constrained optimization framework that modifies standard techniques to determine polynomial chaos...
Stochastic bifurcation analysis via polynomial chaos: consistency and convergence of branch-approximating solutions
Announce Type: new Abstract: Parameter-dependent dynamical systems that exhibit bifurcations pose significant computational challenges, as traditional continuation methods require repeated, costly simulations across large ranges of parameter values to capture sudden qualitative changes in the solution. In this work, we propose a systematic approach to reconstruct the branches of the entire bifurcation diagram in a single numerical solver leveraging generalized Polynomial Chaos (PC)...