Accurate data‐driven surrogates of dynamical systems for forward propagation of uncertainty

Stochastic collocation (SC) is a well‐known non‐intrusive method of constructing surrogate models for uncertainty quantification. In dynamical systems, SC is especially suited for full‐field uncertainty propagation that characterizes the distributions of the high‐dimensional solution fields of a mod...

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Vydáno v:International journal for numerical methods in engineering Ročník 125; číslo 23
Hlavní autoři: De, Saibal, Jones, Reese E., Kolla, Hemanth
Médium: Journal Article
Jazyk:angličtina
Vydáno: Hoboken, USA John Wiley & Sons, Inc 15.12.2024
Wiley Subscription Services, Inc
Wiley
Témata:
Approximation
collocation
Dynamical systems
ENGINEERING
Nonlinear dynamics
Ordinary differential equations
Parameter identification
Parameter uncertainty
Partial differential equations
Solid mechanics
stochastic problems
ISSN:0029-5981, 1097-0207
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Popis
Shrnutí:Stochastic collocation (SC) is a well‐known non‐intrusive method of constructing surrogate models for uncertainty quantification. In dynamical systems, SC is especially suited for full‐field uncertainty propagation that characterizes the distributions of the high‐dimensional solution fields of a model with stochastic input parameters. However, due to the highly nonlinear nature of the parameter‐to‐solution map in even the simplest dynamical systems, the constructed SC surrogates are often inaccurate. This work presents an alternative approach, where we apply the SC approximation over the dynamics of the model, rather than the solution. By combining the data‐driven sparse identification of nonlinear dynamics framework with SC, we construct dynamics surrogates and integrate them through time to construct the surrogate solutions. We demonstrate that the SC‐over‐dynamics framework leads to smaller errors, both in terms of the approximated system trajectories as well as the model state distributions, when compared against full‐field SC applied to the solutions directly. We present numerical evidence of this improvement using three test problems: a chaotic ordinary differential equation, and two partial differential equations from solid mechanics.
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USDOE National Nuclear Security Administration (NNSA), Office of Defense Programs (DP)
SAND--2024-16993J
NA0003525
USDOE Laboratory Directed Research and Development (LDRD) Program
ISSN:0029-5981
1097-0207
DOI:10.1002/nme.7576