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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 1,009 records · Page 56
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

Anti-survivin single-domain antibodies derived from an artificial library including three synthetic random regions by in vitro selection using cDNA display

Highlights: • Single-domain antibodies can be selected with an artificial DNA library synthesized chemically. • cDNA display method is useful for in vitro selection from a large single-domain antibodies library (e.g. 1013). • A Brevibacillus protein expression system is suitable for synthesis of functional single-domain antibodies. Single-domain antibodies (variable domain of the heavy chain of a heavy chain antibody; VHH) are promising reagents for therapeutics and diagnostics because of their stability, cost-effective production and material workability as a small antibody. Currently, general acquisition of a VHH using immunization of camelids is inconvenient from the standpoint of animal protection, cost and the process is time-consuming. Thus, a straightforward and efficient method for screening VHHs against a target molecule is required. In this study, we examined whether in vitro selection of a VHH against a target protein could be performed by a cDNA display method with an artificial VHH library that had the three complementarity-determining regions (CDRs) randomized by chemical synthesis. The results revealed that a particular VHH against survivin, which is a member of the inhibitor of apoptosis family, was selected with affinity in the range of 10{sup −7} to 10{sup −8} M. The in vitro selection of a VHH using cDNA display with an artificial synthesized library without animal immunization was shown to be effective for rapid and inexpensive screening of VHHs against a target protein.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2020

Effective pair potential for random fcc CoCrFeMnNi alloys

The single-phase equiatomic CoCrFeMnNi alloy is a random solid solution of five elements on the face-centered cubic lattice, whose pure constituents crystallize in very different structures and exhibit diverse magnetic properties. Due to the randomness of the alloy, 80% of nearest neighbor bonds are between unlike elements and thus the details of bonding in pure structures are less important. The elastic moduli of this alloy give rise to small Cauchy pressure C 12 - C 44 , which suggests that the dominant part of bonding may be described by a simple pair potential. We test this hypothesis by developing a long-range Lennard-Jones potential in which the equilibrium crystal structures of pure constituents are taken as reference. The standard mixing rules for regular solutions are then adopted to obtain parameters for bonds between unlike elements in the quinary system. The transferability of this potential to quaternary CoCrFeNi, ternary CoCrNi, and binary FeNi alloys is investigated and the predictions compared with experiments and density functional theory calculations. By sampling over a large number of random configurations, we investigate the effect of compositional randomness on misfit volumes, energies of point defects and stacking faults, and the dislocation friction stresses experienced by moving edge and screw dislocations.

Materials Science↗
DOE OSTI2024

Securing Grid-interactive Efficient Buildings (GEB) through Cyber Defense and Resilient System (CYDRES)

The DOE CYDRES project is driven by the urgent need to address critical research gaps in the domain of cyber-physical security of smart buildings, including Grid-interactive Efficient Buildings (GEBs). CYDRES, a real-time advanced building resilient platform, aims to enhance the cyber-attack-immune capabilities of buildings through multi-layered prevention, detection, and adaptation mechanisms. CYDRES consists of five key modules: a multi-layer network analyzer, an Automatic Fault Detection, Diagnosis, and Prognosis (AFDDP) framework, an intelligent mode selector, a cyber-resilient control framework, and a situation awareness platform. The Network Analyzer employs a data-driven framework that includes a protocol state learning tool and a CRF (Conditional Random Field) command validator. In Hardware-In-the-Loop (HIL) testbeds, it achieved 100% detection accuracy with a false alarm rate of 3%, validating its efficacy in identifying selected cyber-attacks. The AFDDP framework leverages pattern matching, PCA (Principal Component Analysis)-based strategies, and a DBN (Dynamic Bayesian Network)-based fault diagnosis approach to pinpoint the causes of physical system abnormalities using Building Automation System (BAS) data. In HIL experiments, the AFDDP module attained a detection accuracy of over 95% with a false alarm rate below 7%. Additionally, the fault detector utilized machine learning (Random Forest) and deep learning (Multi-Layer Perceptron) methods with acoustic sensor data to achieve a 100% fault detection accuracy in Heating, Ventilation, and Air-Conditioning (HVAC) equipment. The Mode Selector offered real-time impact analysis, allowing immediate actions to protect BASs in the face of emerging threats. The cyber-resilient control framework included an adaptive Model Predictive Control (MPC) and a measurement compensator, reducing temperature violations by up to 94% and improving the total demand flexibility by up to 70% in HIL experiments. Such HIL experiments covered a cyber-attack case and a physical fault case, showcasing CYDRES’ efficiency in maintaining operational continuity during threats. The situation awareness platform in Grafana enhanced real-time threat detection and response visualization, augmenting the operational awareness for building operators. CYDRES demonstrated high technical effectiveness in various test scenarios, particularly in HIL environments. The project's phased development approach ensured efficient use of resources, highlighting its practical feasibility and readiness for commercialization. By enhancing the security and resilience of building operations, CYDRES represents a significant advance in mitigating risks associated with cyber-physical systems, thereby enhancing public confidence in the safety of modern building infrastructure. Future directions for the project include expanding testing protocols, refining AFDDP methodologies, exploring more comprehensive resilient control strategies, and testing in real commercial buildings.

