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DOE OSTI2014

Breaking Computational Barriers: Real-time Analysis and Optimization with Large-scale Nonlinear Models via Model Reduction

Model reduction for dynamical systems is a promising approach for reducing the computational cost of large-scale physics-based simulations to enable high-fidelity models to be used in many- query (e.g., Bayesian inference) and near-real-time (e.g., fast-turnaround simulation) contexts. While model reduction works well for specialized problems such as linear time-invariant systems, it is much more difficult to obtain accurate, stable, and efficient reduced-order models (ROMs) for systems with general nonlinearities. This report describes several advances that enable nonlinear reduced-order models (ROMs) to be deployed in a variety of time-critical settings. First, we present an error bound for the Gauss-Newton with Approximated Tensors (GNAT) nonlinear model reduction technique. This bound allows the state-space error for the GNAT method to be quantified when applied with the backward Euler time-integration scheme. Second, we present a methodology for preserving classical Lagrangian structure in nonlinear model reduction. This technique guarantees that important properties--such as energy conservation and symplectic time-evolution maps--are preserved when performing model reduction for models described by a Lagrangian formalism (e.g., molecular dynamics, structural dynamics). Third, we present a novel technique for decreasing the temporal complexity --defined as the number of Newton-like iterations performed over the course of the simulation--by exploiting time-domain data. Fourth, we describe a novel method for refining projection-based reduced-order models a posteriori using a goal-oriented framework similar to mesh-adaptive h -refinement in finite elements. The technique allows the ROM to generate arbitrarily accurate solutions, thereby providing the ROM with a 'failsafe' mechanism in the event of insufficient training data. Finally, we present the reduced-order model error surrogate (ROMES) method for statistically quantifying reduced- order-model errors. This enables ROMs to be rigorously incorporated in uncertainty-quantification settings, as the error model can be treated as a source of epistemic uncertainty. This work was completed as part of a Truman Fellowship appointment. We note that much additional work was performed as part of the Fellowship. One salient project is the development of the Trilinos-based model-reduction software module Razor , which is currently bundled with the Albany PDE code and currently allows nonlinear reduced-order models to be constructed for any application supported in Albany. Other important projects include the following: 1. ROMES-equipped ROMs for Bayesian inference: K. Carlberg, M. Drohmann, F. Lu (Lawrence Berkeley National Laboratory), M. Morzfeld (Lawrence Berkeley National Laboratory). 2. ROM-enabled Krylov-subspace recycling: K. Carlberg, V. Forstall (University of Maryland), P. Tsuji, R. Tuminaro. 3. A pseudo balanced POD method using only dual snapshots: K. Carlberg, M. Sarovar. 4. An analysis of discrete v. continuous optimality in nonlinear model reduction: K. Carlberg, M. Barone, H. Antil (George Mason University). Journal articles for these projects are in progress at the time of this writing.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2014

Planck 2013 results. XV. CMB power spectra and likelihood

This paper presents the Planck 2013 likelihood, a complete statistical description of the two-point correlation function of the CMB temperature fluctuations that accounts for all known relevant uncertainties, both instrumental and astrophysical in nature. We use this likelihood to derive our best estimate of the CMB angular power spectrum from Planck over three decades in multipole moment, &ell;, covering 2 ≤ &ell; ≤ 2500. The main source of uncertainty at &ell; ≤ 1500 is cosmic variance. Uncertainties in small-scale foreground modelling and instrumental noise dominate the error budget at higher &ell;s. For &ell; < 50, our likelihood exploits all Planck frequency channels from 30 to 353 GHz, separating the cosmological CMB signal from diffuse Galactic foregrounds through a physically motivated Bayesian component separation technique. At &ell; ≤ 50, we employ a correlated Gaussian likelihood approximation based on a fine-grained set of angular cross-spectra derived from multiple detector combinations between the 100, 143, and 217 GHz frequency channels, marginalising over power spectrum foreground templates. We validate our likelihood through an extensive suite of consistency tests, and assess the impact of residual foreground and instrumental uncertainties on the final cosmological parameters. We find good internal agreement among the high-&ell; cross-spectra with residuals below a few μK 2 at &ell; ≲ 1000, in agreement with estimated calibration uncertainties. We compare our results with foreground-cleaned CMB maps derived from all Planck frequencies, as well as with cross-spectra derived from the 70 GHz Planck map, and find broad agreement in terms of spectrum residuals and cosmological parameters. We further show that the best-fit CDM cosmology is in excellent agreement with preliminary Planck EE and TE polarisation spectra. We find that the standard ΛCDM cosmology is well constrained by Planck from the measurements at &ell; ≲ 1500. One specific example is the spectral index of scalar perturbations, for which we report a 5.4σ deviation from scale invariance, n s = 1. Increasing the multipole range beyond &ell; ≃ 1500 does not increase our accuracy for the ΛCDM parameters, but instead allows us to study extensions beyond the standard model. We find no indication of significant departures from the ΛCDM framework. Finally, we report a tension between the Planck best-fit ΛCDM model and the low-&ell; spectrum in the form of a power deficit of 5–10% at &ell; ≲ 40, with a statistical significance of 2.5–3σ. Without a theoretically motivated model for this power deficit, we do not elaborate further on its cosmological implications, but note that this is our most puzzling finding in an otherwise remarkably consistent data set.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2026

