arXiv subjects

Serge Guillas

Publications and source records attributed to Serge Guillas.

At least 19 recordsLinked to original sources

arXiv2026

History matching for functional data: Application to tsunami warnings in the Indian Ocean

Traditional history matching (HM) is widely used as a computationally tractable alternative to Bayesian calibration for ruling out implausible regions of the input space of expensive computer models. Its standard formulation, however, is primarily tailored to scalar or finite-dimensional vector outputs, whereas observations in many physical systems are naturally functional, taking the form of time series or spatial fields. We propose Functional History Matching (FHM), an extension of HM to functional data. FHM defines implausibility through a function-level discrepancy measure together with a scalarized uncertainty term that combines observation error, model discrepancy, and emulator uncertainty. To quantify functional mismatch, we introduce a Wiener-process-based random projection criterion that is sensitive to differences in overall shape and temporal alignment, and we allow derivative information to be incorporated when additional discriminatory power is required. For functional emulation, we adopt a multi-output Gaussian process framework implemented through the Outer Product Emulator, which yields predictive means and uncertainty summaries for functional outputs at practical computational cost. We further motivate threshold selection through a conservative, distribution-free argument based on Chebyshev's inequality. In a synthetic tsunami forecasting case study, FHM progressively contracts the not-ruled-out-yet region and yields more concentrated downstream coastal predictions than landmark-based HM.

stat.AP↗

arXiv2026

Diffusion Distillation for Efficient Weather Ensembles

Diffusion models generate skillful weather ensembles but require costly iterative sampling. We introduce a supervised energy-distance distillation method that compresses a multi-step diffusion teacher into a single-step student by aligning student forecasts with teacher samples and ground-truth observations. Experiments on global forecasting and typhoon-track prediction show that our student outperforms existing distillation methods and preserves skill for extreme events. It matches or surpasses the teacher across key metrics using only one neural function evaluation per autoregressive step.

cs.LG↗

arXiv2026

Neural Operator Processes for Probabilistic Operator Learning under Partial Observations

Neural operators learn mappings between function spaces, but are typically developed with dense input-output training fields and fully observed inputs at inference. Many scientific problems require instead predicting solution fields from sparse, irregular, or partial observations under uncertainty. We introduce Neural Operator Processes (NOPs), a framework that unifies neural-process conditioning with neural-operator decoding to predict full output fields from limited context. NOPs condition on sparse joint input-output observations and support deterministic and probabilistic prediction within a shared encoder-decoder architecture. We study two conditioning strategies, convolutional pooled summaries and query-aligned attention, and analyze how their interaction with latent stochastic variables depends on PDE geometry. Across function regression and three PDE benchmarks, we find that sparse conditional operator learning is viable and can match dense-grid behavior in several regimes, that preserving local context-query geometry is essential in non-periodic settings but less so in spectrally smooth periodic regimes, and that uncertainty-aware operator learning succeeds when latent conditioning complements rather than overwrites the local geometric pathway. These results provide a basis for probabilistic operator learning under partial observations and help bridge operator learning and probabilistic meta-learning in function space.

cs.LG↗

arXiv2026

Deep Gaussian Process Emulation with gradient Information and Sequential Design for Simulators with Sharp Variations

Deep Gaussian Processes (DGPs) compose GP layers to warp inputs, enabling improved emulation of computer models with nonstationary input-output behavior compared with ordinary GPs. In contrast to GPs, the predictive uncertainty for DGP gradients remains relatively underexplored. Quantifying DGP gradient uncertainty can support gradient-based tasks in complex, nonstationary settings where ordinary GPs may struggle. While GP gradient posteriors are analytically tractable, extending such constructions to DGPs is challenging due to their hierarchical composition. In this paper, we propose an efficient approximation to the gradient distribution of a two-layer DGP emulator. Using the chain rule with local linearization, we derive closed-form expressions for the gradient mean and covariance, enabling fast gradient evaluation with uncertainty quantification (UQ). Empirically, our approach delivers promising performance while uniquely providing UQ of gradients. We then use the gradient uncertainties to guide sequential design for models with sharp variations: we define sharp variation regions as those where the gradient norm exceeds a threshold. We subsequently introduce an entropy-based acquisition rule that selects new samples in locations where the classification of points as inside versus outside the sharp-variation region is most uncertain. Experiments on synthetic benchmarks and a real-world application show that the resulting sequential design more accurately emulates functions with sharp variations than existing design methods.

