Numerical models are widely used to simulate the Earth system, but they are computationally expensive and often depend on many uncertain input parameters. Calibration and uncertainty quantification require running them across many input configurations, so their effective use is costly. Statistical emulation provides a practical alternative for efficiently exploring model behavior. We are motivated by the Arctic sea-ice component of the Energy Exascale Earth System Model (MPAS-Seaice), which generates large spatiotemporal outputs at multiple spatial resolutions, with high-resolution (or high-fidelity, HF) simulations being more accurate but computationally more expensive than lower-resolution (low-fidelity, LF) simulations. Multi-fidelity (MF) emulation integrates information across resolutions to construct efficient and accurate surrogate models, yet existing approaches struggle to scale to large spatiotemporal data. We develop a MF emulator that combines tensor decomposition for dimensionality reduction, Gaussian process priors for flexible function approximation, and an additive discrepancy model to capture systematic differences between LF and HF data. The proposed framework scales to complex spatiotemporal fields while keeping predictions accurate and uncertainty well calibrated. In the MPAS-Seaice analysis, it attains the lowest prediction error of all emulators considered, including separable-covariance and neural-network approaches, especially throughout the summer melt season, when sea-ice concentration varies most across model settings and matters most scientifically, and best reproduces the spatiotemporal dependence of the output. By combining many inexpensive low-resolution runs with a few expensive high-resolution ones, the emulator substantially reduces the simulation cost of exploring model behavior, and suits large-scale studies involving complex physical models.
We introduce methodology to construct an emulator for environmental and ecological spatio-temporal processes that uses the higher order singular value decomposition (HOSVD) as an extension of singular value decomposition (SVD) approaches to emulation. Some important advantages of the method are that it allows for the use of a combination of supervised learning methods (e.g., random forests and Gaussian process regression) and also allows for the prediction of process values at spatial locations and time points that were not used in the training sample. The method is demonstrated with two appli…
Thermalizer: Stable autoregressive neural emulation of spatiotemporal chaos
Courant Institute of Mathematical Sciences, New York University, USA（Courant数学科学研究所，纽约大学，美国）；Center for Data Science, New York University, USA（数据科学中心，纽约大学，美国）
MERCURY: A fast and versatile multi-resolution based global emulator of compound climate hazards
University of Oxford（牛津大学）；Montreal Polytechnique（蒙特利尔理工学院）；Columbia Climate School（哥伦比亚气候学院）；International Institute for Applied Systems Analysis（国际应用系统分析研究所）；Universität Leipzig（莱比锡大学）；IRI THESys；Humboldt-Universität zu Berlin（柏林洪堡大学）；Institute Pierre-Simone-Laplace（皮埃尔-西蒙·拉普拉斯研究所）
We present a common framework for Bayesian emulation methodologies for multivariate-output simulators, or computer models, that employ either parametric linear models or nonparametric Gaussian processes. Novel diagnostics suitable for multivariate covariance-separable emulators are developed and techniques to improve the adequacy of an emulator are discussed and implemented. A variety of emulators are compared for a humanitarian relief simulator, modelling aid missions to Sicily after a volcanic eruption and earthquake, and a sensitivity analysis is conducted to determine the sensitivity of th…
Computationally expensive simulators, implementing mathematical models in computer codes, are commonly approximated using statistical emulators. We develop and assess novel emulation methods for systems best modelled via a chain, series or network of simulators. Using a Bayes linear framework, we link statistical emulators of the component simulators to explicitly account for the simulator input uncertainty induced by links between models in arbitrarily large networks. We demonstrate the advantages of these methods compared to use of a single emulator of the composite simulator network for a v…
Many applications require stochastic processes specified on two- or higher-dimensional domains; spatial or spatial-temporal modelling, for example. In these applications it is attractive, for conceptual simplicity and computational tractability, to propose a covariance function that is separable; e.g., the product of a covariance function in space and one in time. This paper presents a representation theorem for such a proposal, and shows that all processes with continuous separable covariance functions are second-order identical to the product of second-order uncorrelated processes. It discus…
Gaussian process (GP) models are widely used to emulate propagation uncertainty in computer experiments. GP emulation sits comfortably within an analytically tractable Bayesian framework. Apart from propagating uncertainty of the input variables, a GP emulator trained on finitely many runs of the experiment also offers error bars for response surface estimates at unseen input values. This helps select future input values where the experiment should be run to minimize the uncertainty in the response surface estimation. However, traditional GP emulators use stationary covariance functions, which…
It is often desirable to build a statistical emulator of a complex computer simulator in order to perform analysis which would otherwise be computationally infeasible. We propose methodology to model multivariate output from a computer simulator taking into account output structure in the responses. The utility of this approach is demonstrated by applying it to a chemical and biological hazard prediction model. Predicting the hazard area that results from an accidental or deliberate chemical or biological release is imperative in civil and military planning and also in emergency response. The …
Computer models are now widely used across a range of scientific disciplines to describe various complex physical systems, however to perform full uncertainty quantification we often need to employ emulators. An emulator is a fast statistical construct that mimics the complex computer model, and greatly aids the vastly more computationally intensive uncertainty quantification calculations that a serious scientific analysis often requires. In some cases, the complex model can be solved far more efficiently for certain parameter settings, leading to boundaries or hyperplanes in the input paramet…
