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At least 595 records · Page 33

Need for Uncertainty Quantification in Predictions [Slides]

Natural and engineered systems are often modeled through mathematical equations using computer codes. Finite resources, inability to accurately control experimental conditions, encounter, or explore the entire parameter space of interest are a few reasons that scientists and engineers rely on numerical simulations for predictive capability. Associated with every prediction is an uncertainty, since our ability to simulate a physical process is limited by our knowledge of the physics, and the parameters. In the last two decades, the need for Uncertainty Quantification (UQ) has been recognized in several fields and we often ask questions about the risk or uncertainty associated with events and make decisions accordingly. In this talk, I will illustrate the effects of model and parametric uncertainties and the need to include them in our predictive capabilities.

97 MATHEMATICS AND COMPUTING↗

Analysis of MMU FDIR expert system

This paper describes the analysis of a rulebase for fault diagnosis, isolation, and recovery for NASA's Manned Maneuvering Unit (MMU). The MMU is used by a human astronaut to move around a spacecraft in space. In order to provide maneuverability, there are several thrusters oriented in various directions, and hand-controlled devices for useful groups of them. The rulebase describes some error detection procedures, and corrective actions that can be applied in a few cases. The approach taken in this paper is to treat rulebases as symbolic objects and compute correctness and 'reasonableness' criteria that use the statistical distribution of various syntactic structures within the rulebase. The criteria should identify awkward situations, and otherwise signal anomalies that may be errors. The rulebase analysis agorithms are derived from mathematical and computational criteria that implement certain principles developed for rulebase evaluation. The principles are Consistency, Completeness, Irredundancy, Connectivity, and finally, Distribution. Several errors were detected in the delivered rulebase. Some of these errors were easily fixed. Some errors could not be fixed with the available information. A geometric model of the thruster arrangement is needed to show how to correct certain other distribution nomalies that are in fact errors. The investigations reported here were partially supported by The Aerospace Corporation's Sponsored Research Program.

Landauer, Christopher↗

Can machine learning accelerate process understanding and decision‐relevant predictions of river water quality?

Abstract The global decline of water quality in rivers and streams has resulted in a pressing need to design new watershed management strategies. Water quality can be affected by multiple stressors including population growth, land use change, global warming, and extreme events, with repercussions on human and ecosystem health. A scientific understanding of factors affecting riverine water quality and predictions at local to regional scales, and at sub‐daily to decadal timescales are needed for optimal management of watersheds and river basins. Here, we discuss how machine learning (ML) can enable development of more accurate, computationally tractable, and scalable models for analysis and predictions of river water quality. We review relevant state‐of‐the art applications of ML for water quality models and discuss opportunities to improve the use of ML with emerging computational and mathematical methods for model selection, hyperparameter optimization, incorporating process knowledge into ML models, improving explainablity, uncertainty quantification, and model‐data integration. We then present considerations for using ML to address water quality problems given their scale and complexity, available data and computational resources, and stakeholder needs. When combined with decades of process understanding, interdisciplinary advances in knowledge‐guided ML, information theory, data integration, and analytics can help address fundamental science questions and enable decision‐relevant predictions of riverine water quality.

54 ENVIRONMENTAL SCIENCES↗

Optimal PMU design based on sampling model and sensitivity analysis

The precise measurements of the synchrophasor and frequency from phasor measurement units (PMUs) are widely used in power grid applications. With the improvement of the technique, applications always require stable dynamic performance and higher accuracy for the synchrophasor and frequency measurements, which is challenging for PMU development. To evaluate the contribution of PMU hardware to measurement accuracy, this paper proposes a general-purpose sampling model to analyze the measurement error. In the proposed sampling model, a strict mathematical derivation is derived, where its error is purely determined by the parameters of the PMU hardware. The sensitivity analysis is carried out by three methods, including mathematical analysis, computer simulation, and variance-based sensitivity analysis. Through the sensitivity analysis, this paper establishes the systematic formulation and the inclusion of synchrophasor, frequency, and ROCOF. Experimental results based on the real-world testbench involving distribution-level PMUs match the mathematical analysis conclusion, which verifies the correctness of the general-purpose sampling model. Furthermore, a strategy for the optimal PMU design is proposed, which could guide PMU design in the future.

