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Expected information gain estimates and Bayesian optimal experimental design.
Abstract not provided.
Optimal experimental design for prediction based on push-forward probability measures
Incorporating experimental data is essential for increasing the credibility of simulation-aided decision making and design. This paper presents a method which uses a computational model to guide the optimal acquisition of experimental data to produce data-informed predictions of quantities of interest (QoI). Many strategies for optimal experimental design (OED) select data that maximize some utility that measures the reduction in uncertainty of uncertain model parameters, for example the expected information gain between prior and posterior distributions of these parameters. In this paper, we seek to maximize the expected information gained from the pushforward of an initial (prior) density to the push-forward of the updated (posterior) density through the parameter-to-prediction map. The formulation presented is based upon the solution of a specific class of stochastic inverse problems which seeks a probability density that is consistent with the model and the data in the sense that the push-forward of this density through the parameter-to-observable map matches a target density on the observable data. While this stochastic inverse problem forms the mathematical basis for our approach, we develop a one-step algorithm, focused on push-forward probability measures, that leverages inference-for-prediction to bypass constructing the solution to the stochastic inverse problem. A number of numerical results are presented to demonstrate the utility of this optimal experimental design for prediction and facilitate comparison of our approach with traditional OED.
Analysis and Optimization of Seismo-Acoustic Monitoring Networks with Bayesian Optimal Experimental Design
The Bayesian optimal experimental design (OED) problem seeks to identify data, sensor configurations, or experiments which can optimally reduce uncertainty. The goal of OED is to find an experiment that maximizes the expected information gain (EIG) about quantities of interest given prior knowledge about expected data. Therefore, within the context of seismic monitoring, we can use Bayesian OED to configure sensor networks by choosing sensor locations, types, and fidelity in order to improve our ability to identify and locate seismic sources. In this work, we develop the framework necessary to use Bayesian OED to optimize the ability to locate seismic events from arrival time data of detected seismic phases. In order to do utilize Bayesian OED we must develop four elements:1. A likelihood function that describes the uncertainty of detection and travel times; 2. A Bayesian solver that takes a prior and likelihood to identify the posterior; 3. An algorithm to compute EIG; and, 4. An optimizer that finds a sensor network which maximizes EIG. Once we have developed this framework, we can explore many relevant questions to monitoring such as: how and what multiphenomenology data can be used to optimally reduce uncertainty, how to trade off sensor fidelity and earth model uncertainty, and how sensor types, number, and locations influence uncertainty
Analysis and optimization of seismic monitoring networks with Bayesian optimal experimental design
SUMMARY Monitoring networks increasingly aim to assimilate data from a large number of diverse sensors covering many sensing modalities. Bayesian optimal experimental design (OED) seeks to identify data, sensor configurations or experiments which can optimally reduce uncertainty and hence increase the performance of a monitoring network. Information theory guides OED by formulating the choice of experiment or sensor placement as an optimization problem that maximizes the expected information gain (EIG) about quantities of interest given prior knowledge and models of expected observation data. Therefore, within the context of seismo-acoustic monitoring, we can use Bayesian OED to configure sensor networks by choosing sensor locations, types and fidelity in order to improve our ability to identify and locate seismic sources. In this work, we develop the framework necessary to use Bayesian OED to optimize a sensor network’s ability to locate seismic events from arrival time data of detected seismic phases at the regional-scale. This framework requires five elements: (i) A likelihood function that describes the distribution of detection and traveltime data from the sensor network, (ii) A prior distribution that describes a priori belief about seismic events, (iii) A Bayesian solver that uses a prior and likelihood to identify the posterior distribution of seismic events given the data, (iv) An algorithm to compute EIG about seismic events over a data set of hypothetical prior events, (v) An optimizer that finds a sensor network which maximizes EIG. Once we have developed this framework, we explore many relevant questions to monitoring such as: how to trade off sensor fidelity and earth model uncertainty; how sensor types, number and locations influence uncertainty; and how prior models and constraints influence sensor placement.