Field testing and validation of a low-cost MPC for demand flexibility for grid-interactive K-12 schools

K-12 school buildings account for the highest energy consumption within the public sector. Implementing advanced HVAC controls in grid-interactive K-12 schools could bring substantial economic advantages and grid flexibility. Our previous study demonstrated that a low-cost model predictive control (MPC) solution, which coordinates multiple packaged units, can enable demand flexibility without major hardware upgrades. However, a significant gap remains between academic pilots and market-ready scalable solutions. This paper extends the previous single-site pilot to a multi-site demonstration involving three school campuses (95 total units) through a commercial technology transfer process. Addressing the challenge of verifying performance with sparse field data, we present a new statistical approach using Bayesian methods to estimate the MPC’s effect on peak demand. Unlike traditional methods, this approach robustly quantifies uncertainty in non-normal, limited datasets. The results confirm the solution’s replicability, achieving a 21.6–38.9% reduction in HVAC peak demand (10.8–22.1% at the site-level) with > 98% probability across diverse locations. Finally, we document critical barriers to scaling software-as-a-service (SaaS) solutions–such as API instability and diverse legacy systems–and offer practical strategies to accelerate the commercial adoption of grid-interactive efficient buildings.

Ham, Sang Woo↗

DOE OSTI2014

A statistical analysis of seeds and other high-contrast exoplanet surveys: massive planets or low-mass brown dwarfs?

We conduct a statistical analysis of a combined sample of direct imaging data, totalling nearly 250 stars. The stars cover a wide range of ages and spectral types, and include five detections (κ And b, two ∼60 M {sub J} brown dwarf companions in the Pleiades, PZ Tel B, and CD–35 2722B). For some analyses we add a currently unpublished set of SEEDS observations, including the detections GJ 504b and GJ 758B. We conduct a uniform, Bayesian analysis of all stellar ages using both membership in a kinematic moving group and activity/rotation age indicators. We then present a new statistical method for computing the likelihood of a substellar distribution function. By performing most of the integrals analytically, we achieve an enormous speedup over brute-force Monte Carlo. We use this method to place upper limits on the maximum semimajor axis of the distribution function derived from radial-velocity planets, finding model-dependent values of ∼30-100 AU. Finally, we model the entire substellar sample, from massive brown dwarfs to a theoretically motivated cutoff at ∼5 M {sub J}, with a single power-law distribution. We find that p(M, a)∝M {sup –0.65} {sup ±} {sup 0.60} a {sup –0.85} {sup ±} {sup 0.39} (1σ errors) provides an adequate fit to our data, with 1.0%-3.1% (68% confidence) of stars hosting 5-70 M {sub J} companions between 10 and 100 AU. This suggests that many of the directly imaged exoplanets known, including most (if not all) of the low-mass companions in our sample, formed by fragmentation in a cloud or disk, and represent the low-mass tail of the brown dwarfs.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2018

The Coupled Location/Depth/Yield Problem for North Korea’s Declared Nuclear Tests