42 ENGINEERING↗
DOE OSTI2021

Probabilistic Resilience of DER Systems - A Simulation Assisted Optimization Approach

Energy systems resilience is becoming increasingly important as the frequency of major grid outages increases. In this work, we present a methodology to optimize a behind-tlie-meter distributed energy resource system to sustain a site's critical loads during a pre-defined outage period. With the fixed system design, we then propose an outage simulation approach to estimate the resilience potential of the DER system to sustain loads beyond the fixed outage period - a yearlong resilience performance analysis. We apply statistical analysis to assess the system's resilience performance over a broader parametric problem space on an hourly, monthly, and yearly basis. We demonstrate the impact of the pre-defined outage period on the resilience performance through a case study. Results show that the probability of surviving a random outage of a given duration changes from 20% to 95% when the outage is modeled for a weekday instead of a weekend for the given load-profile.

28 EE - Advanced Manufacturing Office (EE-5A)↗
DOE OSTI2017

Role of polarization interaction in photoionization of negative ions of alkali metals

Photoionization processes of negative ions of sodium, potassium, and rubidium were investigated. Calculations of the dependence of the photoionization cross section on the photon energy were performed within the Random Phase Approximation with Exchange for outer subshells (RPAE) and within the Generalized Random Phase Approximation with Exchange (GRPAE) for inner subshells. The latter theoretical approach includes both many-electron correlations and core rearrangement due to escape of one of the electrons from the system. The results of calculations for the negative sodium ion were found to be in good agreement with experimental data. Better agreement was achieved by allowing dynamical polarization of the electron core. It manifests itself as a many-electron response to variation of the external electromagnetic field, which results from the excitation of the many-electron system. Detailed study of the main mechanisms determining the cross section dependence profile was carried out. These mechanisms are the inter- and intrachannel correlations acting as a many-electron response to the external field, the electron core rearrangement, and the dynamic polarization. Besides sodium and potassium ions, photoionization of rubidium ion was investigated. A new method accounting for polarization corrections to optical transition amplitudes based on combination of the Dyson equation and RPAE is proposed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Generating Sequential PV Deployment Scenarios for High Renewable Distribution Grid Planning: Preprint

This paper introduces a novel approach for generating solar photovoltaic (PV) plant deployment scenarios for grid integration planning. The approach guarantees consistency among scenarios of the same deployment by ensuring that higher penetration scenarios contain PV units deployed in lower penetration scenarios. It also constrains the size and spatial distribution of the PV plants and considers three placement types. A case study on a real-world distribution system proves that the precepts of scenario consistency, deployment diversity, and placement are met. The study further investigates the impact of the resulting scenarios via a stochastic hosting capacity analysis. Results indicate that the ratio between PV and load sizes, referred to as the nodal PV penetration factor (NPPF), is a key driver of the grid integration impact. By reducing the NPPF from 5 to 2, the maximum hosting capacity increased by at least 112%. The study also reveals that scenarios under random placement can lead to higher hosting capacity values.

ENERGY PLANNING, POLICY, AND ECONOMY,SOLAR ENERGY↗
DOE OSTI2016

A fingerprint based metric for measuring similarities of crystalline structures

Measuring similarities/dissimilarities between atomic structures is important for the exploration of potential energy landscapes. However, the cell vectors together with the coordinates of the atoms, which are generally used to describe periodic systems, are quantities not directly suitable as fingerprints to distinguish structures. Based on a characterization of the local environment of all atoms in a cell, we introduce crystal fingerprints that can be calculated easily and define configurational distances between crystalline structures that satisfy the mathematical properties of a metric. This distance between two configurations is a measure of their similarity/dissimilarity and it allows in particular to distinguish structures. The new method can be a useful tool within various energy landscape exploration schemes, such as minima hopping, random search, swarm intelligence algorithms, and high-throughput screenings.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

