Principles of low dissipation computing from a stochastic circuit model
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37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
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Results for “STOCHASTIC PROCESSES”
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Robust Scheduling of Microgrids Considering Unintentional Islanding Conditions
This paper proposes a robust scheduling model for microgrids considering the stochastic unintentional islanding conditions. The proposed model minimizes the total operating cost of the microgrid by efficiently coordinating the supply of power from local distributed energy resources and the main grid. To capture the prevailing uncertainties in renewable generation and demand as well as unintentional islanding conditions, a two-stage adaptive robust optimization model is formulated to minimize the total operating cost under the worst realization of the modeled uncertainties. The column and constraint generation (C&CG) method is used to solve the problem in an iterative manner. The solution of the proposed scheduling model ensures robust microgrid operation in consideration of all possible realization of renewable generation, demand and unintentional islanding condition. Numerical simulations on a microgrid consisting of a wind turbine, a PV panel, a fuel cell, two micro-turbines, a diesel generator and a battery demonstrate the effectiveness of the proposed approach.
Liu, Guodong↗
Uncertainty Quantification in Stochastic Economic Dispatch using Gaussian Process Emulation
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Engineering - Power transmission and distribution,↗
Extracting and Generating PV Soiling Profiles for Analysis, Forecasting, and Cleaning Optimization
The identification and prediction of the daily soiling profiles of a photovoltaic site is essential to plan the optimal cleaning schedule. In this article, we analyze and propose various methods to extract and generate photovoltaic soiling profiles, in order to improve the analysis and the forecast of the losses. New soiling rate extraction methods are proposed to reflect the seasonal variability of the soiling rates and, for this reason, are found to identify the most convenient cleaning day with the highest accuracy for the investigated sites. Also, we present an approach that could be used to predict future soiling losses through the implementation of stochastic weather generation algorithms whose ability to identify in advance the best cleaning schedule is also successfully tested. The methods presented in this article can optimize the operation and maintenance schedule and could make it possible, in the future, to predict soiling losses through analysis based only on environmental parameters, such as rainfall and particulate matter, without the need of long-term soiling data.
14 SOLAR ENERGY↗
Efficient Interdependent Systems Recovery Modeling with DeepONets
Modeling the recovery of interdependent critical infrastructure is a key component of quantifying and optimizing societal resilience to disruptive events. However, simulating the recovery of large-scale interdependent systems under random disruptive events is computationally expensive. Therefore, we propose the application of Deep Operator Networks (DeepONets) in this paper to accelerate the recovery modeling of interdependent systems. DeepONets are ML architectures which identify mathematical operators from data. The form of governing equations DeepONets identify and the governing equation of interdependent systems recovery model are similar. Therefore, we hypothesize that DeepONets can efficiently model the interdependent systems recovery with little training data. We applied DeepONets to a simple case of four interdependent systems with sixteen states. DeepONets, overall, performed satisfactorily in predicting the recovery of these interdependent systems for out of training sample data when compared to reference results.
97 MATHEMATICS AND COMPUTING↗
SGD-Net: Efficient Model-Based Deep Learning with Theoretical Guarantees
Deep unfolding networks have recently gained popularity for solving imaging inverse problems. However, the computational and memory complexity of data-consistency layers within traditional deep unfolding networks scales with the number of measurements, limiting their applicability to large-scale imaging inverse problems. We propose SGD-Net as a new methodology for improving the efficiency of deep unfolding through stochastic approximations of the data-consistency layers. Our theoretical analysis shows that SGD-Net can be trained to approximate batch deep unfolding networks to an arbitrary precision. Our simulations on intensity diffraction tomography and sparse-view computed tomography show that SGD-Net can match the performance of the traditional batch network at a fraction of training and testing complexity.Deep unfolding networks have recently gained popularity for solving imaging inverse problems. However, the computational and memory complexity of data-consistency layers within traditional deep unfolding networks scales with the number of measurements, limiting their applicability to large-scale imaging inverse problems. We propose SGD-Net as a new methodology for improving the efficiency of deep unfolding through stochastic approximations of the data-consistency layers. Our theoretical analysis shows that SGD-Net can be trained to approximate batch deep unfolding networks to an arbitrary precision. Our simulations on intensity diffraction tomography and sparse-view computed tomography show that SGD-Net can match the performance of the traditional batch network at a fraction of training and testing complexity.
97 MATHEMATICS AND COMPUTING↗
Distribution System State Estimation With High Penetration of Demand Response Enabled Loads
Demand-side operations incentivize utility customers to take part in various grid services. A demand response enabled load (DREL) is a flexible grid asset that schedules electricity consumption in response to a time-of-use (TOU) energy price. Consequently, its energy profile differs from that of a conventional load that is insensitive to price. This difference may cause new challenges for distribution system state estimation (DSSE). It is well known that DSSE often needs to use pseudo-measurements based on historic load profiles to increase system observability. However, historic profiles of conventional loads are not representative of DREL behaviors. Additionally, the inaccuracy impacts DSSE results and other DSSE-dependent operations. In this paper, we propose an online pseudo-measurement generation approach for DSSE with DRELs. We formulate an optimization model to represent DRELs self-adjusting actions. Sampling-based stochastic optimization techniques are proposed to account for uncertainties in DRELs. A set of representative DREL behavior data corresponding to the samples are used to characterize DREL pseudo-measurements. Case studies with modified IEEE 123-bus test system verify the validity of the proposed work.
