Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Algorithms and theoretical developments”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 469 records · Page 26

A Single Thread to Fortran Coarray Transition Process for the Control Algorithm in the Space Radiation Code HZETRN

Exa-scale computing is the direction by industry and government are going to generate solutions to problems they deem necessary. Computing hardware is being developed to achieve the transition from Peta-scale to Exa-scale with more CPUs (Central Processing Units) that have more cores per CPU and more accelerators (GPGPUs (General Purpose Graphics Processing Units) and MICs (Many Integrated Cores)) per node. To fully utilize the hardware available now and in the future, algorithms must become multi-threaded. There are a few methods to generate multi-threaded software such as MPI (Message Passing Interface) and OpenMP (Multi-Processing) / OpenACC (ACCelerator). This paper concentrates on using Coarray Fortran to convert the Fortran 95 based HZETRN (High Z and Energy TRaNsport) code's control algorithm from a single threaded code to a multithreaded code. The resultant Coarray code was 32.5 times faster (with a theoretical speed-up of 74.5 times) than the single threaded version on the hardware tested, as reliable as the Fortran 95 version, and, as it uses native Fortran, was as maintainable as the Fortran 95 version. The Coarray code can be maintained by the same project engineers and scientists who created the original single threaded code. This transition process can be utilized on a C language based code with a compiler that has the UPC (Universal Parallel C) extensions to C.

Singleterry, Robert C., Jr.↗

PemNet: A Transfer Learning-Based Modeling Approach of High-Temperature Polymer Electrolyte Membrane Electrochemical Systems

Widespread adoption of high-temperature electrochemical systems such as polymer electrolyte membrane fuel cells (HT-PEMFCs) requires models and computational tools for accurate optimization and guiding new materials for enhancing fuel cell performance and durability. Furthermore, while robust and better suited for extrapolation, knowledge-based modeling has limitations as it is time-consuming and requires information about the system that is not always available (e.g., material properties and interfacial behavior between different materials). Data-driven modeling, on the other hand, is easier to implement but often necessitates large datasets that could be difficult to obtain. In this contribution, knowledge-based modeling and data-driven modeling are combined by implementing a few-shot learning (FSL) approach. A knowledge-based model originally developed for a HT-PEMFCs was used to generate simulated data (887,735 points) and used to pretrain a neural network source model tuned via a genetic algorithm-based AutoML. Then, experimental datasets from HT-PEMFCs with different materials and operating conditions (~50 points each) were used to train six target models via FSL. Models for the unseen data reached high accuracies in all cases (rRMSE < 10%).

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

A Novel Approach for Adaptive Signal Processing

Adaptive linear predictors have been used extensively in practice in a wide variety of forms. In the main, their theoretical development is based upon the assumption of stationarity of the signals involved, particularly with respect to the second order statistics. On this basis, the well-known normal equations can be formulated. If high- order statistical stationarity is assumed, then the equivalent normal equations involve high-order signal moments. In either case, the cross moments (second or higher) are needed. This renders the adaptive prediction procedure non-blind. A novel procedure for blind adaptive prediction has been proposed and considerable implementation has been made in our contributions in the past year. The approach is based upon a suitable interpretation of blind equalization methods that satisfy the constant modulus property and offers significant deviations from the standard prediction methods. These blind adaptive algorithms are derived by formulating Lagrange equivalents from mechanisms of constrained optimization. In this report, other new update algorithms are derived from the fundamental concepts of advanced system identification to carry out the proposed blind adaptive prediction. The results of the work can be extended to a number of control-related problems, such as disturbance identification. The basic principles are outlined in this report and differences from other existing methods are discussed. The applications implemented are speech processing, such as coding and synthesis. Simulations are included to verify the novel modelling method.

