Vecchia-approximated Deep Gaussian Processes for Computer Experiments

Deep Gaussian processes (DGPs) upgrade ordinary GPs through functional composition, in which intermediate GP layers warp the original inputs, providing flexibility to model non-stationary dynamics. Two DGP regimes have emerged in recent literature. A “big data” regime, prevalent in machine learning, favors approximate, optimization-based inference for fast, high-fidelity prediction. A “small data” regime, preferred for computer surrogate modeling, deploys posterior integration for enhanced uncertainty quantification (UQ). We aim to bridge this gap by expanding the capabilities of Bayesian DGP posterior inference through the incorporation of the Vecchia approximation, allowing linear computational scaling without compromising accuracy or UQ. We are motivated by surrogate modeling of simulation campaigns with upwards of 100,000 runs – a size too large for previous fully-Bayesian implementations – and demonstrate prediction and UQ superior to that of “big data” competitors. All methods are implemented in the deepgp package on CRAN.</p

Understanding the transient flow behavior of abbreviated impactors for testing of dry-powder inhalers

We present the results of a computer model of the transient flow behavior of abbreviated impactors (AIM) during testing of dry-powder inhalers. The principles of the model were established in a cross-industry study of full-resolution Next Generation Impactors (NGI) and Andersen impactors (ACI). Here, we apply the model to abbreviated impactors that were examined experimentally in a preliminary study of the reduced NGI (rNGI), of the Fast Screening Impactor (FSI), and of the Fast Screening Andersen (FSA) impactor, reported in a companion abstract at this conference (Mitchell et al.). The flow rate rise times of the FSI and FSA predicted by the model were significantly shorter than those of the rNGI and full-resolution impactors NGI and ACI, as expected, and in agreement with experimental results. The correlation between the system volume and flow rate rise time of AIM impactors was good, which suggests that the rise time is mainly associated with evacuation of air out of the impactor system to reduce the pressure by 4 kPa, which is the surrogate DPI resistance. The final nozzle stages and the MOC in the rNGI have high resistance but have only a modest effect because of the small volume between these components and the vacuum outlet. Some quantitative differences between model predictions and experimental results were found, particularly with the rNGI where the experimental results are sparse. The cause of these differences is at present unknown, and further experimental work is needed to develop a fuller understanding of these AIM systems.</p

Shoreline change for Ptolemais headland and to the northeast (VHR images).

DSAS shoreline change transects classified into statistically significant categories based on LRR and 90% LCI, or EPR and 90% ECI as obtained from VHR imagery. Quantified LRR or EPR (metres/year) is plotted on the inset graph with negative values (red) indicating erosion/retreat and positive values (blue) indicating accretion/advance. Shoreline proxy is the waterline. A) Full times series: 1974–2016; B) Recent: 2009–2016 and C) Historic to recent: 1974–2009. Basemap: ©Maxar (25/04/2016), provided by European Space Imaging.</p

Shoreline forecasts for Ptolemais based on recent LRR from VHR images.

A) area southwest and B) northeast of Ptolemais headland. Text shows generalized magnitude of retreat for the backshore cliffline relative to 2019 for different sections of coastline and for 2032 (red) and 2042 (blue). Values only refer to erosion/retreat not advance/accretion: Zones with 0 values show where stability/advance has also been forecast. Values in brackets show the maximum retreat based on the uncertainty bands. Archaeological structures/material forecast to be at risk are also annotated. Basemap: ©Maxar (25/04/2016), provided by European Space Imaging.</p

Shoreline forecasts for Tocra based on recent LRR from VHR images.

Text shows generalized magnitude of retreat for the backshore cliffline relative to 2019 for different sections of coastline and for 2032 (red) and 2042 (blue). Values only refer to erosion/retreat not advance/accretion: Zones with 0 values show where stability/advance has also been forecast. Values in brackets show the maximum retreat based on the uncertainty bands. Archaeological structures/material forecast to be at risk are also annotated. Basemap: ©Maxar (21/03/2020), provided by European Space Imaging.</p

Shoreline change for southwest of Ptolemais (VHR images).

DSAS shoreline change transects classified into statistically significant categories based on LRR and 90% LCI, or EPR and 90% ECI as obtained from VHR imagery. Quantified LRR or EPR (metres/year) is plotted on the inset graph with negative values (red) indicating erosion/retreat and positive values (blue) indicating accretion/advance. Shoreline proxy is the waterline. A) Full times series: 1974–2016; B) Recent: 2009–2016 and C) Historic to recent: 1974–2009. Basemap: ©Maxar (25/04/2016), provided by European Space Imaging.</p

Erosion examples at Apollonia from historic map and VHR imagery.

A) Close-up of the incipient tombolo’s western side and adjacent shoreline (VHR image: ©Maxar [7/11/2019], provided by European Space Imaging). Earlier positions of the eroding backshore scarp are superimposed. Note difference in former scarp positions on the tombolo versus the more stable coastline to the west. B) Excerpt from the Beecheys’ map of Apollonia [6], georeferenced and co-registered to a recent VHR satellite image. Red line marks location of the backshore scarp from the 2019 VHR image. Orange and yellow arrows respectively mark locations where extensive and minor coastal change are suggested by the VHR image–historic map comparison.</p

Study area topography and key placenames.

A) Elevation above sea-level from the NASA Digital Elevation Model (DEM [29]) and overlaid with local fluvial systems as represented by the HydroSHEDS Free Flowing Rivers dataset [30] B) Geological map of the study area (modified from [27]).</p

Summary DSAS results based on Landsat imagery for wider areas around Apollonia, Ptolemais and Tocra.

Summary DSAS results based on Landsat imagery for wider areas around Apollonia, Ptolemais and Tocra.</p

Shoreline change for the wider Ptolemais area (Landsat: 1985–2020).

DSAS shoreline change transects classified into statistically significant categories based on LRR and 90% LCI as obtained from Landsat imagery. Quantified LRR (metres/year) is plotted on the inset graph with negative values (red) indicating erosion/retreat and positive values (blue) indicating accretion/advance. Label Ptolemais indicates the ancient site. Basemap: Sentinel-2 (from the Copernicus Program; 2020 annual composite created using GEE).</p