stat.CO↗

arXiv2025

Multi-fidelity Batch Active Learning for Gaussian Process Classifiers

Many science and engineering problems rely on expensive computational simulations, where a multi-fidelity approach can accelerate the exploration of a parameter space. We study efficient allocation of a simulation budget using a Gaussian Process (GP) model in the binary simulation output case. This paper introduces Bernoulli Parameter Mutual Information (BPMI), a batch active learning algorithm for multi-fidelity GP classifiers. BPMI circumvents the intractability of calculating mutual information in the probability space by employing a first-order Taylor expansion of the link function. We evaluate BPMI against several baselines on two synthetic test cases and a complex, real-world application involving the simulation of a laser-ignited rocket combustor. In all experiments, BPMI demonstrates superior performance, achieving higher predictive accuracy for a fixed computational budget.

cs.LG↗

arXiv2025

Real-scale Smoothed Particle Hydrodynamics Tsunami Runup Modelling, with application to 3-D tsunami urban flows in Cilacap, South Java, Indonesia

The risk posed by tsunami waves is currently modelled over bare-earth representations by tsunami models. The complex flows around buildings and structures are crucial to represent the true state of the tsunami wave elevation, speed and forces exerted on buildings. Such 3D simulations have been unachievable for real scale modelling at a reasonable computational cost. We present here for the first time the use of Smoothed Particle Hydrodynamics (SPH) for tsunami simulation in a real setting of large scale (around 1 km). Our illustration is for Cilacap, Indonesia as constitutes a blueprint for future scenarios in South Java. SPH allows for the efficient modelling of shocks and complex interations of the flows with the structures. We also offer a range of test cases of increasing complexity and realism to tune and validate such realistic simulations, including the well known simplified beach of Seaside, Oregon at scale 1:50. We are able to reproduce realistic wave heights, velocities and even observed eddies. We provide guidance and discuss the various choices in terms of flow parametrisations, boundary conditions, and the trade-off of fidelity. computational cost. As a result, Probabilistic Tsunami Risk Assessments (PTRA) will become possible by making use a of combination of regional modelling of tsunamis with depth-average models (generation and propagation) as well as coastal modelling using SPH.

physics.flu-dyn↗

arXiv2024

Embedding machine-learnt sub-grid variability improves climate model biases

The under-representation of cloud formation is a long-standing bias associated with climate simulations. Parameterisation schemes are required to capture cloud processes within current climate models but have known biases. We overcome these biases by embedding a Multi-Output Gaussian Process (MOGP) trained on high resolution Unified Model simulations to represent the variability of temperature and specific humidity within a climate model. A trained MOGP model is coupled in-situ with a simplified Atmospheric General Circulation Model named SPEEDY. The temperature and specific humidity profiles of SPEEDY are perturbed at fixed intervals according to the variability predicted from the MOGP. Ten-year predictions are generated for both control and ML-hybrid models. The hybrid model reduces the global precipitation bias by 18\% and over the tropics by 22\%. To further understand the drivers of these improvements, physical quantities of interest are explored, such as the distribution of lifted index values and the alteration of the Hadley cell. The control and hybrid set-ups are also run in a plus 4K sea-surface temperature experiment to explore the effects of the approach on patterns relating to cloud cover and precipitation in a warmed climate setting.

physics.ao-ph↗

arXiv2023

Multilevel Bayesian Quadrature

Multilevel Monte Carlo is a key tool for approximating integrals involving expensive scientific models. The idea is to use approximations of the integrand to construct an estimator with improved accuracy over classical Monte Carlo. We propose to further enhance multilevel Monte Carlo through Bayesian surrogate models of the integrand, focusing on Gaussian process models and the associated Bayesian quadrature estimators. We show, using both theory and numerical experiments, that our approach can lead to significant improvements in accuracy when the integrand is expensive and smooth, and when the dimensionality is small or moderate. We conclude the paper with a case study illustrating the potential impact of our method in landslide-generated tsunami modelling, where the cost of each integrand evaluation is typically too large for operational settings.

stat.ME↗

arXiv2022

An adaptive strategy for sequential designs of multilevel computer experiments

Investigating uncertainties in computer simulations can be prohibitive in terms of computational costs, since the simulator needs to be run over a large number of input values. Building an emulator, i.e. a statistical surrogate model of the simulator constructed using a design of experiments made of a comparatively small number of evaluations of the forward solver, greatly alleviates the computational burden to carry out such investigations. Nevertheless, this can still be above the computational budget for many studies. Two major approaches have been used to reduce the budget needed to build the emulator: efficient design of experiments, such as sequential designs, and combining training data of different degrees of sophistication in a so-called multi-fidelity method, or multilevel in case these fidelities are ordered typically for increasing resolutions. We present here a novel method that combines both approaches, the multilevel adaptive sequential design of computer experiments (MLASCE) in the framework of Gaussian process (GP) emulators. We make use of reproducing kernel Hilbert spaces as a tool for our GP approximations of the differences between two consecutive levels. This dual strategy allows us to allocate efficiently limited computational resources over simulations of different levels of fidelity and build the GP emulator. The allocation of computational resources is shown to be the solution of a simple optimization problem in a special case where we theoretically prove the validity of our approach. Our proposed method is compared with other existing models of multi-fidelity Gaussian process emulation. Gains in orders of magnitudes in accuracy or computing budgets are demonstrated in some of numerical examples for some settings.