CTT: Tools for Fine Alignment of Flash X-ray Systems

The CTT code is a compilation of the python code that was prototyped in the interest of making a method for fine alignment of Flash X-ray Systems at the lab. It contains python code for interacting with LTT and running optimization loops using LTT simulations or ray tracing with RaySpace. It Includes classes for creating phantom objects and modular geometry objects in the simulations. It allows one to generate a random phantom that has been optimized to stay with a certain cubic volume and maximize the minimum distance between any two ball phantom centers in all projections. It was primarily made to work on ball phantoms which were simulated as Teflon spheres. It allows the alignment from some nominal position to some displaced position to simulate recovery of a real geometry from the nominal geometry of the system. Fine alignment can be done with the projections in LTT while a rough alignment is faster using rayspace. If rayspace works well for the use case it should be preferred since it is considerably faster and less resource intensive in general. Some Notes about using this code is that one will have to edit the imports for the files to get to the correct LTT path, LTT GUI path and to the CTT path when importing. This was made by using anaconda with python 3 on windows 10. The LTT code was stored in a anaconda environment which seemed to help the python find the LTT although it shouldn’t be necessary if you append the path in your code using sys.path.append(r'add the path you want here’). The sys.path.append method is a quick way to give your python code access to a given folder when running it (such as LTT or CTT). Note that since the code was originally made with paths for a specific machine that a new user will have to edit those paths to make it work in all the files that use the old paths. This is somewhat tedious but will be required to run the code on a new machine. The methodology used to run and make these notebooks starts with opening a command prompt as administrator in windows 10. After this one would activate the anaconda environment in the appropriate directory using “conda activate myenv” in the command prompt. After this open a jupyter-notebook using the keyword “jupyter-notebook". After that a notebook should open in a browser. Note that some libraries used may not come with anaconda so those may have to be installed. There shouldn’t be much though since the main things used are scipy, numpy, matplotlib, and LTT. LTTQuicksetup also requires some paths that will be specific to the computer so that should be changed as well.

42 ENGINEERING↗
DOE OSTI2022

System and method for x-ray compatible 2D streak camera for a snapshot multiframe imager

The present disclosure is directed to a snapshot multiframe imager having an aperture element having at least one aperture, an adjacently positioned random mask, an imaging element and a computer. The random mask has a plurality of micron scale apertures and receives light passing through the aperture element, which represents the spatial information from the scene being imaged, and generates a plurality of image frames encoded in a spatial domain. The imaging element may operate in a drift-scan mode receives the encoded image frames and generates a streaked pattern of electrons representing a plurality of images of the scene at a plurality of different times. The computer analyzes the streaked pattern of electrons and mathematically reconstructs the plurality of images.

Dayton, Matthew S.↗
DOE OSTI2016

Mortandad Canyon seismic modeling (Progress Report)

The goal of this project is to assess site amplification for LANL through modeling of site and topography effects. Such assessment is difficult due to the lack of data documenting site effects for large normal faulting earthquakes such as the Pajarito Fault System that was found to be governing the seismic hazard at LANL. LANL site is also characterized by unique geologic settings, a series of mesa at the edge of the huge volcanic complex of the Jemez caldera. The latter has produced a series of successive and intertwined deposits of volcanic flow and sedimentary layer. Such layering of material with different elastic properties is expected to create large amplification effects magnified further by the presence at the surface of tuff materials. In 2014, a seismic campaign was performed in the Mortandad Canyon with a network of sensors on and near a local mesa. That campaign was designed to provide experimental data to estimation and prediction of amplification and site effects at LANL. An analysis on the seismic noise records of that campaign shows evidence of amplification of the seismic amplitude for the stations on the top of the mesa. Our goal is to reproduce the effect observed (both retrieving the resonance frequencies and amplification levels). We also plan to test if amplification effects observed for seismic noise can be extended to shaking produced by earthquakes. We are using a 3D modeling tool based on the Spectral Element Method (SEM) that is a particular type of high-order finite element modeling. Two types of seismic sources will be considered: (1) earthquakes for purpose of seismic hazard evaluation, (2) ambient noise. We show 2 series of numerical computations: (1) seismic waves are generated by random sources to simulate ambient noise. (2) seismic waves are planar waves to simulate a distant earthquake. We plan in the future to model rupture scenario on the Pajarito Fault System.