42 ENGINEERING↗

PNNL Strategic Goods Testbed: A Data Library for Illicit Nuclear Trafficking

Pacific Northwest National Laboratory (PNNL) has put significant effort into nonproliferation activities as an institution, both in terms of the classical nuclear material focused approach and in the examination of other strategic goods necessary to implement a nuclear program. To assist in these efforts, several projects in the Analysis in Motion (AIM) and Signature Discovery (SDI) Initiatives at PNNL are developing machine learning methodology for human-computer interaction in real time environments to assist analysts in this domain. All of these technical projects require access to data – whether it is in terms of detector data, shipping records, financial information, company relations, or other communications. The first question that mathematical and computational researchers come up with when asked to build analyst assist or automated tools is “What does the data look like? ” They become frustrated when basic questions like this can not be easily answered and this can have the effect of pushing researchers away from the nuclear trafficking domain, especially in strategic commodity and export control areas where data sets can not easily be generated through standard experimental techniques. For small projects that are building a proof of concept for their methodology, obtaining this data can be arduous and expensive. To relieve the burden of data collection from these projects and grow a lab-wide capability, the Strategic Goods Testbed Team has taken over data collection and placed subscriptions and access to flat data files in a centralized location so that all projects can benefit from these items. We have collected shipping data in the form of PIERS records, judicial information about export control cases, NAC data on the nuclear fuel industry, and financial data from Dun and Bradstreet and our data sets are continuing to expand. With a single access agreement, researchers in data-mining and other fields can utilize all of the records that have been downloaded, make requests through subscription services, and interact with other researchers through our interface. Our testbed team provides more than a simply static repository by working with researchers to refine their data needs and insure data quality as well as quantity. We are currently working with laboratory and initiative specific management to examine effective ways for continuing data growth and sustainability.

data capability↗

Explainable and trustworthy artificial intelligence for correctable modeling in chemical sciences

Data science has primarily focused on big data, but for many physics, chemistry, and engineering applications, data are often small, correlated and, thus, low dimensional, and sourced from both computations and experiments with various levels of noise. Typical statistics and machine learning methods do not work for these cases. Expert knowledge is essential, but a systematic framework for incorporating it into physics-based models under uncertainty is lacking. Here, we develop a mathematical and computational framework for probabilistic artificial intelligence (AI)–based predictive modeling combining data, expert knowledge, multiscale models, and information theory through uncertainty quantification and probabilistic graphical models (PGMs). We apply PGMs to chemistry specifically and develop predictive guarantees for PGMs generally. Our proposed framework, combining AI and uncertainty quantification, provides explainable results leading to correctable and, eventually, trustworthy models. The proposed framework is demonstrated on a microkinetic model of the oxygen reduction reaction.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Stable vacua with realistic phenomenology and cosmology in heterotic M-theory satisfying Swampland conjectures

We recently described a protocol for computing the potential energy in heterotic M-theory for the dilaton, complex structure and Kähler moduli. This included the leading order non-perturbative contributions to the complex structure, gaugino condensation and worldsheet instantons assuming a hidden sector that contains an anomalous U(1) structure group embedded in E8. In this paper, we elucidate, in detail, the mathematical and computational methods required to utilize this protocol. These methods are then applied to a realistic heterotic M-theory model, the B – L MSSM, whose observable sector is consistent with all particle physics requirements. Within this context, it is shown that the dilaton and universal moduli can be completely stabilized at values compatible with every phenomenological and mathematical constraint — as well as with ΛCDM cosmology. We also show that the heterotic M-theory vacua are consistent with all well-supported Swampland conjectures based on considerations of string theory and quantum gravity, and we discuss the implications of dark energy theorems for compactified theories.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Residuals-based distributionally robust optimization with covariate information

We consider data-driven approaches that integrate a machine learning prediction model within distributionally robust optimization (DRO) given limited joint observations of uncertain parameters and covariates. Our framework is flexible in the sense that it can accommodate a variety of regression setups and DRO ambiguity sets. We investigate asymptotic and finite sample properties of solutions obtained using Wasserstein, sample robust optimization, and phi-divergence-based ambiguity sets within our DRO formulations, and explore cross-validation approaches for sizing these ambiguity sets. Through numerical experiments, we validate our theoretical results, study the effectiveness of our approaches for sizing ambiguity sets, and illustrate the benefits of our DRO formulations in the limited data regime even when the prediction model is misspecified.

97 MATHEMATICS AND COMPUTING↗

Technology Needs for Teachers Web Development and Curriculum Adaptations

Computer-based mathematics and science curricula focusing on NASA inventions and technologies will enhance current teacher knowledge and skills. Materials and interactive software developed by educators will allow students to integrate their various courses, to work cooperatively, and to collaborate with both NASA scientists and students at other locations by using computer networks, email and the World Wide Web.

Carroll, Christy J.↗

Computer-aided analysis and design of the shape rolling process for producing turbine engine airfoils

Mild steel (AISI 1018) was selected as model cold rolling material and Ti-6A1-4V and Inconel 718 were selected as typical hot rolling and cold rolling alloys, respectively. The flow stress and workability of these alloys were characterized and friction factor at the roll/workpiece interface was determined at their respective working conditions by conducting ring tests. Computer-aided mathematical models for predicting metal flow and stresses, and for simulating the shape rolling process were developed. These models utilized the upper bound and the slab methods of analysis, and were capable of predicting the lateral spread, roll separating force, roll torque, and local stresses, strains and strain rates. This computer-aided design system was also capable of simulating the actual rolling process, and thereby designing the roll pass schedule in rolling of an airfoil or a similar shape.

