Tuesday, Aug 5: 8:30 AM - 10:20 AM
4084
Contributed Papers
Music City Center
Room: CC-210
This session brings together research on statistical modeling tools for complex systems and new insights on inference and uncertainty quantification for problems in the physical and engineering sciences.
Main Sponsor
Section on Physical and Engineering Sciences
Presentations
Gaussian process (GP) regression is widely used for modeling responses in both physical and computer experiments. In practice, data from physical experiments may include replications and be subject to censoring due to equipment limitations or contextual constraints. Motivated by real-world manufacturing data, we develop a GP modeling framework that efficiently analyzes replicated and potentially censored data. Our approach leverages recent advances in likelihood-based inference and latent-variable methods for GPs, effectively exploiting replication while rigorously incorporating censoring information-analogous to exact simulation techniques for truncated distributions. We demonstrate the effectiveness of our method on synthetic manufacturing data, showing that it provides enhanced prediction, uncertainty quantification, and computational scalability, making it well-suited for large-scale applications with structured replication and incomplete data.
Keywords
Censored data
Gaussian process
Replication
Truncated multivariate normal
Many problems in science and engineering involve observing sample trajectories from processes with partially known dynamics. Often the systems
are driven by an ODE with nonlinear dependence between elements of the state vector, and require solutions require expert knowledge to build mathematical
models. Recently, a growing literature has explored solving such systems using machine learning, with results suggesting data-driven modeling can
facilitate faster discovery. However, sparsity, missing data, and observation error limit existing methods.
We propose to address these challenges in two stages: First, we address sparsity and observation errors using data assimilation (DA) to in-fill trajectories of observed data. Second, we estimate dynamics using an MCMC-based model based on spline estimation and a sparse prior for the dynamics of the ODE. We also strengthen the sparse prior of the MCMC model with additional knowledge of the closure terms to improve model estimation. Considering the DA trajectories as additional priors, we average over DA ensembles to improve forecasting.
Keywords
Spline estimation
Gaussian processes
Koopman operators
dynamical systems
missing data
uncertainty quantification
The Electric Propulsion Electrostatic Analyzer Experiment (ÈPÈE) is a compact ion energy bandpass filter deployed on the International Space Station (ISS) in March 2023 and providing continuous measurements through April 2024. This period coincides with the Solar Cycle 25 maximum, capturing unique observations of solar activity extremes in the mid- to low-latitude regions of the topside ionosphere. Derived plasma parameters from in-situ measurements enhance understanding of local space weather and its impact on satellite navigation, communication, and GPS accuracy. We present a statistical pipeline for processing ÈPÈE data, addressing challenges such as instrument noise floor, temporal data density, and signal extraction. Unlike traditional methods that discard data due to noise, our approach learns a baseline noise and fits the surface using a scaled Vecchia Gaussian Process, enabling recovery of previously discarded values and creating possibilities for noise-assisted ionospheric monitoring.
Keywords
signal processing
Gaussian Processes
background estimation
time series
astrophysics
Ionospheric science
Gaussian processes (GPs) are canonical as surrogates for computer experiments because they enjoy a degree of analytic tractability. But that breaks when the response surface is constrained, say to be monotonic. Here, we provide a "mono-GP" construction for a single input that is highly efficient even though the calculations are non-analytic. Key ingredients include transformation of a reference process and elliptical slice sampling. We then show how mono-GP may be deployed effectively in two ways. One is additive, extending monotonicity to more inputs; the other is as a prior on injective latent warping variables in a deep Gaussian process for (non-monotonic, multi-input) non-stationary surrogate modeling. We provide illustrative and benchmarking examples throughout, showing that our methods yield improved performance over the state-of-the-art on examples from those two classes of problems.
Keywords
computer experiment
surrogate modeling
constrained response surface
elliptical slice sampling
uncertainty quantification
Bayesian inference
Estimating galaxy redshifts is crucial for constraining key physical quantities like dark energy. Modern spectroscopic telescopes such as the James Webb Space Telescope (JWST) are producing massive amounts of high-resolution data that enable precise redshift estimation. However, this is only possible when spectral lines are present in the data, which is not known a priori. We adopt a fully Bayesian approach to estimate redshift, using Bayes factors to test for multiple spectral lines. The main challenge is computational, as the known physical constraints between redshift and spectral line signal intensities lead to a highly multimodal posterior distribution. To address this, we develop a fast Laplace approximation-based method that explicitly accounts for multimodality and apply it to new JWST spectra.
Keywords
Bayes factors
Astrostatistics
Laplace approximation
Inferring the distortion of imaged galaxies due to weak gravitational lensing is a challenging inverse problem involving pixelization, instrument bias, and a low signal-to-noise ratio. Most traditional approaches to this task produce point estimates of weak lensing shear and convergence by measuring, averaging, and calibrating galaxy ellipticities, a multistage procedure that is subject to image noise, selection bias, and model misspecification. As an alternative, we propose a Bayesian method for weak lensing inference that jointly estimates shear and convergence maps from multiband images using a type of likelihood-free amortized variational inference called neural posterior estimation (NPE). NPE is computationally efficient due to its utilization of deep neural networks and implicit marginalization of nuisance latent variables, and it provides estimates of posterior uncertainty that can be propagated to downstream cosmological analyses. When evaluated on synthetic images from the LSST-DESC DC2 Simulated Sky Survey, the proposed algorithm produces posterior shear and convergence maps that are well-calibrated and consistent with the ground truth.
Keywords
neural posterior estimation
weak gravitational lensing
likelihood-free inference
variational inference
cosmology
astronomical images
Exploring the full parameter space of planet formation conditions and processes is computationally impractical as each simulation can take weeks to complete, and the parameter space remains vast. In this work, we propose a framework to infer planet formation conditions while reducing computational costs. Our approach accounts for intrinsic variations in conditions and the stochastic nature of outcomes within a given set of conditions. We employ statistical emulators to model the relationship between planet formation parameters - such as solid normalization, radial distribution of solids, and gas disk depletion - and key observables, including period ratio, transit multiplicity, transit ratio, and hill spacing. Since these observables are inherently stochastic and represented by probability distributions, we first map the stochastic outputs to a reduced-dimensional space. We then use Gaussian processes (GP) to model the relationships within this reduced space. Once the emulators are trained on existing simulation data, we apply a Bayesian modular approach to infer the underlying parameters. Fast GP predictions within the likelihood ensure computationally feasible inference.
Keywords
Emulators
Gaussian Process
Stochastic Simulator
Astrostatistics
Planet formation