58 GEOSCIENCES↗
DOE OSTI2018

Additive manufacturing of short and mixed fibre-reinforced polymer

Additive manufacturing of a fiber-reinforced polymer (FRP) product using an additive manufacturing print head; a reservoir in the additive manufacturing print head; short carbon fibers in the reservoir, wherein the short carbon fibers are randomly aligned in the reservoir; an acrylate, methacrylate, epoxy, cyanate ester or isocyanate resin in the reservoir, wherein the short carbon fibers are dispersed in the acrylate, methacrylate, epoxy, cyanate ester or isocyanate resin; a tapered nozzle in the additive manufacturing print head operatively connected to the reservoir, the tapered nozzle produces an extruded material that forms the fiber-reinforced polymer product; baffles in the tapered nozzle that receive the acrylate, methacrylate, epoxy, cyanate ester or isocyanate resin with the short carbon fibers dispersed in the acrylate, methacrylate, epoxy, cyanate ester or isocyanate resin; and a system for driving the acrylate, methacrylate, epoxy, cyanate ester or isocyanate resin with the short carbon fibers dispersed in the acrylate, methacrylate, epoxy, cyanate ester or isocyanate resin from the reservoir through the tapered nozzle wherein the randomly aligned short carbon fibers in the acrylate, methacrylate, epoxy, cyanate ester or isocyanate resin are aligned by the baffles and wherein the extruded material has the short carbon fibers aligned in the acrylate, methacrylate, epoxy, cyanate ester or isocyanate resin that forms the fiber-reinforced polymer product.

36 MATERIALS SCIENCE↗
DOE OSTI2017

Noise Radar Approach for Interrogating SAW Sensors Using Software Defined Radio

Passive, wireless surface acoustic wave (SAW) sensor systems can be approached from a radar perspective, where the SAW device is thought of as a cooperative target. Here, this paper investigates the use of a commercial-off-the-shelf software defined radio to interrogate wireless SAW sensors with a randomly generated interrogation pulse. The USRP B200mini is utilized as the transceiver platform with custom field-programmable gate array (FPGA) modifications to generate the random interrogation waveform and provide synchronization and buffering to the received signal. Each transmit sample bit in the FPGA is fed by an independent linear-feedback shift register, which generates pseudo-random I and Q samples for the interrogation pulse. An RF daughterboard has also been developed and integrated with the B200mini to increase the transmit power, provide filtering of the RF signals, and switch a signal antenna between the transmit and receive channels. Radio control and matched filter correlator post-processing are accomplished using Python. Design and implementation details for the FPGA modifications, RF daughterboard, and post-processing are discussed. Lastly, the system is demonstrated by wirelessly interrogating SAW temperature sensors at 915 MHz.

47 OTHER INSTRUMENTATION↗
DOE OSTI2017

HPC formulations of optimization algorithms for tensor completion

Tensor completion is a powerful tool used to estimate or recover missing values in multi-way data. It has seen great success in domains such as product recommendation and healthcare. Tensor completion is most often accomplished via low-rank sparse tensor factorization, a computationally expensive non-convex optimization problem which has only recently been studied in the context of parallel computing. In this work, we study three optimization algorithms that have been successfully applied to tensor completion: alternating least squares (ALS), stochastic gradient descent (SGD), and coordinate descent (CCD++). We explore opportunities for parallelism on shared- and distributed-memory systems and address challenges such as memory- and operation-efficiency, load balance, cache locality, and communication. Among our advancements are a communication-efficient CCD++ algorithm, an ALS algorithm rich in level-3 BLAS routines, and an SGD algorithm which combines stratification with asynchronous communication. Furthermore, we show that introducing randomization during ALS and CCD++ can accelerate convergence. We evaluate our parallel formulations on a variety of real datasets on a modern supercomputer and demonstrate speedups through 16384 cores. Further, these improvements reduce time-to-solution from hours to seconds on real-world datasets. We show that after our optimizations, ALS is advantageous on parallel systems of small-to-moderate scale, while both ALS and CCD++ provide the lowest time-to-solution on large-scale distributed systems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Nominal and adversarial synthetic PMU data for standard IEEE test systems