Chen, Ya-Chin↗

Empirical STORM-E Model

Auroral nighttime infrared emission observed by the Sounding of the Atmosphere using Broadband Emission Radiometry (SABER) instrument onboard the Thermosphere-Ionosphere-Mesosphere Energetics and Dynamics (TIMED) satellite is used to develop an empirical model of geomagnetic storm enhancements to E-region peak electron densities. The empirical model is called STORM-E and will be incorporated into the 2012 release of the International Reference Ionosphere (IRI). The proxy for characterizing the E-region response to geomagnetic forcing is NO+(v) volume emission rates (VER) derived from the TIMED/SABER 4.3 lm channel limb radiance measurements. The storm-time response of the NO+(v) 4.3 lm VER is sensitive to auroral particle precipitation. A statistical database of storm-time to climatological quiet-time ratios of SABER-observed NO+(v) 4.3 lm VER are fit to widely available geomagnetic indices using the theoretical framework of linear impulse-response theory. The STORM-E model provides a dynamic storm-time correction factor to adjust a known quiescent E-region electron density peak concentration for geomagnetic enhancements due to auroral particle precipitation. Part II of this series describes the explicit development of the empirical storm-time correction factor for E-region peak electron densities, and shows comparisons of E-region electron densities between STORM-E predictions and incoherent scatter radar measurements. In this paper, Part I of the series, the efficacy of using SABER-derived NO+(v) VER as a proxy for the E-region response to solar-geomagnetic disturbances is presented. Furthermore, a detailed description of the algorithms and methodologies used to derive NO+(v) VER from SABER 4.3 lm limb emission measurements is given. Finally, an assessment of key uncertainties in retrieving NO+(v) VER is presented

Mertens, Christopher J.↗

A reference open-source controller for fixed and floating offshore wind turbines

Abstract. This paper describes the development of a new reference controller framework for fixed and floating offshore wind turbines that greatly facilitates controller tuning and represents standard industry practices. The reference wind turbine controllers that are most commonly cited in the literature have been developed to work with specific reference wind turbines. Although these controllers have provided standard control functionalities, they are often not easy to modify for use on other turbines, so it has been challenging for researchers to run representative, fully dynamic simulations of other wind turbine designs. The Reference Open-Source Controller (ROSCO) has been developed to provide a modular reference wind turbine controller that represents industry standards and performs comparably to or better than existing reference controllers. The formulation of the ROSCO controller logic and tuning processes is presented in this paper. Control capabilities such as tip speed ratio tracking generator torque control, minimum pitch saturation, wind speed estimation, and a smoothing algorithm at near-rated operation are included to provide modern controller features. A floating offshore wind turbine feedback module is also included to facilitate growing research in the floating offshore arena. All of the standard controller implementations and control modules are automatically tuned such that a non-controls engineer or automated optimization routine can easily improve the controller performance. This article provides the framework and theoretical basis for the ROSCO controller modules and generic tuning processes. Simulations of the National Renewable Energy Laboratory (NREL) 5 MW reference wind turbine and International Energy Agency 15 MW reference turbine on the University of Maine semisubmersible platform are analyzed to demonstrate the controller's performance in both fixed and floating configurations, respectively. The simulation results demonstrate ROSCO's peak shaving routine to reduce maximum rotor thrusts by over 10 % compared to the NREL 5 MW reference wind turbine controller on the land-based turbine and to reduce maximum platform pitch angles by nearly 30 % when using the platform feedback routine instead of a more traditional low-bandwidth controller.

17 WIND ENERGY↗

Nonlinear transient analysis by energy minimization: A theoretical basis for the ACTION computer code

The formulation basis for establishing the static or dynamic equilibrium configurations of finite element models of structures which may behave in the nonlinear range are provided. With both geometric and time independent material nonlinearities included, the development is restricted to simple one and two dimensional finite elements which are regarded as being the basic elements for modeling full aircraft-like structures under crash conditions. Representations of a rigid link and an impenetrable contact plane are added to the deformation model so that any number of nodes of the finite element model may be connected by a rigid link or may contact the plane. Equilibrium configurations are derived as the stationary conditions of a potential function of the generalized nodal variables of the model. Minimization of the nonlinear potential function is achieved by using the best current variable metric update formula for use in unconstrained minimization. Powell's conjugate gradient algorithm, which offers very low storage requirements at some slight increase in the total number of calculations, is the other alternative algorithm to be used for extremely large scale problems.

Kamat, M. P.↗

Neutronics Calculation Advances at Los Alamos: Manhattan Project to Monte Carlo

The history and advances of neutronics calculations at Los Alamos during the Manhattan Project through the present are reviewed. Substantial improvements to neutron diffusion methods and the invention of both the Monte Carlo neutron transport methods in 1947 and deterministic discrete ordinates Sn in 1953 were all made at Los Alamos just after the Manhattan Project. We briefly summarize early simpler and more approximate neutronics methods and then describe the need to better predict neutronics behavior through consideration of theoretical equations, models and algorithms, experimental measurements, and available computing capabilities and their limitations. This paper briefly covers key advances in deterministic methods during the Manhattan Project. These capabilities, coupled with increasing postwar defense needs and the invention of electronic computing with the Electronic Numeric Integrator and Computer, known as ENIAC, and the Mathematical Analyzer Numerical Integrator and Automatic Computer Model, known as MANIAC, led to the creation of Monte Carlo and deterministic discrete ordinates neutronics transport methods. We note the important role that the scientific comradery between the Los Alamos scientists played in the process. This paper briefly covers the early methods, algorithms, computers, and electronic and women pioneers that enabled Monte Carlo to spread to all areas of science. We focus heavily on these early developments and the subsequent creation of the MCNP® code, advances in its associated nuclear data, and its applications to problems of national defense at Los Alamos.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