Active learning path-dependent properties using a cloud-based materials acceleration platform
Solid state materials are central to many modern technologies in which a given material may be exposed to a variety of environments. The material properties often vary with the sequence of environments in an irreversible manner, resulting in a quintessential path-dependency in experimental observables. While sequential learning techniques have been effectively deployed for accelerating learning of state properties of materials, they often use a consistent environment path in all experiments. To elevate such techniques for making optimal decisions in experimental investigations of path-dependent properties, we introduce an iterated expected information gain acquisition function that optimizes over entire experimental trajectories. This approach is implemented within a cloud-based Materials Acceleration Platform architecture utilizing an event-driven stateful broker coupled with remote HELAO (Hierarchical Experimental Laboratory Automation and Orchestration) instances and an AI science manager. The platform's efficacy was demonstrated through a case study optimizing multi-step spectro-electrochemical experiments to identify optically stable potential windows in (Co–Ni–Sb)O z metal oxides. The system successfully integrated AI-driven experiment design, remote laboratory automation, and cloud-based data infrastructure, validating the platform's capability for managing complex, adaptive, path-dependent workflows in materials discovery.
Supercharging simulation-based inference for Bayesian optimal experimental design
Abstract Bayesian optimal experimental design (BOED) seeks to maximize the expected information gain (EIG) of experiments. This requires a likelihood estimate, which in many settings is intractable. Simulation-based inference (SBI) provides powerful tools for this regime. However, existing work explicitly connecting SBI and BOED is restricted to a single contrastive EIG bound. We show that the EIG admits multiple formulations which can directly leverage modern SBI density estimators, encompassing neural posterior, likelihood, and ratio estimation. Building on this perspective, we define a novel EIG estimator using neural likelihood estimation. Further, we identify optimization as a key bottleneck of gradient based EIG maximization and show that a simple multi-start parallel gradient ascent procedure can substantially improve reliability and performance. With these innovations, our SBI-based BOED methods are able to match or outperform by up to 22% existing state-of-the-art approaches across standard BOED benchmarks.
Advancements in Constitutive Model Calibration: Leveraging the Power of Full‐Field DIC Measurements and In Situ Load Path Selection for Reliable Parameter Inference
Accurate material characterization and model calibration are essential for computationally supported high-consequence engineering decisions. Historically, characterization and calibration methods (1) use simplified test specimen geometries and global data, (2) cannot guarantee that sufficient characterization data are collected for a specific model of interest, (3) use deterministic methods that provide best-fit parameter values with no uncertainty quantification, and (4) are sequential, inflexible, and time-consuming. This work brings together several recent advancements into an improved workflow called interlaced characterization and calibration (ICC) that advances the state-of-the-art in constitutive model calibration. The ICC paradigm (1) employs tools to efficiently use full-field data to calibrate high-fidelity material models, (2) aligns the data needed with the data collected by adopting an optimal experimental design protocol, (3) quantifies parameter uncertainty through Bayesian inference and (4) incorporates these advancements into a quasi real-time feedback loop. The ICC framework is demonstrated here on the calibration of a material model using simulated full-field data for an aluminium cruciform specimen being deformed biaxially. The cruciform is actively driven through the myopically preferred load path using Bayesian optimal experimental design, which selects load steps that yield the maximum expected information gain (EIG). Principal component analysis (PCA) is performed on the model predictions of full-field displacements, and fast surrogate models are built to approximate the input-output relationships of the expensive finite element model. Furthermore, the tools developed and demonstrated here show that high-fidelity constitutive models can be efficiently and reliably calibrated with quantified uncertainty, thus supporting credible decision-making and potentially increasing the agility of solid mechanics modelling by enabling utilization of computational simulations at earlier stages of the design cycle.
Robust Optimal Experimental Design of Infinite-Dimensional Bayesian Nonlinear Inverse Problems
Abstract. We consider robust optimal experimental design (ROED) for nonlinear Bayesian inverse problems governed by partial differential equations (PDEs). An optimal design is one that maximizes some utility quantifying the quality of the solution of an inverse problem. However, the optimal design is dependent on elements of the inverse problem such as the simulation model, the prior, or the measurement error model. ROED aims to produce an optimal design that is aware of the additional uncertainties encoded in the inverse problem and remains optimal even after variations in them. We follow a worst-case scenario approach to develop a new framework for robust optimal design of nonlinear Bayesian inverse problems. The proposed framework (a) is scalable and designed for infinite-dimensional Bayesian nonlinear inverse problems constrained by PDEs; (b) develops efficient approximations of the utility, namely the expected information gain; (c) employs eigenvalue sensitivity techniques to develop analytical forms and efficient evaluation methods of the gradient of the utility with respect to the uncertainties against which we wish to be robust; and (d) employs a probabilistic optimization paradigm that properly defines and efficiently solves the resulting combinatorial max-min optimization problem. The effectiveness of the proposed approach is illustrated for optimal sensor placement problem in an inverse problem governed by an elliptic PDE.