GridSTAGE (Spatio-Temporal Adversarial scenario GEneration) is a framework for the simulation of adversarial scenarios and the generation of multivariate spatio-temporal data in cyber-physical systems. GridSTAGE is developed based on Matlab and leverages Power System Toolbox (PST) where the evolution of the power network is governed by nonlinear differential equations. Using GridSTAGE, one can create several event scenarios that correspond to several operating states of the power network by enabling or disabling any of the following: faults, AGC control, PSS control, exciter control, load changes, generation changes, and different types of cyber-attacks. Standard IEEE bus system data is used to define the power system environment. GridSTAGE emulates the data from PMU and SCADA sensors. The rate of frequency and location of the sensors can be adjusted as well. Detailed instructions on generating data scenarios with different system topologies, attack characteristics, load characteristics, sensor configuration, control parameters are available in the Github repository - https://github.com/pnnl/GridSTAGE. There is no existing adversarial data-generation framework that can incorporate several attack characteristics and yield adversarial PMU data. The GridSTAGE framework currently supports simulation of False Data Injection attacks (such as a ramp, step, random, trapezoidal, multiplicative, replay, freezing) and Denial of Service attacks (such as time-delay, packet-loss) on PMU data. Furthermore, it supports generating spatio-temporal time-series data corresponding to several random load changes across the network or corresponding to several generation changes. A Koopman mode decomposition (KMD) based algorithm to detect and identify the false data attacks in real-time is proposed in https://ieeexplore.ieee.org/document/9303022. Machine learning-based predictive models are developed to capture the dynamics of the underlying power system with a high level of accuracy under various operating conditions for IEEE 68 bus system. The corresponding machine learning models are available at https://github.com/pnnl/grid_prediction.

99 GENERAL AND MISCELLANEOUS↗
DOE OSTI2018

Hanford Direct Feed Low Activity Waste Program Throughput Optimization Through Modeling - 18587

The Direct Feed Low Activity Waste (DFLAW) program at Hanford allows for the early treatment of tank wastes years earlier than previously planned. Operational Research (OR) modeling is being used to provide invaluable insight into how complex and integrated processes will operate. The DFLAW OR models are used to help optimize the design and operation of the integrated system. The DFLAW OR models include the processes and real-life complexities involved in the day-to-day operation of the systems and equipment, and can predict key performance characteristics including throughput, mission timescale, equipment and labor utilization, lag storage and capacity requirements. The DFLAW OR models also have the in-built capability to simulate random events such as equipment failures. Adding random variability to models introduces a real-life element to model results. For example, OR modeling breakdown analysis of equipment failure and restoration times may inform specific improvements to a design and plant operation, including areas where the provision of spare (duty/standby) equipment would prove beneficial; the optimum number and capacity of lag storage tanks (for waste intermediate storage, reagents, etc.); operational issues, including scheduling constraints, labor resource constraints, effect of shift schedules (e.g. days only, extended shifts, 24/7),, maintenance strategies, including planned maintenance, equipment upgrades, on-hand spare part stockholding, etc. At Hanford, standalone OR models to date, have been used to help identify key operational issues and improve the design and operation of individual systems within the Tank Farms, Low Activity Waste Pretreatment System (LAWPS), Low Activity Waste (LAW) Vitrification and Effluent Management Facility (EMF) and Integrated Disposal Facility (IDF), logistics and infrastructure, 222-S laboratory [References 1 and 2] including: - Identification of critical spares including transfer pumps; - Underpin size and number of lag storage tanks to maintain continuous LAW feed to the LAW melters; - Underpin sample turnaround times at the 222-S Laboratory (e.g. feed prequalification and evaporator campaign samples) and determine how targets can be achieved without impacting waste feed delivery to LAWPS and the LAW Vitrification Facility; - Determine operational strategy required at IDF including shift schedules and sizes and the number of ILAW transporters that can support DFLAW throughput; - Identification of lag storage management strategies for glass formers, reagents, other consumables due to delivery distance and delays due to bad weather; and - Truck delivery badging needs to support 24/7 operation and management of shift in/out times required to reduce congestion. An Integrated DFLAW OR model has been developed and combines the standalone OR models such that integrated throughput and availability can be assessed from a program perspective. The Integrated OR model will provide a more detailed understanding of the interactions between Tank Farms, LAWPS, LAW VIT and IDF such that key bottleneck areas can be identified and ensure improvements are focused. Examples of future improvements that may be considered include identification of critical spare parts, required on-site maintenance capabilities, shift scheduling, and craft and labor availability. The methods, results and insights derived by DFLAW OR modeling efforts are expected to provide useful applications to other projects that involve combinations of mechanical handling, chemical processing, waste treatment/packaging or environmental remediation operations. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2018

