Tensor Decomposition of Large-Scale Data with GenTen
Explore the source record for details and available documents.
Phipps, Eric T.↗
Engineering topics
De, Saibal
Publications and source records attributed to De, Saibal.
Quantum surrogate models for uncertainty quantification
Surrogate models are a critical ingredient to computation-based design and validation of many DOE mission-relevant physical systems. When first-principles computation of properties of a physical systems becomes pro hibitive, surrogate models are the only path towards achieving tasks such as uncertainty quantification (UQ), exploration of design space, and validation of design choices. In this project we have developed and demonstrated a new surro gate modeling paradigm for complex models that is data-driven, non-intrusive, and has the potential to be versatile and equipped with performance guaran tees. This combination of features is absent in existing surrogate modeling tools. The framework we have developed in this project exploits a quantum-classical correspondence to establish a quantum system that mimics the dynamics of the classical Hamiltonian system from which data in the form of temporal snapshots is provided. Since quantum dynamics propagates distributions over observables, the framework is naturally suited to propagation of epistemic uncertainties in the form of distributions over initial state and parametric uncertainties. In this project, we take the first step in establishing this novel framework by deriving a quantization and de-quantization procedure, demonstrating the accuracy of the quantum surrogate models these define using two model systems, and defining the next steps in maturing the framework towards a tool applicable to Sandia mission-relevant problems.
97 MATHEMATICS AND COMPUTING↗
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 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. Here, 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.
42 ENGINEERING↗