Gaussian process emulation of dynamic computer codes

Conti, Stefano; Gosling, John Paul; Oakley, Jeremy E.; O'Hagan, Anthony

doi:10.1093/biomet/asp028

Cited by 173 publications

(148 citation statements)

References 13 publications

Supporting

Mentioning

142

Contrasting

Order By: Relevance

“…Moreover, GPR possesses additional properties which were not explored in this paper and that explain its first choice for emulation (e.g., [34,74]). GPR can give some information about the relative relevance of the inputs, it can provide associated uncertainty intervals (referred to as code uncertainty of the emulator) for the predictions, and the Jacobian and Hessians of the prediction function can be explicitly derived [50,75].…”

Section: Interpreting Emulator Resultsmentioning

confidence: 99%

Emulation of Leaf, Canopy and Atmosphere Radiative Transfer Models for Fast Global Sensitivity Analysis

et al. 2016

View full text Add to dashboard Cite

Abstract:Physically-based radiative transfer models (RTMs) help understand the interactions of radiation with vegetation and atmosphere. However, advanced RTMs can be computationally burdensome, which makes them impractical in many real applications, especially when many state conditions and model couplings need to be studied. To overcome this problem, it is proposed to substitute RTMs through surrogate meta-models also named emulators. Emulators approximate the functioning of RTMs through statistical learning regression methods, and can open many new applications because of their computational efficiency and outstanding accuracy. Emulators allow fast global sensitivity analysis (GSA) studies on advanced, computationally expensive RTMs. As a proof-of-concept, three machine learning regression algorithms (MLRAs) were tested to function as emulators for the leaf RTM PROSPECT-4, the canopy RTM PROSAIL, and the computationally expensive atmospheric RTM MODTRAN5. Selected MLRAs were: kernel ridge regression (KRR), neural networks (NN) and Gaussian processes regression (GPR). For each RTM, 500 simulations were generated for training and validation. The majority of MLRAs were excellently validated to function as emulators with relative errors well below 0.2%. The emulators were then put into a GSA scheme and compared against GSA results as generated by original PROSPECT-4 and PROSAIL runs. NN and GPR emulators delivered identical GSA results, while processing speed compared to the original RTMs doubled for PROSPECT-4 and tripled for PROSAIL. Having the emulator-GSA concept successfully tested, for six MODTRAN5 atmospheric transfer functions (outputs), i.e., direct and diffuse at-surface solar irradiance (E di f , E dir ), direct and diffuse upward transmittance (T dir , T di f ), spherical albedo (S) and path radiance (L 0 ), the most accurate MLRA's were subsequently applied as emulator into the GSA scheme. The sensitivity analysis along the 400-2500 nm spectral range took no more than a few minutes on a contemporary computer-in comparison, the same analysis in the original MODTRAN5 would have taken over a month. Key atmospheric drivers were identified, which are on the one hand aerosol optical properties, i.e., aerosol optical thickness (AOT), Angstrom coefficient (AMS) and scattering asymmetry variable (G), mostly driving diffuse atmospheric components, E di f and T di f ; and those affected by atmospheric scattering, L 0 and S. On the other hand, as expected, AOT, AMS and columnar water vapor (CWV) in the absorption regions mostly drive E dir and T dir atmospheric functions. The presented emulation schemes showed very promising results in replacing costly RTMs, and we think they can contribute to the adoption of machine learning techniques in remote sensing and environmental applications.

show abstract

Section: Interpreting Emulator Resultsmentioning

confidence: 99%

Emulation of Leaf, Canopy and Atmosphere Radiative Transfer Models for Fast Global Sensitivity Analysis

et al. 2016

View full text Add to dashboard Cite

show abstract

“…While we have not done so in this work, the inclusion of parameter trajectories predicted by dynamic vegetation models [15] or crop models [70] might also be of interest. Given the complexity of these models, particular care should be paid to their emulation [71,72]. Complexities of dynamic models arise from the fact that the output is an update of the input (e.g., in a vegetation or crop model, the LAI at one time step is used as an input to the model, and is modified internally to provide an update on the value of LAI for the next time step).…”

Section: Discussion and Outlookmentioning

confidence: 99%

Efficient Emulation of Radiative Transfer Codes Using Gaussian Processes and Application to Land Surface Parameter Inferences