Tensor-variate Gaussian process regression for efficient emulation of complex systems: comparing regressor and covariance structures in outer product and parallel partial emulators
Computer models are used as replacements for physical experiments in a large variety of applications. Nevertheless, direct use of the computer model for the ultimate scientific objective is often limited by the complexity and cost of the model. Historically, Gaussian process regression has proven to be the almost ubiquitous choice for a fast statistical emulator for such a computer model, due to its flexible form and analytical expressions for measures of predictive uncertainty. However, even this statistical emulator can be computationally intractable for large designs, due to computing time …
Swiss Federal Institute of Aquatic Science and Technology, Eawag（瑞士联邦水科学与技术研究所（Eawag））
Many model based scientific and engineering methodologies, such as system identification, sensitivity analysis, optimization and control, require a large number of model evaluations. In particular, model based real-time control of urban water infrastructures and online flood alarm systems require fast prediction of the network response at different actuation and/or parameter values. General purpose urban drainage simulators are too slow for this application. Fast surrogate models, so-called emulators, provide a solution to this efficiency demand. Emulators are attractive, because they sacrific…
Observing system uncertainty experiments (OSUEs) have been recently proposed as a cost-effective way to perform probabilistic assessment of retrievals for NASA's Orbiting Carbon Observatory-2 (OCO-2) mission. One important component in the OCO-2 retrieval algorithm is a full-physics forward model that describes the mathematical relationship between atmospheric variables such as carbon dioxide and radiances measured by the remote sensing instrument. This forward model is complicated and computationally expensive but large-scale OSUEs require evaluation of this model numerous times, which makes …
Renewable energy projects, such as large offshore wind farms, are critical to achieving low-emission targets set by governments. Stochastic computer models allow us to explore future scenarios to aid decision making whilst considering the most relevant uncertainties. Complex stochastic computer models can be prohibitively slow and thus an emulator may be constructed and deployed to allow for efficient computation. We present a novel heteroscedastic Gaussian Process emulator which exploits cheap approximations to a stochastic offshore wind farm simulator. We also conduct a probabilistic sensiti…
The state-of-the-art linked Gaussian process offers a way to build analytical emulators for systems of computer models. We generalize the closed form expressions for the linked Gaussian process under the squared exponential kernel to a class of Matérn kernels, that are essential in advanced applications. An iterative procedure to construct linked Gaussian processes as surrogate models for any feed-forward systems of computer models is presented and illustrated on a feed-back coupled satellite system. We also introduce an adaptive design algorithm that could increase the approximation accuracy …
Computer models are widely used across a range of scientific disciplines to describe various complex physical systems, however to perform full uncertainty quantification we often need to employ emulators. An emulator is a fast statistical construct that mimics the slow to evaluate computer model, and greatly aids the vastly more computationally intensive uncertainty quantification calculations that an important scientific analysis often requires. We examine the problem of emulating computer models that possess multiple, partial discontinuities occurring at known non-linear location. We introdu…
We calibrate a Natural History Model, which is a class of computer simulator used in the health industry, and here has been used to characterise bowel cancer incidence for the UK. The simulator tracks the development of bowel cancer in a sample of people, and its output mostly stratifies bowel cancer occurrence by patient age and bowel cancer type. Its output relies on 25 unknown inputs, which we are required to calibrate. In order to do this we must address that not only is the output count data, but it is also stochastic, due to the simulation procedure. We cannot feasibly achieve calibratio…
In applied sciences, we often deal with deterministic simulation models that are too slow for simulation-intensive tasks such as calibration or real-time control. In this paper, an emulator for a generic dynamic model, given by a system of ordinary non-linear differential equations, is developed. The non-linear differential equations are linearized and Gaussian white noise is added to account for the non-linearities. The resulting linear stochastic system is conditioned on a set of solutions of the non-linear equations that have been calculated prior to the emulation. A path-integral approach …
Gaussian process models are commonly used as emulators for computer experiments. However, developing a Gaussian process emulator can be computationally prohibitive when the number of experimental samples is even moderately large. Local Gaussian process approximation (Gramacy and Apley, 2015) was proposed as an accurate and computationally feasible emulation alternative. However, constructing local sub-designs specific to predictions at a particular location of interest remains a substantial computational bottleneck to the technique. In this paper, two computationally efficient neighborhood sea…
Hurricane-driven storm surge is one of the most deadly and costly natural disasters, making precise quantification of the surge hazard of great importance. Surge hazard quantification is often performed through physics-based computer models of storm surges. Such computer models can be implemented with a wide range of fidelity levels, with computational burdens varying by several orders of magnitude due to the nature of the system. The threat posed by surge makes greater fidelity highly desirable, however such models and their high-volume output tend to come at great computational cost, which c…
In many areas of science and engineering, computer simulations are widely used as proxies for physical experiments, which can be infeasible or unethical. Such simulations can often be computationally expensive, and an emulator can be trained to efficiently predict the desired response surface. A widely-used emulator is the Gaussian process (GP), which provides a flexible framework for efficient prediction and uncertainty quantification. Standard GPs, however, do not capture structured sparsity on the underlying response surface, which is present in many applications, particularly in the physic…