Mathematical Model of Heat Transfer in the Catalyst Granule with Point Reaction Centers

This paper considers a catalyst granule with a porous ceramic chemically inert base and active point centers, at which an exothermic reaction of synthesis takes place. The rate of a chemical reaction depends on temperature by the Arrhenius law. The heat is removed from the catalyst granule surface to the synthesis products by heat transfer. Based on the idea of self-consistent field, a closed system of equations is constructed for calculating the temperatures of the active centers. As an example, a catalyst granule of the Fischer–Tropsch synthesis with active metallic cobalt particles is considered. The stationary temperatures of the active centers are calculated by the timedependent technique by solving a system of ordinary differential equations. The temperature distribution inside the granule has been found for the local centers located on one diameter of the granule and distributed randomly in the granule’s volume. The existence of the critical temperature inside the reactor has been established, the excess of which leads to substantial superheating of local centers. The temperature distribution with local reaction centers differs qualitatively from the granule temperature calculated in the homogeneous approximation. The results of calculations are given.

42 ENGINEERING↗
DOE OSTI2023

A computational study of how surfaces affect slip family activity

Plastic deformation behavior is most conveniently assessed by characterization on a surface, but whether such observations are representative of bulk properties is uncertain. Motivated by reported inconsistencies in slip resistance probed at different depths, we investigated (i) whether the average slip family activity is affected by the presence of a surface and (ii) how the kinematic nature of available slip families influences a potential surface effect. The slip family activity as a function of distance from the surface was extracted from full-field crystal plasticity simulations of random polycrystalline hexagonal close-packed (HCP) and body-centered cubic (BCC) metals as examples of mixed in contrast to universally-high numbers of slip systems per family. Under certain conditions, a deviation from bulk slip activity is observed up to about two grains from the surface. For the easiest (least slip-resistant) family, a surface effect of decreasing activity with depth emerges if the number of slip systems falls below about six. For harder families, slip activity always increases with depth. Furthermore, these phenomena are explained on the basis of varying constraints with depth in connection with the kinematic properties of slip families in the material.

36 MATERIALS SCIENCE↗
DOE OSTI2016

Gaussian processes with built-in dimensionality reduction: Applications to high-dimensional uncertainty propagation

Uncertainty quantification (UQ) tasks, such as model calibration, uncertainty propagation, and optimization under uncertainty, typically require several thousand evaluations of the underlying computer codes. To cope with the cost of simulations, one replaces the real response surface with a cheap surrogate based, e.g., on polynomial chaos expansions, neural networks, support vector machines, or Gaussian processes (GP). However, the number of simulations required to learn a generic multivariate response grows exponentially as the input dimension increases. This curse of dimensionality can only be addressed, if the response exhibits some special structure that can be discovered and exploited. A wide range of physical responses exhibit a special structure known as an active subspace (AS). An AS is a linear manifold of the stochastic space characterized by maximal response variation. The idea is that one should first identify this low dimensional manifold, project the high-dimensional input onto it, and then link the projection to the output. If the dimensionality of the AS is low enough, then learning the link function is a much easier problem than the original problem of learning a high-dimensional function. The classic approach to discovering the AS requires gradient information, a fact that severely limits its applicability. Furthermore, and partly because of its reliance to gradients, it is not able to handle noisy observations. The latter is an essential trait if one wants to be able to propagate uncertainty through stochastic simulators, e.g., through molecular dynamics codes. In this work, we develop a probabilistic version of AS which is gradient-free and robust to observational noise. Our approach relies on a novel Gaussian process regression with built-in dimensionality reduction. In particular, the AS is represented as an orthogonal projection matrix that serves as yet another covariance function hyper-parameter to be estimated from the data. To train the model, we design a two-step maximum likelihood optimization procedure that ensures the orthogonality of the projection matrix by exploiting recent results on the Stiefel manifold, i.e., the manifold of matrices with orthogonal columns. The additional benefit of our probabilistic formulation, is that it allows us to select the dimensionality of the AS via the Bayesian information criterion. We validate our approach by showing that it can discover the right AS in synthetic examples without gradient information using both noiseless and noisy observations. We demonstrate that our method is able to discover the same AS as the classical approach in a challenging one-hundred-dimensional problem involving an elliptic stochastic partial differential equation with random conductivity. Finally, we use our approach to study the effect of geometric and material uncertainties in the propagation of solitary waves in a one dimensional granular system.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