On the remote sensing of cloud properties from satellite infrared sounder data

A method for remote sensing of cloud parameters by using infrared sounder data has been developed on the basis of the parameterized infrared transfer equation applicable to cloudy atmospheres. The method is utilized for the retrieval of the cloud height, amount, and emissivity in 11 micro m region. Numerical analyses and retrieval experiments have been carried out by utilizing the synthetic sounder data for the theoretical study. The sensitivity of the numerical procedures to the measurement and instrument errors are also examined. The retrieved results are physically discussed and numerically compared with the model atmospheres. Comparisons reveal that the recovered cloud parameters agree reasonably well with the pre-assumed values. However, for cases when relatively thin clouds and/or small cloud fractional cover within a field of view are present, the recovered cloud parameters show considerable fluctuations. Experiments on the proposed algorithm are carried out utilizing High Resolution Infrared Sounder (HIRS/2) data of NOAA 6 and TIROS-N. Results of experiments show reasonably good comparisons with the surface reports and GOES satellite images.

Yeh, H. Y. M.↗

Acoustic Travel-Time Tomography for Wind Energy

New remote sensing technologies for direct observation of the atmospheric flow in the proximity of operating wind turbines are necessary for the advancement of wind turbine design, wind plant control, and the validation of high-fidelity numerical models; fundamental goals of the DOE Wind Energy Technology Office's (WETO's) A2e program. Modern remote sensing technologies for commercial and research applications rely on the backscatter of light or sound waves, which limits spatial and temporal resolution and cannot produce reliable flow estimates near solid bodies or reflective surfaces. Acoustic tomography (AT) is an innovative sensing technology based on fundamental thermodynamic properties of the atmosphere and an inverse algorithm that can reconstruct both velocity and temperature fields within a network of acoustic transducers. AT relies on the direct travel path of acoustic signals between speakers and microphones in the network and can achieve much higher resolutions than conventional backscatter technologies. For wind energy R&D applications, AT represents an extremely economical option over other remote sensing technologies, integrating mature and commonly available acoustic and signal processing hardware. This report is intended as an update on the development of the AT array on the NREL Flatirons Campus (FC) and includes a brief review of the instrumentation, the calibration of equipment, signal processing, and resulting flow field estimates. Designs for future AT systems and applications are detailed in this report, including summaries of new capabilities, engineering and theoretical challenges, and anticipated costs help to outline future directions for AT technology R\&D. The potential for application of AT to utility-scale turbines is also discussed. Investing in the development of the proposed instrument will establish AT as a transformational RS technique that represents a significant advance in measurement instrumentation, enabling new fundamental insights into the structure of the atmospheric boundary layer and supporting applications for wind energy, pollution transport, and resource characterization. AT is also an extremely economical option over other RS instruments, integrating mature and commonly available acoustic and signal processing hardware.

17 WIND ENERGY↗

Advances in machine-learning-based sampling motivated by lattice quantum chromodynamics

Sampling from known probability distributions is a ubiquitous task in computational science, underlying calculations in domains from linguistics to biology and physics. Generative machine-learning (ML) models have emerged as a promising tool in this space, building on the success of this approach in applications such as image, text, and audio generation. Often, however, generative tasks in scientific domains have unique structures and features—such as complex symmetries and the requirement of exactness guarantees—that present both challenges and opportunities for ML. This Perspective outlines the advances in ML-based sampling motivated by lattice quantum field theory, in particular for the theory of quantum chromodynamics. Enabling calculations of the structure and interactions of matter from our most fundamental understanding of particle physics, lattice quantum chromodynamics is one of the main consumers of open-science supercomputing worldwide. Here, the design of ML algorithms for this application faces profound challenges, including the necessity of scaling custom ML architectures to the largest supercomputers, but also promises immense benefits, and is spurring a wave of development in ML-based sampling more broadly. In lattice field theory, if this approach can realize its early promise it will be a transformative step towards first-principles physics calculations in particle, nuclear and condensed matter physics that are intractable with traditional approaches.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Group-Invariant Quantum Machine Learning