stat.ME↗

arXiv2022

Deep Gaussian Process Emulation using Stochastic Imputation

Deep Gaussian processes (DGPs) provide a rich class of models that can better represent functions with varying regimes or sharp changes, compared to conventional GPs. In this work, we propose a novel inference method for DGPs for computer model emulation. By stochastically imputing the latent layers, our approach transforms a DGP into a linked GP: a novel emulator developed for systems of linked computer models. This transformation permits an efficient DGP training procedure that only involves optimizations of conventional GPs. In addition, predictions from DGP emulators can be made in a fast and analytically tractable manner by naturally utilizing the closed form predictive means and variances of linked GP emulators. We demonstrate the method in a series of synthetic examples and empirical applications, and show that it is a competitive candidate for DGP surrogate inference, combining efficiency that is comparable to doubly stochastic variational inference and uncertainty quantification that is comparable to the fully-Bayesian approach. A $\texttt{Python}$ package $\texttt{dgpsi}$ implementing the method is also produced and available at https://github.com/mingdeyu/DGP.

stat.ML↗

arXiv2022

Geometrically adapted Langevin dynamics for Markov chain Monte Carlo simulations

Markov Chain Monte Carlo (MCMC) is one of the most powerful methods to sample from a given probability distribution, of which the Metropolis Adjusted Langevin Algorithm (MALA) is a variant wherein the gradient of the distribution is used towards faster convergence. However, being set up in the Euclidean framework, MALA might perform poorly in higher dimensional problems or in those involving anisotropic densities as the underlying non-Euclidean aspects of the geometry of the sample space remain unaccounted for. We make use of concepts from differential geometry and stochastic calculus on Riemannian manifolds to geometrically adapt a stochastic differential equation with a non-trivial drift term. This adaptation is also referred to as a stochastic development. We apply this method specifically to the Langevin diffusion equation and arrive at a geometrically adapted Langevin dynamics. This new approach far outperforms MALA, certain manifold variants of MALA, and other approaches such as Hamiltonian Monte Carlo (HMC), its adaptive variant the no-U-turn sampler (NUTS) implemented in Stan, especially as the dimension of the problem increases where often GALA is actually the only successful method. This is evidenced through several numerical examples that include parameter estimation of a broad class of probability distributions and a logistic regression problem.

stat.AP↗

arXiv2021

Linked Gaussian Process Emulation for Systems of Computer Models using Matérn Kernels and Adaptive Design

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 of linked Gaussian process surrogates with reduced computational costs on running expensive computer systems, by allocating runs and refining emulators of individual sub-models based on their heterogeneous functional complexity.

stat.ME↗

arXiv2020

Performance analysis of Volna-OP2 -- massively parallel code for tsunami modelling

The software package Volna-OP2 is a robust and efficient code capable of simulating the complete life cycle of a tsunami whilst harnessing the latest High Performance Computing (HPC) architectures. In this paper, a comprehensive error analysis and scalability study of the GPU version of the code is presented. A novel decomposition of the numerical errors into the dispersion and dissipation components is explored. Most tsunami codes exhibit amplitude smearing and/or phase lagging/leading, so the decomposition shown here is a new approach and novel tool for explaining these occurrences. It is the first time that the errors of a tsunami code have been assessed in this manner. To date, Volna-OP2 has been widely used by the tsunami modelling community. In particular its computational efficiency has allowed various sensitivity analyses and uncertainty quantification studies. Due to the number of simulations required, there is always a trade-off between accuracy and runtime when carrying out these statistical studies. The analysis presented in this paper will guide the user towards an acceptable level of accuracy within a given runtime.

physics.comp-ph↗

arXiv2019

Computationally efficient surrogate-based optimization of coastal storm waves heights and run-ups

Storm surges cause coastal inundations due to the setup of the water surface resulting from atmospheric pressure, surface winds and breaking waves. The latter is particularly difficult to be accounted for. For instance, it was observed that during Typhoon Haiyan (2013, Philippines), a stretch of coral reef near the coast, which was expected to protect the coastal communities, actually amplified the waves. The propagation and breaking process of such large nearshore waves can be successfully captured by a phase-resolving wave model. Building defences requires estimating not only the maximum storm surge height, but also maxima of breaking wave height and run-up on land, under consideration of a variety of storm characteristics. However, the computational complexity of the simulator makes optimization tasks impractical. To find the maximum breaking wave (bore) height and the maximum run-up, we employ optim-MICE, a new surrogate-based optimization scheme based on Gaussian Process emulation and information theory. In two idealised settings, we efficiently identify the conditions that create the largest storm waves at the coast using a minimal number of simulations. This is the first surrogate-based optimization of storm waves. It opens the door to previously inconceivable coastal risk assessments.