2016

View full text Add to dashboard Cite

Abstract:There is an increasing need to consistently combine observations from different sensors to monitor the state of the land surface. In order to achieve this, robust methods based on the inversion of radiative transfer (RT) models can be used to interpret the satellite observations. This typically results in an inverse problem, but a major drawback of these methods is the computational complexity. We introduce the concept of Gaussian Process (GP) emulators: surrogate functions that accurately approximate RT models using a small set of input (e.g., leaf area index, leaf chlorophyll, etc.) and output (e.g., top-of-canopy reflectances or at sensor radiances) pairs. The emulators quantify the uncertainty of their approximation, and provide a fast and easy route to estimating the Jacobian of the original model, enabling the use of e.g., efficient gradient descent methods. We demonstrate the emulation of widely used RT models (PROSAIL and SEMIDISCRETE) and the coupling of vegetation and atmospheric (6S) RT models targetting particular sensor bands. A comparison with the full original model outputs shows that the emulators are a viable option to replace the original model, with negligible bias and discrepancies which are much smaller than the typical uncertainty in the observations. We also extend the theory of GP to cope with models with multivariate outputs (e.g., over the full solar reflective domain), and apply this to the emulation of PROSAIL, coupled 6S and PROSAIL and to the emulation of individual spectral components of 6S. In all cases, emulators successfully predict the full model output as well as accurately predict the gradient of the model calculated by finite differences, and produce speed ups between 10,000 and 50,000 times that of the original model. Finally, we use emulators to invert leaf area index (LAI), leaf chlorophyll content (C ab ) and equivalent leaf water thickness (C w ) from a time series of observations from Sentinel-2/MSI, Sentinel-3/SLSTR and Proba-V observations. We use sophisticated Hamiltonian Markov Chain Monte Carlo (MCMC) methods that exploit the speed of the emulators as well as the gradient estimation, a variational data assimilation (DA) method that extends the problem with temporal regularisation, and a particle filter using a regularisation model. The variational and particle filter approach appear more successful (meaning parameters closer to the truth, and smaller uncertainties) than the MCMC approach as a result of using the temporal regularisation mode. These work therefore suggests that GP emulators are a practical way to implement sophisticated parameter retrieval schemes in an era of increasing data volumes.

show abstract

“…The application of emulators has emerged in many different fields of science and thus the theoretical background is relatively well developed (e.g. O'Hagan, 2000, 2001;Phillips, 2003;Lucia et al, 2004;van der Merwe et al, 2007;Bliznyuk et al, 2008;Conti et al, 2009;Liu and West, 2009;Castelletti et al, 2012). Two distinct approaches to emulation exist, which we refer to as dynamic emulation and statistical emulation.…”

Section: Emulator Approachesmentioning

confidence: 99%

Reviews and syntheses: parameter identification in marine planktonic ecosystem modelling

et al. 2017

View full text Add to dashboard Cite

Abstract. To describe the underlying processes involved in oceanic plankton dynamics is crucial for the determination of energy and mass flux through an ecosystem and for the estimation of biogeochemical element cycling. Many planktonic ecosystem models were developed to resolve major processes so that flux estimates can be derived from numerical simulations. These results depend on the type and number of parameterizations incorporated as model equations. Furthermore, the values assigned to respective parameters specify a model's solution. Representative model results are those that can explain data; therefore, data assimilation methods are utilized to yield optimal estimates of parameter values while fitting model results to match data. Central difficulties are (1) planktonic ecosystem models are imperfect and (2) data are often too sparse to constrain all model parameters. In this review we explore how problems in parameter identification are approached in marine planktonic ecosystem modelling.We provide background information about model uncertainties and estimation methods, and how these are considered for assessing misfits between observations and model results. We explain differences in evaluating uncertainties in parameter estimation, thereby also discussing issues of parameter identifiability. Aspects of model complexity are addressed and we describe how results from cross-validation studies provide much insight in this respect. Moreover, approaches are discussed that consider time-and spacedependent parameter values. We further discuss the use of dynamical/statistical emulator approaches, and we elucidate issues of parameter identification in global biogeochemical models. Our review discloses many facets of parameter identification, as we found many commonalities between the objectives of different approaches, but scientific insight differed between studies. To learn more from results of planktonic ecosystem models we recommend finding a good balance in the level of sophistication between mechanistic modelling and statistical data assimilation treatment for parameter estimation.

show abstract

Gaussian process emulation of dynamic computer codes

Cited by 173 publications

References 13 publications

Emulation of Leaf, Canopy and Atmosphere Radiative Transfer Models for Fast Global Sensitivity Analysis

Emulation of Leaf, Canopy and Atmosphere Radiative Transfer Models for Fast Global Sensitivity Analysis

Efficient Emulation of Radiative Transfer Codes Using Gaussian Processes and Application to Land Surface Parameter Inferences

Reviews and syntheses: parameter identification in marine planktonic ecosystem modelling

Contact Info

Product

Resources

About