Quantum machine learning (QML) models are aimed at learning from data encoded in quantum states. Recently, it has been shown that models with little to no inductive biases (i.e., with no assumptions about the problem embedded in the model) are likely to have trainability and generalization issues, especially for large problem sizes. As such, it is fundamental to develop schemes that encode as much information as available about the problem at hand. In this work we present a simple, yet powerful, framework where the underlying invariances in the data are used to build QML models that, by construction, respect those symmetries. These so-called group-invariant models produce outputs that remain invariant under the action of any element of the symmetry group $\mathfrak{G}$ associated with the dataset. We present theoretical results underpinning the design of $\mathfrak{G}$-invariant models, and exemplify their application through several paradigmatic QML classification tasks, including cases when $\mathfrak{G}$ is a continuous Lie group and also when it is a discrete symmetry group. Notably, our framework allows us to recover, in an elegant way, several well-known algorithms for the literature, as well as to discover new ones. Taken together, we expect that our results will help pave the way towards a more geometric and group-theoretic approach to QML model design.

97 MATHEMATICS AND COMPUTING↗

Modeling the Activity of Single Genes

The central dogma of molecular biology states that information is stored in DNA, transcribed to messenger RNA (mRNA) and then translated into proteins. This picture is significantly augmentated when we consider the action of certain proteins in regulating transcription. These transcription factors provide a feedback pathway by which genes can regulate one another's expression as mRNA and then as protein. To review: DNA, RNA and proteins have different functions. DNA is the molecular storehouse of genetic information. When cells divide, the DNA is replicated, so that each daughter cell maintains the same genetic information as the mother cell. RNA acts as a go-between from DNA to proteins. Only a single copy of DNA is present, but multiple copies of the same piece of RNA may be present, allowing cells to make huge amounts of protein. In eukaryotes (organisms with a nucleus), DNA is found in the nucleus only. RNA is copied in the nucleus then translocates(moves) outside the nucleus, where it is transcribed into proteins. Along the way, the RNA may be spliced, i.e., may have pieces cut out. RNA then attaches to ribosomes and is translated to proteins. Proteins are the machinery of the cell other than DNA and RNA, all the complex molecules of the cell are proteins. Proteins are specialized machines, each of which fulfills its own task, which may be transporting oxygen, catalyzing reactions, or responding to extracellular signals, just to name a few. One of the more interesting functions a protein may have is binding directly or indirectly to DNA to perform transcriptional regulation, thus forming a closed feedback loop of gene regulation. The structure of DNA and the central dogma were understood in the 50s; in the early 80s it became possible to make arbitrary modifications to DNA and use cellular machinery to transcribe and translate the resulting genes; more recently, genomes (i.e., the complete DNA sequence) of many organisms have been sequenced. This large-scale sequencing began with simple organisms, viruses and bacteria, progressed to eukaryotes such as yeast, and more recently (1998) progressed to a multi-cellular animal, the nematode Caenorhabditis elegans. Sequencers have now moved on to the fruit fly Drosophila melanogaster, whose sequence is slated for completion by the end of 1999. The human genome project is expected to determine the complete sequence of all 3 billion bases of human DNA within the next five years. In the wake of genome-scale sequencing, further instrumentation is being developed to assay gene expression and function on a comparably large scale. Much of the work in computational biology focuses on computational tools used in sequencing, finding genes that are related to a particular gene, finding which parts of the DNA code for proteins and which do not, understanding what proteins will be formed from a given length of DNA, predicting how the proteins will fold from a one-dimensional structure into a three dimensional structure, and so on. Much less computational work has been done regarding the function of proteins. One reason for this is that different proteins function very differently, and so work on protein function is very specific to certain classes of proteins. There are, for example, proteins such enzymes that catalyze various intracellular reactions, receptors that respond to extracellular signals and ion channels that regulate the flow of charged particles into and out of the cell. In this chapter, we will consider a particular class of proteins called transcription factors(TFs), which are responsible for regulating when a certain gene is expressed in a certain cell, which cells it is express in, and how much is expressed. Understanding these processes will involve developing a deeper understanding of transcription, translation, and the cellular processes that control those processes. All of these elements fall under the aegis of gene regulation or more narrowly transcriptional regulation. Some of the key questions in gene regulation are: What genes are expressed in a certain cell at a certain time? How does gene expression differ from cell to cell in a multicellular organism? Which proteins act as transcription factors, i.e., are important in regulating gene expression? From questions like these, we hope to understand which genes are important for various macroscopic processes. Nearly all of the cells of a multicellular organism contain the same DNA. Yet this same genetic information yields a large number of different cell types. The fundamental difference between a neuron and a liver cell, for example, is which genes are expressed. Thus understanding gene regulation is an important step in understanding development. Furthermore, understanding the usual genes that are expressed in cells may give important clues about various diseases. Some diseases, such as sickle cell anemia and cystic fibrosis, are caused by defects in single, non-regulatory genes; others, such as certain cancers, are caused when the cellular control circuitry malfunctions - an understanding of these diseases will involve pathways of multiple interacting gene products. There are numerous challenges in the area of understanding and modeling gene regulation. First and foremost, biologists would like to develop a deeper understanding of the processes involved, including which genes and families of genes are important, how they interact, etc. From a computation point of view, there has been embarrassingly little work done. In this chapter there are many areas in which we can phrase meaningful, non-trivial computational questions, but questions that have not been addressed. Some of these are purely computational (what is a good algorithm for dealing with a model of type X) and others are more mathematical (given a system with certain characteristics, what sort of model can one use? How does one find biochemical parameters from system-level behavior using as few experiments as possible?). In addition to biological and algorithmic problems, there is also the ever-present issue of theoretical biology - what general principles can be derived from these systems, what can one do with models other than just simulate time-courses, what can be deduced about a class of systems without knowing all the details? The fundamental challenge to computationalists and theorists is to add value to the biology - to use models, modeling techniques and algorithms to understand the biology in new ways.