Application of the Tasseled Cap concept to simulated thematic mapper data
Thematic Mapper signal counts in the six reflective bands (i.e., excluding the thermal band) are simulated using field and laboratory spectrometer measurements of a variety of crops, crop conditions, and soil types. The Dave atmospheric model and prelaunch sensor characteristics comprise the other components of the simulation. The simulated data are found to occupy essentially three dimensions, two of which are equivalent to the MSS Tasseled Cap Greennes and Brightness features, and a third which is substantially influenced by the mid-infrared bands of the TM. This new dimension is primarily related to soil characteristics, including soil moisture. The nature and characteristics of each dimension are discussed, as are some of the expected information gains (over MSS data) resulting from the additional dimensionality of the data.
Cosmological Constraints from Combining Photometric Galaxy Surveys and Gravitational Wave Observatories
Spatial variations in survey properties due to selection effects generate substantial systematic errors in large-scale structure measurements in optical galaxy surveys on very large scales. On such scales, the statistical sensitivity of optical surveys is also limited by their finite sky coverage. By contrast, gravitational wave (GW) sources appear to be relatively free of these issues, provided the angular sensitivity of GW experiments can be accurately characterized. We quantify the expected cosmological information gain from combining the forecast LSST 3$\times$2pt analysis (combination of three 2-point correlations of galaxy density and weak lensing shear fields) with the large-scale auto-correlation of GW sources from proposed next-generation GW experiments. We find that in $\Lambda$CDM and $w$CDM models, there is no significant improvement in cosmological constraints from combining GW with LSST 3$\times$2pt over LSST alone, due to the large shot noise for the former; however, this combination does enable a $\sim6\%$ constraint on the linear galaxy bias of GW sources. More interestingly, the optical-GW data combination provides tight constraints on models with primordial non-Gaussianity (PNG), due to the predicted scale-dependent bias in PNG models on large scales. Assuming that the largest angular scales that LSST will probe are comparable to those in Stage III surveys ($\ell_{\rm min}\sim50$), the inclusion of next-generation GW measurements could improve constraints on the PNG parameter $f_{\rm NL}$ by up to a factor of $\simeq6.6$ compared to LSST alone, yielding $\sigma(f_{\rm NL})=8.5$. These results assume the expected capability of a network of Einstein Telescope-like GW observatories, with a detection rate of $10^6$ events/year. We investigate the sensitivity of our results to different assumptions about future GW detectors as well as different LSST analysis choices.
Robust A-Optimal Experimental Design for Sensor Placement in Bayesian Linear Inverse Problems
Optimal design of experiments for Bayesian inverse problems has recently gained wide popularity and attracted much attention, especially in the computational science and Bayesian inversion communities. An optimal design maximizes a predefined utility function that is formulated in terms of the elements of an inverse problem, an example being optimal sensor placement for parameter identification. The state-of-the-art algorithmic approaches following this simple formulation generally overlook misspecification of the elements of the inverse problem, such as the prior or the measurement uncertainties. This work presents an efficient algorithmic approach for designing optimal experimental design schemes for Bayesian linear inverse problems such that the optimal design is robust to misspecification of elements of the inverse problem. Specifically, we consider a worst-case scenario approach for the uncertain or misspecified parameters, formulate robust objectives, and propose an algorithmic approach for optimizing such objectives. Furthermore, both relaxation and stochastic solution approaches are discussed with detailed analysis and insight into the interpretation of the problem and the proposed algorithmic approach. Extensive numerical experiments to validate and analyze the proposed approach are carried out for sensor placement in a parameter identification problem.