24 POWER TRANSMISSION AND DISTRIBUTION↗
Observability Analysis of a Power System Stochastic Dynamic Model Using a Derivative-Free Approach
Serving as a prerequisite to power system dynamic state estimation, the observability analysis of a power system dynamic model has recently attracted the attention of many power engineers. However, because this model is typically nonlinear and large-scale, the analysis of its observability is a challenge to the traditional derivative-based methods. Indeed, the linear-approximation-based approach may provide unreliable results while the nonlinear-technique-based approach inevitably faces extremely complicated derivations. Furthermore, because power systems are intrinsically stochastic, the traditional deterministic approaches may lead to inaccurate observability analyses. In this work, facing these challenges, we propose a novel polynomial-chaos-based derivative-free observability analysis approach that not only is free of any linear approximations, but also accounts for the stochasticity of the dynamic model while bringing a low implementation complexity. Furthermore, this approach enables us to quantify the degree of observability of a stochastic model, what conventional deterministic methods cannot do. The excellent performance of the proposed method has been demonstrated by performing extensive simulations using a synchronous generator model with IEEE-DC1A exciter and the TGOV1 turbine governor.
24 POWER TRANSMISSION AND DISTRIBUTION↗
Bi-Level Adaptive Storage Expansion Strategy for Microgrids Using Deep Reinforcement Learning
Battery energy storage (BES) is a versatile resource for the secure and economic operation of microgrids (MGs). Prevailing stochastic optimization-based approaches for BES expansion planning for MGs are computationally complicated. This work proposes a data-driven bi-level multi-period BES expansion planning framework to determine the siting, sizing, and timing of BES installations. The proposed planning framework unifies deep reinforcement learning (DRL) and linear programming, thereby decoupling the determinations for the integer and continuous decision variables in two time scales, respectively. In the upper level, a rainbow DRL agent with quantile regression is trained to provide dynamic planning policies to accommodate stochastic renewable energy resources (RESs), load, and battery price changes efficiently. Further, the lower level computes the optimal operation of MGs with frequency constraints to hedge the islanding contingency. The two levels communicate with one another by exchanging storage configuration and operating expenses in order to accomplish the shared goal of minimizing investment and operation costs. Comparative case studies on an MG are carried out to demonstrate the superiority of the proposed DRL-based solution to the mixed-integer linear programming counterpart on efficiency, scalability, and adaptability.
24 POWER TRANSMISSION AND DISTRIBUTION↗
Estimation of elastic properties of an additively manufactured lattice using resonant ultrasound spectroscopy
Development of improved approaches in the characterization of additively manufactured structures continues to be a topic of interest for the advanced manufacturing community. This article will investigate an approach using resonant ultrasound spectroscopy (RUS) to determine the effective elastic constants of an orthotropic lattice structure. The evaluation is performed on a cube shaped 316 L stainless steel test specimen, constructed using selective laser melting techniques. The approach uses RUS techniques in conjunction with the assumption that in the frequency regime of interest, the wavelength of the diagnostic ultrasound is greater than the discrete structural features of the unit cell of the lattice; thus, the AM structure can be treated as an anisotropic continuum with effective material properties and symmetry inherited from the unit cell. The RUS analysis estimates the nine elastic coefficients associated with orthotropic sample symmetry, which, in turn, are used to determine the elastic moduli and Poisson ratios. Current results show good agreement between experiments and modeled data. Comparisons to published results are also in good agreement, indicating the potential applicability of this characterization technique for estimating the linear elastic properties of innovative additive manufactured metal lattice structures.
36 MATERIALS SCIENCE↗
Maximum likelihood estimation of difference scaling functions for suprathreshold judgments
Maximum likelihood estimation (MLE) has been used to produce perceptual scales from binary judgments of triads and quadruples. This method relies on Thurstone’s theory of a stochastic perceptual process where the perceived difference of two stimuli is the difference in their perceived strengths. It is possible that the perception of a suprathreshold difference is overestimated when adding smaller differences, a phenomenon referred to as diminishing returns. The current approach to construct a perceptual scale using MLE does not account for this phenomenon. We present a way to model the perception of differences using MLE and Thurstone’s theory, adapted to allow the possibility of diminishing returns. This method is validated using Monte Carlo simulated responses to experimental triads and can correctly model diminishing returns, the absence of diminishing returns, and the opposite of diminishing returns both in the cases when a perceptual scale is known and when the true perceived strengths of the stimuli are unknown. Additionally, this method was applied to empirical data sets to determine its feasibility in investigations of perception. Ultimately, it was found that this analysis allows for more accurate modeling of suprathreshold difference judgments, a more complete understanding of the perceptual processes underlying comparisons, and the evaluation of Thurstone’s theory of difference judgments.