On 3 September 2017, the Democratic People's Republic of Korea (DPRK) conducted its sixth and largest declared nuclear test at the Pung'gye Ri test site. Recently, we have been using regional waveform envelopes to estimate the explosive yield and overburden of chemical and nuclear explosions by coupling explosion source models to propagation parameters. Like most yield determination methods, there can be tradeoffs between yield and depth, leading to uncertainties in both parameters. The relative locations are well-constrained by small timing differences in seismic-phase arrivals at stations that recorded multiple events, but there are potential uncertainties on the absolute locations. Depths are poorly constrained by the relative arrival times. In this study, we have performed a coupled location and yield analysis of the DPRK nuclear tests. We use correlation methods to get highly accurate travel times and relative locations using a Bayesian location method. Then, while keeping the relative locations of the six tests constant, we consider the consequences of shifts to the absolute locations on the resulting overburden for each event. Given that overburden, we determine the yield that minimizes the waveform misfit. We also test and compare a number of explosion source models. By considering the coupled location/depth/yield problem, we reduce uncertainties in the absolute locations, and yield and depth estimates of the events. Based on statistical analysis, we estimate that the 2017 test has a yield of 125 kilotons (equivalent TNT) with a 1 sigma uncertainty range of 103-150 ktons at about 600 m of overburden.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗

DOE OSTI2020

Characterization of Partially Observed Epidemics - Application to COVID-19

This report documents a statistical method for the "real-time" characterization of partially observed epidemics. Observations consist of daily counts of symptomatic patients, diagnosed with the disease. Characterization, in this context, refers to estimation of epidemiological parameters that can be used to provide short-term forecasts of the ongoing epidemic, as well as to provide gross information for the time-dependent infection rate. The characterization problem is formulated as a Bayesian inverse problem, and is predicated on a model for the distribution of the incubation period. The model parameters are estimated as distributions using a Markov Chain Monte Carlo (MCMC) method, thus quantifying the uncertainty in the estimates. The method is applied to the COVID-19 pandemic of 2020, using data at the country, provincial (e.g., states) and regional (e.g. county) levels. The epidemiological model includes a stochastic component due to uncertainties in the incubation period. This model-form uncertainty is accommodated by a pseudo-marginal Metropolis-Hastings MCMC sampler, which produces posterior distributions that reflect this uncertainty. We approximate the discrepancy between the data and the epidemiological model using Gaussian and negative binomial error models; the latter was motivated by the over-dispersed count data. For small daily counts we find the performance of the calibrated models to be similar for the two error models. For large daily counts the negative-binomial approximation is numerically unstable unlike the Gaussian error model. Application of the model at the country level (for the United States, Germany, Italy, etc.) generally provided accurate forecasts, as the data consisted of large counts which suppressed the day-to-day variations in the observations. Further, the bulk of the data is sourced over the duration before the relaxation of the curbs on population mixing, and is not confounded by any discernible country-wide second wave of infections. At the state-level, where reporting was poor or which evinced few infections (e.g., New Mexico), the variance in the data posed some, though not insurmountable, difficulties, and forecasts were able to capture the data with large uncertainty bounds. The method was found to be sufficiently sensitive to discern the flattening of the infection and epidemic curve due to shelter-in-place orders after around 90% quantile for the incubation distribution (about 10 days for COVID-19). The proposed model was also used at a regional level to compare the forecasts for the central and north-west regions of New Mexico. Modeling the data for these regions illustrated different disease spread dynamics captured by the model. While in the central region the daily counts peaked in the late April, in the north-west region the ramp-up continued for approximately three more weeks.

59 BASIC BIOLOGICAL SCIENCES↗

NASA NTRS2005

An Ensemble Approach to Building Mercer Kernels with Prior Information

This paper presents a new methodology for automatic knowledge driven data mining based on the theory of Mercer Kernels, which are highly nonlinear symmetric positive definite mappings from the original image space to a very high, possibly dimensional feature space. we describe a new method called Mixture Density Mercer Kernels to learn kernel function directly from data, rather than using pre-defined kernels. These data adaptive kernels can encode prior knowledge in the kernel using a Bayesian formulation, thus allowing for physical information to be encoded in the model. Specifically, we demonstrate the use of the algorithm in situations with extremely small samples of data. We compare the results with existing algorithms on data from the Sloan Digital Sky Survey (SDSS) and demonstrate the method's superior performance against standard methods. The code for these experiments has been generated with the AUTOBAYES tool, which automatically generates efficient and documented C/C++ code from abstract statistical model specifications. The core of the system is a schema library which contains templates for learning and knowledge discovery algorithms like different versions of EM, or numeric optimization methods like conjugate gradient methods. The template instantiation is supported by symbolic-algebraic computations, which allows AUTOBAYES to find closed-form solutions and, where possible, to integrate them into the code.