Mjolsness, Eric↗

Benchmarking Coordination Number Prediction Algorithms on Inorganic Crystal Structures

Coordination numbers and geometries form a theoretical framework for understanding and predicting materials properties. Algorithms to determine coordination numbers automatically are increasingly used for machine learning and automatic structural analysis. In this work, we introduce MaterialsCoord, a benchmark suite containing 56 experimentally-derived crystal structures (spanning elements, binaries, and ternary compounds) and their corresponding coordination environments as described in the research literature. We also describe CrystalNN, a novel algorithm for determining near neighbors. We compare CrystalNN against 7 existing near-neighbor algorithms on the MaterialsCoord benchmark, finding CrystalNN to perform similarly to several well-established algorithms. For each algorithm, we also assess computational demand and sensitivity towards small perturbations that mimic thermal motion. Finally, we investigate the similarity between bonding algorithms when applied to the Materials Project database. Finally, we expect that this work will aid the development of coordination prediction algorithms as well as improve structural descriptors for machine learning and other applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Demonstration of Algorithmic Quantum Speedup

Despite the development of increasingly capable quantum computers, an experimental demonstration of a provable algorithmic quantum speedup employing today’s non-fault-tolerant devices has remained elusive. Here, in this study, we unequivocally demonstrate such a speedup within the oracular model, quantified in terms of the scaling with the problem size of the time-to-solution metric. We implement the single-shot Bernstein-Vazirani algorithm, which solves the problem of identifying a hidden bitstring that changes after every oracle query, using two different 27-qubit IBM Quantum superconducting processors. The speedup is observed on only one of the two processors when the quantum computation is protected by dynamical decoupling but not without it. The quantum speedup reported here does not rely on any additional assumptions or complexity-theoretic conjectures and solves a bona fide computational problem in the setting of a game with an oracle and a verifier.

97 MATHEMATICS AND COMPUTING↗

Global electric field determination in the Earth's outer magnetosphere using energetic charged particles

Although many properties of the Earth's magnetosphere have been measured and quantified in the past 30 years since it was discovered, one fundamental measurement (for zeroth order MHD equilibrium) has been made infrequently and with poor spatial coverage - the global electric field. This oversight is due in part to the neglect of theorists. However, there is renewed interest in the convection electric field because it is now realized to be central to many magnetospheric processes, including the global MHD equilibrium, reconnection rates, Region 2 Birkeland currents, magnetosphere ionosphere coupling, ring current and radiation belt transport, substorm injections, and several acceleration mechanisms. Unfortunately the standard experimental methods have not been able to synthesize a global field (excepting the pioneering work of McIlwain's geostationary models) and we are left with an overly simplistic theoretical field, the Volland-Stern electric field model. Single point measurements of the plasmapause were used to infer the appropriate amplitudes of this model, parameterized by K(sub p). Although this result was never intended to be the definitive electric field model, it has gone nearly unchanged for 20 years. The analysis of current data sets requires a great deal more accuracy than can be provided by the Volland-Stern model. The variability of electric field shielding has not been properly addressed although effects of penetrating magnetospheric electric fields has been seen in mid-and low-latitude ionospheric data sets. The growing interest in substorm dynamics also requires a much better assessment of the electric fields responsible for particle injections. Thus we proposed and developed algorithms for extracting electric fields from particle data taken in the Earth's magnetosphere. As a test of the effectiveness of these new techniques, we analyzed data taken by the AMPTE/CCE spacecraft in equatorial orbit from 1984 to 1989.

