Nonlinear information fusion algorithms for data-efficient multi-fidelity modelling

By Paris Perdikaris, Maizar Raissi, Andreas C. Damianou, Neil D. Lawrence, G. Em Karniadakis. 2017

474 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computational Theory and Mathematics, Statistical and Nonlinear Physics

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Citations in the corpus

Conditional deep surrogate models for stochastic, high-dimensional, and multi-fidelity systems (2019, methodology): “Moreover, ρ is a parameter that controls the degree to which the two stochastic processes exhibit linear correlations [63, 64].”
Deep UQ: Learning deep neural network surrogate models for high dimensional uncertainty quantification (2018, methodology): “DNNs are also naturally suited for tasks for multilevel/multiﬁdelity UQ [73, 74, 75].”
Inferring solutions of differential equations using noisy multi-fidelity data (2016, background): “, ρ(x)), yielding a more expressive scheme that can capture increasingly complex cross correlations [20, 21].”
Remarks on multi-output Gaussian process regression (2018, background): “Similar to the CoKGb, the nlCoKG also runs in a decomposed fashion, see the details in [80].”
Multi-fidelity classification using Gaussian processes: accelerating the prediction of large-scale computational models (2019, background): “In general, ρi can also be a function of x leading to more complex schemes that can capture non-linear correlations [28].”
A physics-aware, probabilistic machine learning framework for coarse-graining high-dimensional systems in the Small Data regime (2019, background): “…or reduced-order models may readily be constructed by utilizing potentially much coarser spatio-temporal discretizations which, in conjunction with appropriate statistical models, are capable of providing fully probabilistic predictions Koutsourelakis (2009); Perdikaris et al. (2017).”
Recent Advances in Bayesian Optimization (2022, methodology): “26 has been generalized by replacing the scaling factor ρ with a non-linear mapping function [140].”
The statistical finite element method (statFEM) for coherent synthesis of observation data and model predictions (2019, background): “A possible further extension of statFEM concerns the refinement of the postulated statistical model to incorporate computational models of different fidelity by incorporating ideas from recursive cokriging [51–53].”
Discovering variable fractional orders of advection-dispersion equations from field data using multi-fidelity Bayesian optimization (2017, background): “[30] to safeguard against the lower fidelity levels having poor surrogate accuracy.”
A composite neural network that learns from multi-fidelity data: Application to function approximation and inverse PDE problems (2019, methodology): “Although great progress has already been made, the multi-ﬁdelity approaches based on GPR still have some limitations, e.g., approximations of discontinuous functions [7], high-dimensional problems [9], and inverse problems with strong nonlinearities (i.e., nonlinear partial diﬀerential equations) [8”