Bayesian sequential optimal experimental design for nonlinear models using policy gradient reinforcement learning
We present a mathematical framework and computational methods for optimally designing a finite sequence of experiments. This sequential optimal experimental design (sOED) problem is formulated as a finite-horizon partially observable Markov decision process (POMDP) under a Bayesian setting and with information-theoretic utilities. The formulation is general and may accommodate continuous random variables, non-Gaussian posteriors, and nonlinear forward models. The sOED design policy incorporates elements of feedback and lookahead simultaneously, and we show it to generalize the commonly-used batch and greedy design strategies. We solve for the sOED policy using the policy gradient (PG) method from reinforcement learning, and provide a derivation for the PG expression in the sOED context. Adopting an actor-critic approach, the policy and value functions are parameterized using deep neural networks and improved via PG estimates produced from simulated episodes of designs and observations. The new PG-sOED algorithm is first validated on a linear-Gaussian benchmark, and then compared against other design baselines on a sensor movement problem for contaminant source inversion in a convection-diffusion field. As a result, we provide explanation for the policy behaviors using knowledge of the underlying physical process.
Bayesian optimal experimental design for constitutive model calibration
Computational simulation is increasingly relied upon for high/consequence engineering decisions, which necessitates a high confidence in the calibration of and predictions from complex material models. However, the calibration and validation of material models is often a discrete, multi-stage process that is decoupled from material characterization activities, which means the data collected does not always align with the data that is needed. To address this issue, an integrated workflow for delivering an enhanced characterization and calibration procedure—Interlaced Characterization and Calibration (ICC)—is introduced and demonstrated. Further, this framework leverages Bayesian optimal experimental design (BOED), which creates a line of communication between model calibration needs and data collection capabilities in order to optimize the information content gathered from the experiments for model calibration. Eventually, the ICC framework will be used in quasi real-time to actively control experiments of complex specimens for the calibration of a high-fidelity material model. This work presents the critical first piece of algorithm development and a demonstration in determining the optimal load path of a cruciform specimen with simulated data. Calibration results, obtained via Bayesian inference, from the integrated ICC approach are compared to calibrations performed by choosing the load path a priori based on human intuition, as is traditionally done. The calibration results are communicated through parameter uncertainties which are propagated to the model output space (i.e. stress–strain). In these exemplar problems, data generated within the ICC framework resulted in calibrated model parameters with reduced measures of uncertainty compared to the traditional approaches.
Empirical Study of Effect of Dynamic Travel Time Information on Driver Route Choice Behavior
The objective of this paper is to study the effect of travel time information on day-to-day driver route choice behavior. A real-world experimental study is designed to have participants repeatedly choose between two alternative routes for five origin-destination pairs over multiple days after providing them with dynamically updated travel time information (average travel time and travel time variability). The results demonstrate that historical travel time information enhances behavioral rationality by 10% on average and reduces inertial tendencies to increase risk seeking in the gain domain. Furthermore, expected travel time information is demonstrated to be more effective than travel time variability information in enhancing rational behavior when drivers have limited experiences. After drivers gain sufficient knowledge of routes, however, the difference in behavior associated with the two information types becomes insignificant. The results also demonstrate that, when drivers lack experience, the faster less reliable route is more attractive than the slower more reliable route. However, with cumulative experiences, drivers become more willing to take the more reliable route given that they are reluctant to become risk seekers once experience is gained. Furthermore, the effect of information on driver behavior differs significantly by participant and trip, which is, to a large extent, dependent on personal traits and trip characteristics.
UAS in the NAS: Survey Responses by ATC, Manned Aircraft Pilots, and UAS Pilots
NASA currently is working with industry and the Federal Aviation Administration (FAA) to establish future requirements for Unmanned Aircraft Systems (UAS) flying in the National Airspace System (NAS). To work these issues NASA has established a multi-center UAS Integration in the NAS project. In order to establish Ground Control Station requirements for UAS, the perspective of each of the major players in NAS operations was desired. Three on-line surveys were administered that focused on Air Traffic Controllers (ATC), pilots of manned aircraft, and pilots of UAS. Follow-up telephone interviews were conducted with some survey respondents. The survey questions addressed UAS control, navigation, and communications from the perspective of small and large unmanned aircraft. Questions also addressed issues of UAS equipage, especially with regard to sense and avoid capabilities. From the ATC and military ATC perspective, of particular interest is how mixed-operations (manned/UAS) have worked in the past and the role of aircraft equipage. Knowledge gained from this information is expected to assist the NASA UAS in the NAS project in directing research foci thus assisting the FAA in the development of rules, regulations, and policies related to UAS in the NAS.