stat.AP↗

arXiv2019

Surrogate-based Optimization using Mutual Information for Computer Experiments (optim-MICE)

The computational burden of running a complex computer model can make optimization impractical. Gaussian Processes (GPs) are statistical surrogates (also known as emulators) that alleviate this issue since they cheaply replace the computer model. As a result, the exploration vs. exploitation trade-off strategy can be accelerated by building a GP surrogate. In this paper, we propose a new surrogate-based optimization scheme that minimizes the number of evaluations of the computationally expensive function. Taking advantage of parallelism of the evaluation of the unknown function, the uncertain regions are explored simultaneously, and a batch of input points is chosen using Mutual Information for Computer Experiments (MICE), a sequential design algorithm which maximizes the information theoretic Mutual Information over the input space. The computational efficiency of interweaving the optimization scheme with MICE (optim-MICE) is examined and demonstrated on test functions. Optim-MICE is compared with state-of-the-art heuristics such as Efficient Global Optimization (EGO) and GP-Upper Confidence Bound (GP-UCB). We demonstrate that optim-MICE outperforms these schemes on a large range of computational experiments.

stat.CO↗

arXiv2018

Computer model calibration with large non-stationary spatial outputs: application to the calibration of a climate model

Bayesian calibration of computer models tunes unknown input parameters by comparing outputs with observations. For model outputs that are distributed over space, this becomes computationally expensive because of the output size. To overcome this challenge, we employ a basis representation of the model outputs and observations: we match these decompositions to carry out the calibration efficiently. In the second step, we incorporate the non-stationary behaviour, in terms of spatial variations of both variance and correlations, in the calibration. We insert two integrated nested Laplace approximation-stochastic partial differential equation parameters into the calibration. A synthetic example and a climate model illustration highlight the benefits of our approach.

stat.ME↗

arXiv2016

Dimension reduction for Gaussian process emulation: an application to the influence of bathymetry on tsunami heights

High accuracy complex computer models, or simulators, require large resources in time and memory to produce realistic results. Statistical emulators are computationally cheap approximations of such simulators. They can be built to replace simulators for various purposes, such as the propagation of uncertainties from inputs to outputs or the calibration of some internal parameters against observations. However, when the input space is of high dimension, the construction of an emulator can become prohibitively expensive. In this paper, we introduce a joint framework merging emulation with dimension reduction in order to overcome this hurdle. The gradient-based kernel dimension reduction technique is chosen due to its ability to drastically decrease dimensionality with little loss in information. The Gaussian process emulation technique is combined with this dimension reduction approach. Our proposed approach provides an answer to the dimension reduction issue in emulation for a wide range of simulation problems that cannot be tackled using existing methods. The efficiency and accuracy of the proposed framework is demonstrated theoretically, and compared with other methods on an elliptic partial differential equation (PDE) problem. We finally present a realistic application to tsunami modeling. The uncertainties in the bathymetry (seafloor elevation) are modeled as high-dimensional realizations of a spatial process using a geostatistical approach. Our dimension-reduced emulation enables us to compute the impact of these uncertainties on resulting possible tsunami wave heights near-shore and on-shore. We observe a significant increase in the spread of uncertainties in the tsunami heights due to the contribution of the bathymetry uncertainties. These results highlight the need to include the effect of uncertainties in the bathymetry in tsunami early warnings and risk assessments.

stat.CO↗

arXiv2016

Quantifying Uncertainties in the 2004 Sumatra-Andaman Earthquake Source Parameters by Stochastic Inversion

Usual inversion for earthquake source parameters from tsunami wave data incorporates subjective elements. Noisy and possibly insufficient data also results in instability and non-uniqueness in most deterministic inversions. Here we employ the satellite altimetry data for the 2004 Sumatra-Andaman tsunami event to invert the source parameters. Using a finite fault model that represents the extent of rupture and the geometry of the trench, we perform a non-linear joint inversion of the slips, rupture velocities and rise times with minimal a priori constraints. Despite persistently good waveform fits, large variance and skewness in the joint parameter distribution constitute a remarkable feature of the inversion. These uncertainties suggest the need for objective inversion strategies that should incorporate more sophisticated physical models in order to significantly improve the performance of early warning systems.

physics.geo-ph↗