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At least 343 records · Page 19

Solar Radiation Transport in the Cloudy Atmosphere: A 3D Perspective on Observations and Climate Impacts

The interplay of sunlight with clouds is a ubiquitous and often pleasant visual experience, but it conjures up major challenges for weather, climate, environmental science and beyond. Those engaged in the characterization of clouds (and the clear air nearby) by remote sensing methods are even more confronted. The problem comes, on the one hand, from the spatial complexity of real clouds and, on the other hand, from the dominance of multiple scattering in the radiation transport. The former ingredient contrasts sharply with the still popular representation of clouds as homogeneous plane-parallel slabs for the purposes of radiative transfer computations. In typical cloud scenes the opposite asymptotic transport regimes of diffusion and ballistic propagation coexist. We survey the three-dimensional (3D) atmospheric radiative transfer literature over the past 50 years and identify three concurrent and intertwining thrusts: first, how to assess the damage (bias) caused by 3D effects in the operational 1D radiative transfer models? Second, how to mitigate this damage? Finally, can we exploit 3D radiative transfer phenomena to innovate observation methods and technologies? We quickly realize that the smallest scale resolved computationally or observationally may be artificial but is nonetheless a key quantity that separates the 3D radiative transfer solutions into two broad and complementary classes: stochastic and deterministic. Both approaches draw on classic and contemporary statistical, mathematical and computational physics.

Davis, Anthony B.↗

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↗

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↗

Theorem Proving In Higher Order Logics

The TPHOLs International Conference serves as a venue for the presentation of work in theorem proving in higher-order logics and related areas in deduction, formal specification, software and hardware verification, and other applications. Fourteen papers were submitted to Track B (Work in Progress), which are included in this volume. Authors of Track B papers gave short introductory talks that were followed by an open poster session. The FCM 2002 Workshop aimed to bring together researchers working on the formalisation of continuous mathematics in theorem proving systems with those needing such libraries for their applications. Many of the major higher order theorem proving systems now have a formalisation of the real numbers and various levels of real analysis support. This work is of interest in a number of application areas, such as formal methods development for hardware and software application and computer supported mathematics. The FCM 2002 consisted of three papers, presented by their authors at the workshop venue, and one invited talk.

Carreno, Victor A.↗

Latent Twins

Over the past decade, scientific machine learning has transformed the development of mathematical and computational frameworks for analyzing, modeling, and predicting complex systems. From inverse problems to numerical partial differential equations (PDEs), dynamical systems, and model reduction, these advances have pushed the boundaries of what can be simulated. Yet they have often progressed in parallel, with representation learning and algorithmic solution methods evolving largely as separate pipelines. With Latent Twins, we propose a unifying mathematical framework that creates a hidden surrogate in latent space for the underlying equations. Whereas digital twins mirror physical systems in the digital world, Latent Twins mirror mathematical systems in a learned latent space governed by operators. Through this lens, classical modeling, inversion, model reduction, and operator approximation all emerge as special cases of a single principle. We establish the fundamental approximation properties of Latent Twins for both ordinary differential equations (ODEs) and PDEs and demonstrate the framework across three representative settings: (i) canonical ODEs, capturing diverse dynamical regimes; (ii) a PDE benchmark using the shallow-water equations, contrasting Latent Twin simulations with deep operator network and forecasts with a four-dimensional variational method baseline; and (iii) a challenging real-data geopotential reanalysis dataset, reconstructing and forecasting from sparse, noisy observations. Latent Twins provide a compact, interpretable surrogate for solution operators that evaluate across arbitrary time gaps in a single-shot, while remaining compatible with scientific pipelines such as assimilation, control, and uncertainty quantification. Looking forward, this framework offers scalable, theory-grounded surrogates that bridge data-driven representation learning and classical scientific modeling across disciplines.

Latent Twins↗

Characterization and Optimization of the Fitting of Quantum Correlation Functions

This case study presents a characterization and optimization of an application code for extracting parton distribution functions from high energy electron-proton scattering data. Profiling this application code reveals that the phase-space density computation accounts for 93% of the overall execution time for a single iteration on a single core. When executing multiple iterations in parallel on a multicore system, the application spends 78% of its overall execution time idling due to load imbalance. We address these issues by first transforming the application code from Python to C++ and then tackling the application load imbalance via a hybrid scheduling strategy that combines dynamic and static scheduling. These techniques result in a 62% reduction in CPU idle time and a 2.46x speedup in overall execution time per node. In addition, the typically enabled power-management mechanisms in supercomputers (e.g., AMD Turbo Core, Intel Turbo Boost, and RAPL) can significantly impact intra-node scalability when more than 50% of the CPU cores are used. This finding underscores the importance of understanding system interactions with power management, as they can adversely impact application performance, and highlights the necessity of intra-node scaling tests to identify performance degradation that inter-node scaling tests might otherwise overlook.

Chuang, Pi-Yueh [Virginia Tech,Dept. of Computer S↗

buhito

buhito is a Python library for graph analysis and machine learning. Graphs can represent networks with objects as nodes and their relationships as edges. buhito focuses on graphlet methods that study graphs through enumerating their component subgraphs to enable interpretable and fast models of complex systems. The package provides tools for different algorithmic designs for computing, analyzing, and applying graphlets to research problems such as machine learning, data compression, and anomaly detection in graph-structured data. A central feature is performing decomposition data analysis on graphs for machine learning models. Implemented in Python and built upon open-source scientific libraries such as NetworkX, NumPy, and SciPy, buhito provides high-performance methods for researchers exploring the mathematical and computational foundations of graphlet analysis applicable to systems of different sizes.

Pimonova, Yulia↗

Recent trends in digital human modeling and the concurrent issues that face human modeling approach

Tremendous strides have been made in the recent years to digitally represent human beings in computer simulation models ranging from assembly plant maintenance operations to occupants getting in and out of vehicles to action movie scenarios. While some of these tools are being actively pursued by the engineering communities, there is still a lot of work that remains to be done for the newly planned planetary exploration missions. For example, certain unique and several common challenges are seen in developing computer generated suited human models for designing the next generation space vehicle. The purpose of this presentation is to discuss NASA s potential needs for better human models and to show also many of the inherent yet not too obvious pitfalls that still are left unresolved in this new arena of digital human modeling. As part of NASA s Habitability and Human Factors Branch, the Anthropometry and Biomechanics Facility has been engaged in studying the various facets of computer generated human physical performance models; for instance, it has been engaged in utilizing three-dimensional laser scan data along with three dimensional video based motion and reach data to gather suited anthropometric and shape and size information that are not available yet in the form of computer mannequins. Our goal is to bring in new approaches to deal with heavily clothed humans (such as, suited astronauts) and to overcome the current limitations of wrongly identifying humans (either real or virtual) as univariate percentiles. We are looking at whole-body posture based anthropometric models as a means to identify humans of significantly different shapes and sizes to arrive at mathematically sound computer models for analytical purposes.

Rajulu, Sudhakar↗