Srivastava, Ashok N.↗

DOE OSTI2019

Impacts of Observational Constraints Related to Sea Level on Estimates of Climate Sensitivity

Reduced complexity climate models are necessary tools for quantifying decision-relevant uncertainties, given their flexibility, computational efficiency, and suitability for large-ensemble frameworks necessary for statistical estimation using resampling techniques (e.g. Markov chain Monte Carlo—MCMC). Here we document a new version of the simple, open-source, global climate model Hector, coupled with a one-dimensional diffusive heat and energy balance model (Diffusion Ocean Energy balance CLIMate model; DOECLIM) and a sea-level change module (Building blocks for Relevant Ice and Climate Knowledge; BRICK) that also represents contributions from thermal expansion, glaciers and ice caps, and polar ice sheets. We apply a Bayesian calibration approach to quantify model uncertainties surrounding 39 model parameters with prescribed radiative forcing, using observational information from global surface temperature, ocean heat uptake, and sea-level change. Furthermore, we find sea-level change as an observational constraint sharpens inference for the upper tail of posterior climate sensitivity estimates (the 97.5 percentile is tightened from 6.5 K to 5.3 K). The addition of sea-level change as an observational constraint also has implications for probabilistic projections of global surface temperature (the 97.5 percentile for RCP8.5 2100 temperature decreases 0.3 K) and sea-level rise (the 97.5 percentile for RCP8.5 2100 sea level decreases 0.5 m).

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2024

Toward machine-learning-assisted PW-class high-repetition-rate experiments with solid targets

We present progress in utilizing a machine learning (ML) assisted optimization framework to study the trends in a parameter space defined by spectrally shaped, high-intensity, petawatt-class (8 J, 45 fs) laser pulses interacting with solid targets and give the first simulation-based overview of predicted trends. A neural network (NN) incorporating uncertainty quantification is trained to predict the number of hot electrons generated by the laser–target interaction as a function of pulse shaping parameters. The predictions of this NN serve as the basis function for a Bayesian optimization framework to navigate this space. For post-experimental evaluation, we compare two separate neural network (NN) models. One is based solely on data from experiments, and the other is trained only on ensemble particle-in-cell simulations. Reviewing the predicted and observed trends across the experiment-capable laser parameter search space, we find that both ML models predict a maximal increase in hot electron generation at a level of approximately 12%–18%; however, no statistically significant enhancement was observed in experiments. On direct comparison of the NN models, the average discrepancy is 8.5%, with a maximum of 30%. Since shot-to-shot fluctuations in experiments affect the observations, we evaluate the behavior of our optimization framework by performing virtual experiments that vary the number of repeated observations and the noise levels. Here, we discuss the implications of such a framework for future autonomous exploration platforms in high-repetition-rate experiments.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS2016

Modeling Forest Biomass and Growth: Coupling Long-Term Inventory and Lidar Data

Combining spatially-explicit long-term forest inventory and remotely sensed information from Light Detection and Ranging (LiDAR) datasets through statistical models can be a powerful tool for predicting and mapping above-ground biomass (AGB) at a range of geographic scales. We present and examine a novel modeling approach to improve prediction of AGB and estimate AGB growth using LiDAR data. The proposed model accommodates temporal misalignment between field measurements and remotely sensed data-a problem pervasive in such settings-by including multiple time-indexed measurements at plot locations to estimate AGB growth. We pursue a Bayesian modeling framework that allows for appropriately complex parameter associations and uncertainty propagation through to prediction. Specifically, we identify a space-varying coefficients model to predict and map AGB and its associated growth simultaneously. The proposed model is assessed using LiDAR data acquired from NASA Goddard's LiDAR, Hyper-spectral & Thermal imager and field inventory data from the Penobscot Experimental Forest in Bradley, Maine. The proposed model outperformed the time-invariant counterpart models in predictive performance as indicated by a substantial reduction in root mean squared error. The proposed model adequately accounts for temporal misalignment through the estimation of forest AGB growth and accommodates residual spatial dependence. Results from this analysis suggest that future AGB models informed using remotely sensed data, such as LiDAR, may be improved by adapting traditional modeling frameworks to account for temporal misalignment and spatial dependence using random effects.