UAS in the NAS: Survey Responses by ATC, Manned Aircraft Pilots, and UAS Pilots
NASA currently is working with industry and the Federal Aviation Administration (FAA) to establish future requirements for Unmanned Aircraft Systems (UAS) flying in the National Airspace System (NAS). To work these issues NASA has established a multi-center "UAS Integration in the NAS" project. In order to establish Ground Control Station requirements for UAS, the perspective of each of the major players in NAS operations was desired. Three on-line surveys were administered that focused on Air Traffic Controllers (ATC), pilots of manned aircraft, and pilots of UAS. Follow-up telephone interviews were conducted with some survey respondents. The survey questions addressed UAS control, navigation, and communications from the perspective of small and large unmanned aircraft. Questions also addressed issues of UAS equipage, especially with regard to sense and avoid capabilities. From the civilian ATC and military ATC perspectives, of particular interest are how mixed operations (manned / UAS) have worked in the past and the role of aircraft equipage. Knowledge gained from this information is expected to assist the NASA UAS Integration in the NAS project in directing research foci thus assisting the FAA in the development of rules, regulations, and policies related to UAS in the NAS.
Preparation for an Earth Independent Medical Operations Demonstration using the Tempus ALS™ Medical Device
NASA’s exploration-class missions have severe resource constraints, long return trip durations, significant communication delays and limited resupply opportunities. Validation on the International Space Station (ISS) of medical devices that fit within Earth-Independent Medical Operations (EIMO) systems is a necessary preparation step. Key features of an EIMO medical system include: 1) technologies that support the prevention, diagnosis, and treatment of spaceflight medical events; 2) components that meet mass, volume, power and crew time/training constraints; 3) consideration of the medical skill level of the astronaut caregiver; 4) collection, storage and analysis of medical data within a central data architecture; and 5) incorporation of appropriate guidance and support tools that allow crew autonomy. The Human Research Program’s (HRP) Exploration Medical Capability (ExMC) Element and the Exploration Medical Integrated Product Team (XM-IPT) are planning an ISS technology demonstration to determine the feasibility of including a multifunctional medical device into an EIMO medical system. Demonstration Preparations: The Tempus ALS (Remote Diagnostic Technologies, Ltd., Philips Corp., Farnborough, UK) is a commercial-off-the-shelf medical device, with United States Food and Drug Administration clearance and is Conformité Européene marked in Europe. Several thousand units have been sold and are successfully operating in pre-hospital and in remote settings, such as by European Space Agency (ESA) flight surgeons and some of NASA’s commercial partners during post-flight medical operations. The Tempus ALS provides vital sign measurements such as blood pressure, electrocardiograms, heart rate, end tidal CO2, respiration rate, pulse oximetry and temperature. The device has ultrasound imaging and video laryngoscopy capabilities and has automatic or manual defibrillation modes for treating cardiac arrhythmias. It includes procedural guidance capabilities to assist in the collection of the vital sign measurements and it has various data transmission and report generation features. NASA’s HRP ExMC and XM-IPT are partnering with the ESA to demonstrate the Tempus ALS on ISS, with ESA manifesting the Tempus ALS and its accessories. ESA will compare performance of periodic health status exams and medical contingency drills performed nominally and with the Tempus ALS. NASA’s EIMO demonstration will include the use of Tempus ALS to diagnose a complaint of abdominal pain under increasingly independent circumstances. The caregiver must assess the present illness, collect vital sign measurements, and perform an abdominal ultrasound, under one of three communication situations, including real-time, with a several second delay and with a delay on the order of minutes. Expected Outcomes: Information will be gained about the feasibility, benefits, and challenges of using a multifunctional, all-in-one, medical device for medical diagnosis instead of separate devices with singular functionalities. Information will also be collected about performance differences as communication delays increase and available ground support decreases. Gaining this understanding will allow for further development of exploration medical system capabilities which takes the EIMO construct into consideration.