Eastman, Timothy E.↗

Clouds and the Earth's Radiant Energy System (CERES) algorithm theoretical basis document: Geolocation, calibration, and ERBE-like analyses (subsystems 1-3) - volume 2

The theoretical bases for the Release 1 algorithms that will be used to process satellite data for investigation of the Clouds and Earth's Radiant Energy System (CERES) are described. The architecture for software implementation of the methodologies is outlined. Volume 2 details the techniques used to geolocate and calibrate the CERES scanning radiometer measurements of shortwave and longwave radiance to invert the radiances to top-of-the-atmosphere (TOA) and surface fluxes following the Earth Radiation Budget Experiment (ERBE) approach, and to average the fluxes over various time and spatial scales to produce an ERBE-like product. Spacecraft ephemeris and sensor telemetry are used with calibration coefficients to produce a chronologically ordered data product called bidirectional scan (BDS) radiances. A spatially organized instrument Earth scan product is developed for the cloud-processing subsystem. The ERBE-like inversion subsystem converts BDS radiances to unfiltered instantaneous TOA and surface fluxes. The TOA fluxes are determined by using established ERBE techniques. Hourly TOA fluxes are computed from the instantaneous values by using ERBE methods. Hourly surface fluxes are estimated from TOA fluxes by using simple parameterizations based on recent research. The averaging process produces daily, monthly-hourly, and monthly means of TOA and surface fluxes at various scales. This product provides a continuation of the ERBE record.

Wielicki, B. A.↗

Data-Consistent Inversion for Stochastic Input-to-Output Maps

Data-consistent inversion is a recently developed measure-theoretic framework for solving a stochastic inverse problem involving models of physical systems. The goal is to construct a probability measure on model inputs (i.e., parameters of interest) whose associated push-forward measure matches (i.e., is consistent with) a probability measure on the observable outputs of the model (i.e., quantities of interest). Previous implementations required the map from parameters of interest to quantities of interest to be deterministic. This work generalizes this framework for maps that are stochastic, i.e., contain uncertainties and variation not explainable by variations in uncertain parameters of interest. Generalizations of previous theorems of existence, uniqueness, and stability of the data-consistent solution are provided while new theoretical results address the stability of marginals on parameters of interest. A notable aspect of the algorithmic generalization is the ability to query the solution to generate independent identically distributed samples of the parameters of interest without requiring knowledge of the so-called stochastic parameters. This work therefore extends the applicability of the data-consistent inversion framework to a much wider class of problems. This includes those based on purely experimental and field data where only a subset of conditions are either controllable or can be documented between experiments while the underlying physics, measurement errors, and any additional covariates are either uncertain or not accounted for by the researcher. Finally, numerical examples demonstrate application of this approach to systems with stochastic sources of uncertainties embedded within the modeling of a system and a numerical diagnostic is summarized that is useful for determining if a key assumption is verified among competing choices of stochastic maps.

97 MATHEMATICS AND COMPUTING↗

Data-Driven Compositional Optimization in Misspecified Regimes

With a manifold growth in the scale and intricacy of systems, the challenges of parametric misspecification become pronounced. These concerns are further exacerbated in compositional settings, which emerge in problems complicated by modeling risk and robustness. In “Data-Driven Compositional Optimization in Misspecified Regimes,” the authors consider the resolution of compositional stochastic optimization problems, plagued by parametric misspecification. In considering settings where such misspecification may be resolved via a parallel learning process, the authors develop schemes that can contend with diverse forms of risk, dynamics, and nonconvexity. They provide asymptotic and rate guarantees for unaccelerated and accelerated schemes for convex, strongly convex, and nonconvex problems in a two-level regime with extensions to the multilevel setting. Surprisingly, the nonasymptotic rate guarantees show no degradation from the rate statements obtained in a correctly specified regime and the schemes achieve optimal (or near-optimal) sample complexities for general T-level strongly convex and nonconvex compositional problems.

Business & Economics↗