Babcock, Chad↗

DOE OSTI2012

The application of Plant Reliability Data Information System (PRINS) to CANDU reactor

As risk-informed applications (RIAs) are actively implanted in the nuclear industry, an issue associated with technical adequacy of Probabilistic Safety Assessment (PSA) arises in its modeling and data sourcing. In Korea, PSA for all Korean NPPs has been completed and KHNP(Korea Hydro and Nuclear Power Plant Company) developed the database called the Plant Reliability Data Information System (PRinS). It has several characteristics that distinguish it from other database system such as NPRDs (INPO,1994), PRIS (IAEA), and SRDF (EdF). This database has the function of systematic data management such as automatic data-gathering, periodic data deposition and updating, statistical analysis including Bayesian method, and trend analysis of failure rate or unavailability. In recent PSA for CANDU reactor, the component failure data of EPRI ALWR URD and Component Reliability Database were preferentially used as generic data set. The error factor for most component failure data was estimated by using the information NUREG/CR-4550 and NUREG/CR-4639. Also, annual trend analysis was performed for the functional losses of components using the statistical analysis and chart module of PRinS. Furthermore, the database has been updated regularly and maintained as a living program to reflect the current status. This paper presents the failure data analysis using PRinS which provides Bayesian analysis on main components in the CANDU reactor. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2015

On the Methodology to Calculate the Covariance of Estimated Resonance Parameters

Principles to determine resonance parameters and their covariance from experimental data are discussed. Different methods to propagate the covariance of experimental parameters are compared. A full Bayesian statistical analysis reveals that the level to which the initial uncertainty of the experimental parameters propagates, strongly depends on the experimental conditions. For high precision data the initial uncertainties of experimental parameters, like a normalization factor, has almost no impact on the covariance of the parameters in case of thick sample measurements and conventional uncertainty propagation or full Bayesian analysis. The covariances derived from a full Bayesian analysis and least-squares fit are derived under the condition that the model describing the experimental observables is perfect. When the quality of the model can not be verified a more conservative method based on a renormalization of the covariance matrix is recommended to propagate fully the uncertainty of experimental systematic effects. Finally, neutron resonance transmission analysis is proposed as an accurate method to validate evaluated data libraries in the resolved resonance region.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2024

Scaling and merging time-resolved pink-beam diffraction with variational inference

Time-resolved x-ray crystallography (TR-X) at synchrotrons and free electron lasers is a promising technique for recording dynamics of molecules at atomic resolution. While experimental methods for TR-X have proliferated and matured, data analysis is often difficult. Extracting small, time-dependent changes in signal is frequently a bottleneck for practitioners. Recent work demonstrated this challenge can be addressed when merging redundant observations by a statistical technique known as variational inference (VI). However, the variational approach to time-resolved data analysis requires identification of successful hyperparameters in order to optimally extract signal. In this case study, we present a successful application of VI to time-resolved changes in an enzyme, DJ-1, upon mixing with a substrate molecule, methylglyoxal. We present a strategy to extract high signal-to-noise changes in electron density from these data. Furthermore, we conduct an ablation study, in which we systematically remove one hyperparameter at a time to demonstrate the impact of each hyperparameter choice on the success of our model. We expect this case study will serve as a practical example for how others may deploy VI in order to analyze their time-resolved diffraction data.

47 OTHER INSTRUMENTATION↗

DOE OSTI2016

The orbit and transit prospects for β pictoris b constrained with one milliarcsecond astrometry

