BayesFlow: Learning Complex Stochastic Models With Invertible Neural Networks

Radev, Stefan T.; Mertens, Ulf K.; Voss, Andreas; Ardizzone, Lynton; Köthe, Ullrich

doi:10.1109/tnnls.2020.3042395

Cited by 105 publications

(159 citation statements)

References 38 publications

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“…This loss guarantees that the networks recover the true posterior under perfect convergence [47].…”

Section: Inn-inference and Bayesflowmentioning

confidence: 95%

“…Second, since the number of measurements can vary in practice, we introduce a relatively small summary network h ψ with trainable parameters ψ. It reduces measurements of variable size to fixed-size vectors,x = h ψ (x), by respecting the probabilistic symmetry of the measurements [47]. For independent measurements we use a permutation invariant summary network such that its output is invariant under the ordering in x [47].…”

Section: Inn-inference and Bayesflowmentioning

confidence: 99%

“…It reduces measurements of variable size to fixed-size vectors,x = h ψ (x), by respecting the probabilistic symmetry of the measurements [47]. For independent measurements we use a permutation invariant summary network such that its output is invariant under the ordering in x [47]. The summary network does not have to be invertible, since its output is concatenated with m and fed to s and t, but not directly mapped to z.…”

Section: Inn-inference and Bayesflowmentioning

confidence: 99%

“…Inference BayesFlow [47] provides a cINN framework which we can use to measure fundamental QCD parameters. From the inversion of a detector simulation and QCD radiation [63] we know how, given a single detector-level event, the cINN generates samples from a probability distribution over the phase space of the hard scattering.…”

Section: Inn-inference and Bayesflowmentioning

confidence: 99%

“…Technically, our BayesFlow approach [47] is based on the conditional version [48,49] of invertible networks (INNs) [50][51][52], a specific realization of normalizing flows [53][54][55][56]. These networks have been studied in relation to phase space generation [57][58][59][60], event generation [61], anomaly detection [62], detector and parton shower unfolding [63], and density estimation [64].…”

Section: Introductionmentioning

confidence: 99%

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Measuring QCD Splittings with Invertible Networks

et al. 2021

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QCD splittings are among the most fundamental theory concepts at the LHC. We show how they can be studied systematically with the help of invertible neural networks. These networks work with sub-jet information to extract fundamental parameters from jet samples. Our approach expands the LEP measurements of QCD Casimirs to a systematic test of QCD properties based on low-level jet observables. Starting with an toy example we study the effect of the full shower, hadronization, and detector effects in detail.

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“…This loss guarantees that the networks recover the true posterior under perfect convergence [47].…”

Section: Inn-inference and Bayesflowmentioning

confidence: 95%

Section: Inn-inference and Bayesflowmentioning

confidence: 99%

Section: Inn-inference and Bayesflowmentioning

confidence: 99%

Section: Inn-inference and Bayesflowmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Measuring QCD Splittings with Invertible Networks

et al. 2021

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Model updating of wind turbine blade cross sections with invertible neural networks

2021

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Fabricated wind turbine blades have unavoidable deviations from their designs due to imperfections in the manufacturing processes. Model updating is a common approach to enhance model predictions and therefore improve the numerical blade design accuracy compared to the built blade. An updated model can provide a basis for a digital twin of the rotor blade including the manufacturing deviations. Classical optimization algorithms, most often combined with reduced order or surrogate models, represent the state of the art in structural model updating. However, these deterministic methods suffer from high computational costs and a missing probabilistic evaluation. This feasibility study approaches the model updating task by inverting the model through the application of invertible neural networks, which allow for inferring a posterior distribution of the input parameters from given output parameters, without costly optimization or sampling algorithms. In our use case, rotor blade cross sections are updated to match given cross‐sectional parameters. To this end, a sensitivity analysis of the input (material properties or layup locations) and output parameters (such as stiffness and mass matrix entries) first selects relevant features in advance to then set up and train the invertible neural network. The trained network predicts with outstanding accuracy most of the selected cross‐sectional input parameters for different radial positions; that is, the posterior distribution of these parameters shows a narrow width. At the same time, it identifies some parameters that are hard to recover accurately or contain intrinsic ambiguities. Hence, we demonstrate that invertible neural networks are highly capable for structural model updating.

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Advances in statistical modeling of spatial extremes

Huser

Wadsworth

2020

WIREs Computational Stats

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The classical modeling of spatial extremes relies on asymptotic models (i.e., max-stable or r-Pareto processes) for block maxima or peaks over high thresholds, respectively. However, at finite levels, empirical evidence often suggests that such asymptotic models are too rigidly constrained, and that they do not adequately capture the frequent situation where more severe events tend to be spatially more localized. In other words, these asymptotic models have a strong tail dependence that persists at increasingly high levels, while data usually suggest that it should weaken instead. Another well-known limitation of classical spatial extremes models is that they are either computationally prohibitive to fit in high dimensions, or they need to be fitted using less efficient techniques. In this review paper, we describe recent progress in the modeling and inference for spatial extremes, focusing on new models that have more flexible tail structures that can bridge asymptotic dependence classes, and that are more easily amenable to likelihood-based inference for large datasets. In particular, we discuss various types of random scale constructions, as well as the conditional spatial extremes model, which have recently been getting increasing attention within the statistics of extremes community. We illustrate some of these new spatial models on two different environmental applications. This article is categorized under: Data: Types and Structure > Image and Spatial Data Data: Types and Structure > Time Series, Stochastic Processes, and Functional Data Statistical Learning and Exploratory Methods of the Data Sciences > Modeling Methods K E Y W O R D S asymptotic dependence and independence, extreme-value theory, max-stable process, Pareto process, random scale mixture

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BayesFlow: Learning Complex Stochastic Models With Invertible Neural Networks

Cited by 105 publications

References 38 publications

Measuring QCD Splittings with Invertible Networks

Measuring QCD Splittings with Invertible Networks

Model updating of wind turbine blade cross sections with invertible neural networks

Advances in statistical modeling of spatial extremes

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