Lahoti, G. D.↗

Computer-aided analysis and design of the shape rolling process for producing turbine engine airfoils

Mild steel (AISI 1018) was selected as model cold-rolling material and Ti-6Al-4V and INCONEL 718 were selected as typical hot-rolling and cold-rolling alloys, respectively. The flow stress and workability of these alloys were characterized and friction factor at the roll/workpiece interface was determined at their respective working conditions by conducting ring tests. Computer-aided mathematical models for predicting metal flow and stresses, and for simulating the shape-rolling process were developed. These models utilize the upper-bound and the slab methods of analysis, and are capable of predicting the lateral spread, roll-separating force, roll torque and local stresses, strains and strain rates. This computer-aided design (CAD) system is also capable of simulating the actual rolling process and thereby designing roll-pass schedule in rolling of an airfoil or similar shape. The predictions from the CAD system were verified with respect to cold rolling of mild steel plates. The system is being applied to cold and hot isothermal rolling of an airfoil shape, and will be verified with respect to laboratory experiments under controlled conditions.

Lahoti, G. D.↗

Discrete Abstractions of Hybrid Systems: Verification of Safety and Application to User-Interface Design

Human interaction with a complex control system involves the user, the automation’s discrete mode logic, and the underlying continuous dynamics of the physical system. The user-interface of such systems always displays a reduced set of information about the entire system. Designing interfaces such that all the pertinent information is available and assuring that this information is correct is important for any user-interface, but especially so for safety-critical systems such as automotive systems and autopilots. Here we describe a methodology for the analysis of hybrid control systems that incorporate user interaction, with the goal of assuring that the information provided to the user is correct. That is, the user-interface must contain all information necessary to safely complete a desired procedure or task. We begin with a hybrid system model which incorporates discrete mode logic as well as nonlinear continuous dynamics. Using a hybrid computational tool for reachability, we find the largest region of the state-space in which we can guarantee the state of the system can always remain – this is the safe region of operation. By implementing a controller for safety which arises from this computation, we mathematically guarantee that this safe region is invariant, meaning that the system will always remain within the safe region if the determined controller is used on the boundary of the safe region. Verification within a hybrid framework allows us to account for the continuous dynamics underlying the discrete representations displayed to the user. Using the computed invariant regions as discrete states, we can abstract a discrete event system from this hybrid system with safety restrictions. This abstraction can be used to determine what information must be provided on the display. Furthermore, in cases in which an interface already exists, the abstraction provides the necessary input into existing interface verification methods. We provide two examples: a car traveling through a yellow light at an intersection and an aircraft autopilot in an automatic landing/go-around maneuver. The examples demonstrate the applicability of this methodology to hybrid systems that have operational constraints we can pose in terms of safety. This methodology differs from existing work in hybrid system verification in that we directly account for the user’s interactions with the system.

Meeko Oishi↗

Space-Split Algorithm for Sensitivity Analysis of Discrete Chaotic Systems With Multidimensional Unstable Manifolds

Accurate approximations of the change of a system's output and its statistics with respect to the input are highly desired in computational dynamics. Ruelle's linear response theory provides breakthrough mathematical machinery for computing the linear response of chaotic dynamical systems. In this paper, we propose an algorithm for sensitivity analysis of discrete chaos with an arbitrary number of positive Lyapunov exponents. We combine the concept of perturbation space-splitting, which regularizes Ruelle's original expression, together with measure-based parameterization of the expanding subspace. We use these tools to rigorously derive trajectory-following recursive relations that converge exponentially fast, and construct a memory-efficient Monte Carlo scheme for derivatives of the output statistics. Thanks to the regularization and lack of simplifying assumptions on the system's behavior, our method is immune to the common problems of other popular methods such as the exploding tangent solutions and unphysical shadowing directions. Here, we provide a ready-to-use algorithm, analyze its complexity, and demonstrate several numerical examples of sensitivity computation using physically-inspired low-dimensional systems.

97 MATHEMATICS AND COMPUTING↗

Use of comparative genomics approaches to characterize interspecies differences in response to environmental chemicals: Challenges, opportunities, and research needs

A critical challenge for environmental chemical risk assessment is the characterization and reduction of uncertainties introduced when extrapolating inferences from one species to another. The purpose of this article is to explore the challenges, opportunities, and research needs surrounding the issue of how genomics data and computational and systems level approaches can be applied to inform differences in response to environmental chemical exposure across species. We propose that the data, tools, and evolutionary framework of comparative genomics be adapted to inform interspecies differences in chemical mechanisms of action. We compare and contrast existing approaches, from disciplines as varied as evolutionary biology, systems biology, mathematics, and computer science, that can be used, modified, and combined in new ways to discover and characterize interspecies differences in chemical mechanism of action which, in turn, can be explored for application to risk assessment. We consider how genetic, protein, pathway, and network information can be interrogated from an evolutionary biology perspective to effectively characterize variations in biological processes of toxicological relevance among organisms. We conclude that comparative genomics approaches show promise for characterizing interspecies differences in mechanisms of action, and further, for improving our understanding of the uncertainties inherent in extrapolating inferences across species in both ecological and human health risk assessment. To achieve long-term relevance and consistent use in environmental chemical risk assessment, improved bioinformatics tools, computational methods robust to data gaps, and quantitative approaches for conducting extrapolations across species are critically needed. Specific areas ripe for research to address these needs are recommended.

60 APPLIED LIFE SCIENCES↗