A principal scientific goal of the Gemini Planet Imager (GPI) is obtaining milliarcsecond astrometry to constrain exoplanet orbits. However, astrometry of directly imaged exoplanets is subject to biases, systematic errors, and speckle noise. Here, we describe an analytical procedure to forward model the signal of an exoplanet that accounts for both the observing strategy (angular and spectral differential imaging) and the data reduction method (Karhunen–Loève Image Projection algorithm). We use this forward model to measure the position of an exoplanet in a Bayesian framework employing Gaussian processes and Markov-chain Monte Carlo to account for correlated noise. In the case of GPI data on β Pic b, this technique, which we call Bayesian KLIP-FM Astrometry (BKA), outperforms previous techniques and yields 1σ errors at or below the one milliarcsecond level. We validate BKA by fitting a Keplerian orbit to 12 GPI observations along with previous astrometry from other instruments. The statistical properties of the residuals confirm that BKA is accurate and correctly estimates astrometric errors. Our constraints on the orbit of β Pic b firmly rule out the possibility of a transit of the planet at 10-σ significance. However, we confirm that the Hill sphere of β Pic b will transit, giving us a rare chance to probe the circumplanetary environment of a young, evolving exoplanet. As a result, we provide an ephemeris for photometric monitoring of the Hill sphere transit event, which will begin at the start of April in 2017 and finish at the end of January in 2018.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1991

Autoclass: An automatic classification system

The task of inferring a set of classes and class descriptions most likely to explain a given data set can be placed on a firm theoretical foundation using Bayesian statistics. Within this framework, and using various mathematical and algorithmic approximations, the AutoClass System searches for the most probable classifications, automatically choosing the number of classes and complexity of class descriptions. A simpler version of AutoClass has been applied to many large real data sets, has discovered new independently-verified phenomena, and has been released as a robust software package. Recent extensions allow attributes to be selectively correlated within particular classes, and allow classes to inherit, or share, model parameters through a class hierarchy. The mathematical foundations of AutoClass are summarized.

Stutz, John↗

NASA NTRS1991

Bayesian classification theory

The task of inferring a set of classes and class descriptions most likely to explain a given data set can be placed on a firm theoretical foundation using Bayesian statistics. Within this framework and using various mathematical and algorithmic approximations, the AutoClass system searches for the most probable classifications, automatically choosing the number of classes and complexity of class descriptions. A simpler version of AutoClass has been applied to many large real data sets, has discovered new independently-verified phenomena, and has been released as a robust software package. Recent extensions allow attributes to be selectively correlated within particular classes, and allow classes to inherit or share model parameters though a class hierarchy. We summarize the mathematical foundations of AutoClass.

Hanson, Robin↗

NASA NTRS2007

Bayesian Analysis of the Cosmic Microwave Background

There is a wealth of cosmological information encoded in the spatial power spectrum of temperature anisotropies of the cosmic microwave background! Experiments designed to map the microwave sky are returning a flood of data (time streams of instrument response as a beam is swept over the sky) at several different frequencies (from 30 to 900 GHz), all with different resolutions and noise properties. The resulting analysis challenge is to estimate, and quantify our uncertainty in, the spatial power spectrum of the cosmic microwave background given the complexities of "missing data", foreground emission, and complicated instrumental noise. Bayesian formulation of this problem allows consistent treatment of many complexities including complicated instrumental noise and foregrounds, and can be numerically implemented with Gibbs sampling. Gibbs sampling has now been validated as an efficient, statistically exact, and practically useful method for low-resolution (as demonstrated on WMAP 1 and 3 year temperature and polarization data). Continuing development for Planck - the goal is to exploit the unique capabilities of Gibbs sampling to directly propagate uncertainties in both foreground and instrument models to total uncertainty in cosmological parameters.

methods - statistical↗

NASA NTRS2017

Online Multi-Modal Learning and Adaptive Information Trajectory Planning for Autonomous Exploration

In robotic information gathering missions, scientists are typically interested in understanding variables which require proxy measurements from specialized sensor suites to estimate. However, energy and time constraints limit how often these sensors can be used in a mission. Robots are also equipped with cheaper to use navigation sensors such as cameras. In this paper, we explore a challenging planning problem in which a robot is required to learn about a scientific variable of interest in an initially unknown environment by planning informative paths and deciding when and where to use its sensors. To tackle this we present two innovations: a Bayesian generative model framework to automatically learn correlations between expensive science sensors and cheaper to use navigation sensors online, and a sampling based approach to plan for multiple sensors while handling long horizons and budget constraints. Our approach does not grow in complexity with data and is anytime making it highly applicable to field robotics. We tested our approach extensively in simulation and validated it with real data collected during the 2014 Mojave Volatiles Prospector Mission. Our planning algorithm performs statistically significantly better than myopic approaches and at least as well as a coverage-based algorithm in an initially unknown environment while having added advantages of being able to exploit prior knowledge and handle other intricacies of the real world without further algorithmic modifications.

learning↗