Adaptive experimental design for multi‐fidelity surrogate modeling of multi‐disciplinary systems

Abstract

We present an adaptive algorithm for constructing surrogate models of multi-disciplinary systems composed of a set of coupled components. With this goal we introduce "coupling" variables with a priori unknown distributions that allow surrogates of each component to be built independently. Once built, the surrogates of the components are combined to form an integrated-surrogate that can be used to predict system-level quantities of interest at a fraction of the cost of the original model. The error in the integrated-surrogate is greedily minimized using an experimental design procedure that allocates the amount of training data, used to construct each component-surrogate, based on the contribution of those surrogates to the error of the integrated-surrogate. The multi-fidelity procedure presented is a generalization of multi-index stochastic collocation that can leverage ensembles of models of varying cost and accuracy, for one or more components, to reduce the computational cost of constructing the integrated-surrogate. Extensive numerical results demonstrate that, for a fixed computational budget, our algorithm is able to produce surrogates that are orders of magnitude more accurate than methods that treat the integrated system as a black-box.

Multifidelity neural network formulations for prediction of reactive molecular potential energy surfaces

“…Looking forward, we envision a number of essential refinements to the MF NN PES constructions. First, we expect to apply procedures for the adaptive determination of training set refinements using a multifidelity active learning procedure, as motivated by previous work in adaptive refinement for MF surrogates [61,63,64]. Second, as suggested by Appendix A, we expect to expand beyond bi-fidelity to integrate additional low-fidelity models, enabling greater flexibility in ensemble selection and greater optimality within the adaptive resource allocation problem.…”

“…Sampling approaches are more tolerant of high dimensionality and low regularity, whereas surrogate approaches can flexibly support general UQ analysis goals and can detect and exploit special structure when it exists to achieve more rapid convergence. Here, we focus on the latter class 1 and integrate neural network surrogate models within a framework for multifidelity learning, building on experience from surrogate-based UQ contexts [57,[61][62][63][64][65]. While neither optimization nor UQ are the current goals for building multifidelity NN PESs, the central need for accurate and affordable representations of the input-output mapping is shared with quantum chemistry given the cost of high-fidelity ab initio computations of potential energy of large molecules.…”

Multifidelity Neural Network Formulations for Prediction of Reactive Molecular Potential Energy Surfaces

“…Looking forward, we envision a number of essential refinements to the MF NN PES constructions. First, we expect to apply procedures for the adaptive determination of training set refinements using a multifidelity active learning procedure, as motivated by previous work in adaptive refinement for MF surrogates. ,, Second, as suggested by Section , we expect to expand beyond bifidelity to integrate additional low-fidelity models, enabling greater flexibility in ensemble selection and greater optimality within the adaptive resource allocation problem. Third, it will be essential to assess the performance of these MF NN PES approaches when generalizing to other chemical systems and involving additional modeling alternatives.…”

“…Sampling approaches are generally more tolerant of high dimensionality and low regularity, whereas surrogate approaches can flexibly support general UQ analysis goals and can detect and exploit a special structure when it exists to achieve more rapid convergence. Here, we focus on the latter class and integrate neural network surrogate models within a framework for multifidelity learning, building on experience from surrogate-based UQ contexts. ,− While neither optimization nor UQ are the current goals for building multifidelity NN PESs, the central need for accurate and affordable representations of the input–output mapping is shared with quantum chemistry given the cost of high-fidelity ab initio computations of potential energy of large molecules.…”