An efficient dimension reduction for the Gaussian process emulation of two nested codes with functional outputs

2019 ◽  
Vol 35 (3) ◽  
pp. 1059-1099
Author(s):  
Sophie Marque-Pucheu ◽  
Guillaume Perrin ◽  
Josselin Garnier
Keyword(s):  
Gaussian Process ◽  
Dimension Reduction ◽  
Gaussian Process Emulation ◽  
Nested Codes

Gaussian Process emulation of multi-model ice sheet and glacier projections

2021 ◽  
Author(s):  
Tamsin Edwards ◽  
Keyword(s):  
Gaussian Process ◽  
Sea Level Rise ◽  
Sea Level ◽  
Climate Models ◽  
Ice Sheet ◽  
Surface Air Temperature ◽  
Model Parameters ◽  
Gaussian Process Emulation ◽  
Model Ensembles ◽  
Global Mean

<p><strong>The land ice contribution to global mean sea level rise has not yet been predicted with ice sheet and glacier models for the latest set of socio-economic scenarios (SSPs), nor with coordinated exploration of uncertainties arising from the various computer models involved. Two recent international projects (ISMIP6 and GlacierMIP) generated a large suite of projections using multiple models, but mostly used previous generation scenarios and climate models, and could not fully explore known uncertainties. </strong></p><p><strong>Here we estimate probability distributions for these projections for the SSPs using Gaussian Process emulation of the ice sheet and glacier model ensembles. We model the sea level contribution as a function of global mean surface air temperature forcing and (for the ice sheets) model parameters, with the 'nugget' allowing for multi-model structural uncertainty. Approximate independence of ice sheet and glacier models is assumed, because a given model responds very differently under different setups (such as initialisation). </strong></p><p><strong>We find that limiting global warming to 1.5</strong>°<strong>C </strong><strong>would halve the land ice contribution to 21<sup>st</sup> century </strong><strong>sea level rise</strong><strong>, relative to current emissions pledges: t</strong><strong>he median decreases from 25 to 13 cm sea level equivalent (SLE) by 2100. However, the Antarctic contribution does not show a clear response to emissions scenario, due to competing processes of increasing ice loss and snowfall accumulation in a warming climate. </strong></p><p><strong>However, under risk-averse (pessimistic) assumptions for climate and Antarctic ice sheet model selection and ice sheet model parameter values, Antarctic ice loss could be five times higher, increasing the median land ice contribution to 42 cm SLE under current policies and pledges, with the 95<sup>th</sup> percentile exceeding half a metre even under 1.5</strong>°<strong>C warming. </strong></p><p><strong>Gaussian Process emulation can therefore be a powerful tool for estimating probability density functions from multi-model ensembles and testing the sensitivity of the results to assumptions.</strong></p>

Gaussian Process Emulation for Big Data in Data-Driven Metamaterials Design

2019 ◽  
Author(s):  
Ramin Bostanabad ◽  
Yu-Chin Chan ◽  
Liwei Wang ◽  
Ping Zhu ◽  
Wei Chen
Keyword(s):  
Big Data ◽  
Gaussian Process ◽  
Engineering Design ◽  
Training Data ◽  
Data Driven ◽  
Training Dataset ◽  
Massive Datasets ◽  
Unit Cells ◽  
Gaussian Process Emulation ◽  
Novel Method

Abstract Our main contribution is to introduce a novel method for Gaussian process (GP) modeling of massive datasets. The key idea is to build an ensemble of independent GPs that use the same hyperparameters but distribute the entire training dataset among themselves. This is motivated by our observation that estimates of the GP hyperparameters change negligibly as the size of the training data exceeds a certain level, which can be found in a systematic way. For inference, the predictions from all GPs in the ensemble are pooled to efficiently exploit the entire training dataset for prediction. We name our modeling approach globally approximate Gaussian process (GAGP), which, unlike most largescale supervised learners such as neural networks and trees, is easy to fit and can interpret the model behavior. These features make it particularly useful in engineering design with big data. We use analytical examples to demonstrate that GAGP achieves very high predictive power that matches or exceeds that of state-of-the-art machine learning methods. We illustrate the application of GAGP in engineering design with a problem on data-driven metamaterials design where it is used to link reduced-dimension geometrical descriptors of unit cells and their properties. Searching for new unit cell designs with desired properties is then accomplished by employing GAGP in inverse optimization.

Gaussian Process-Based Dimension Reduction for Goal-Oriented Sequential Design

2019 ◽  
Vol 7 (4) ◽  
pp. 1369-1397
Author(s):  
Malek Ben Salem ◽  
François Bachoc ◽  
Olivier Roustant ◽  
Fabrice Gamboa ◽  
Lionel Tomaso
Keyword(s):  
Gaussian Process ◽  
Dimension Reduction ◽  
Sequential Design

scholarly journals Latent-space time evolution of non-intrusive reduced-order models using Gaussian process emulation

2021 ◽  
Vol 416 ◽  
pp. 132797
Author(s):  
Romit Maulik ◽  
Themistoklis Botsas ◽  
Nesar Ramachandra ◽  
Lachlan R. Mason ◽  
Indranil Pan
Keyword(s):  
Gaussian Process ◽  
Time Evolution ◽  
Space Time ◽  
Reduced Order Models ◽  
Reduced Order ◽  
Latent Space ◽  
Gaussian Process Emulation ◽  
Space Time Evolution

scholarly journals GpABC: a Julia package for approximate Bayesian computation with Gaussian process emulation

2019 ◽  
Author(s):  
Evgeny Tankhilevich ◽  
Jonathan Ish-Horowicz ◽  
Tara Hameed ◽  
Elisabeth Roesch ◽  
Istvan Kleijn ◽  
...  
Keyword(s):  
Gaussian Process ◽  
Stochastic Models ◽  
Approximate Bayesian Computation ◽  
Computational Cost ◽  
Bayesian Computation ◽  
Parameter Inference ◽  
Likelihood Functions ◽  
Gaussian Process Emulation ◽  
Selection For ◽  
Approximate Bayesian

ABSTRACTApproximate Bayesian computation (ABC) is an important framework within which to infer the structure and parameters of a systems biology model. It is especially suitable for biological systems with stochastic and nonlinear dynamics, for which the likelihood functions are intractable. However, the associated computational cost often limits ABC to models that are relatively quick to simulate in practice. We here present a Julia package, GpABC, that implements parameter inference and model selection for deterministic or stochastic models using i) standard rejection ABC or ABC-SMC, or ii) ABC with Gaussian process emulation. The latter significantly reduces the computational cost.URL: https://github.com/tanhevg/GpABC.jl

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