97 MATHEMATICS AND COMPUTING↗
Catalyst: Fast and flexible modeling of reaction networks
We introduce Catalyst.jl, a flexible and feature-filled Julia library for modeling and high-performance simulation of chemical reaction networks (CRNs). Catalyst supports simulating stochastic chemical kinetics (jump process), chemical Langevin equation (stochastic differential equation), and reaction rate equation (ordinary differential equation) representations for CRNs. Through comprehensive benchmarks, we demonstrate that Catalyst simulation runtimes are often one to two orders of magnitude faster than other popular tools. More broadly, Catalyst acts as both a domain-specific language and an intermediate representation for symbolically encoding CRN models as Julia-native objects. This enables a pipeline of symbolically specifying, analyzing, and modifying CRNs; converting Catalyst models to symbolic representations of concrete mathematical models; and generating compiled code for numerical solvers. Leveraging ModelingToolkit.jl and Symbolics.jl, Catalyst models can be analyzed, simplified, and compiled into optimized representations for use in numerical solvers. Finally, we demonstrate Catalyst’s broad extensibility and composability by highlighting how it can compose with a variety of Julia libraries, and how existing open-source biological modeling projects have extended its intermediate representation.
59 BASIC BIOLOGICAL SCIENCES↗
Evaluation of Seismic Artificial Intelligence with Uncertainty
Artificial intelligence has transformed the seismic community with deep learning models (DLMs) that are trained to complete specific tasks within workflows. However, there is still a lack of robust evaluation frameworks for evaluating and comparing DLMs. Here, we address this gap by designing an evaluation framework that jointly incorporates two crucial aspects: performance uncertainty and learning efficiency. To target these aspects, we meticulously construct the training, validation, and test splits using a clustering method tailored to seismic data and enact an expansive training design to segregate performance uncertainty arising from stochastic training processes and random data sampling. The framework’s ability to guard against misleading declarations of model superiority is demonstrated through the evaluation of PhaseNet (Zhu and Beroza, 2018), a popular seismic phase picking DLM, under three training approaches. Our framework helps practitioners choose the best model for their problem and set performance expectations by explicitly analyzing model performance with uncertainty at varying budgets of training data.
58 GEOSCIENCES↗
Post-hoc reweighting of hadron production in the Lund string model
We present a method for reweighting flavor selection in the Lund string fragmentation model. This is the process of calculating and applying event weights enabling fast and exact variation of hadronization parameters on pre-generated event samples. The procedure is post hoc, requiring only a small amount of additional information stored per event, and allowing for efficient estimation of hadronization uncertainties without repeated simulation. Weight expressions are derived from the hadronization algorithm itself, and validated against direct simulation for a wide range of observables and parameter shifts. The hadronization algorithm can be viewed as a hierarchical Markov process with stochastic rejections, a structure common to many complex simulations outside of high-energy physics. This perspective makes the method modular, extensible, and potentially transferable to other domains. We demonstrate the approach in Pythia, including both coverage considerations and timing benefits. For the purpose of this paper, our goal is to develop and demonstrate the the formalism, and we therefore exclude several model variations for baryon production (popcorn model, junction production) needed for proton collisions. These will be the topic of a future paper.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Framework for an adaptive integrated observation system using a hierarchy of machine learning approaches
Focal Area(s): 1. Data acquisition enabled by machine learning, AI, and advanced methods including experimental/network design/optimization, and hardware-related efforts involving AI. 2. Insight gleaned from complex measurements using AI, big data analytics, and other advanced methods, including explainable AI and physics- or knowledge-guided AI Science Challenge and Rationale: Atmospheric processes are stochastic, occur at scales from the micrometer to many kilometers, and are constantly changing over time. Characterizing these interactions and associated environmental conditions using traditional measurement techniques is difficult and can take years to build statistics on atmospheric phenomena that occurs episodically. Developing new innovative approaches to modify sampling strategies in real-time would enable the routine collection of targeted measurements focused on a specific set of science questions.
54 ENVIRONMENTAL SCIENCES↗
A Note on the Probability of Initiation Problem
The purpose of this note is to draw attention to Pál’s derivation of the Pál Bell equation which is used by LLNL and LANL to model Probability of Initiation (POI) problems. Both laboratories credit the equation to Bell and Lee. Although the equation formulated by Bell and Lee and the equation derived by Pál appear to be the same, the derivation by Bell and Lee is flawed. Scattering, which was absent in Bell’s original formulation of a POI problem, was later introduced by Bell and Lee by simply replacing a fission term with a scattering term. Such a replacement, however, leads to an inaccurate average number v̅ of neutrons that is produced by a fission event. By approaching a POI problem from probabilistic point of view, Pál formulates the problem as a branching process that determines v̅ correctly. There are six reasons for writing this report. The first is to clarify the failing in Bell and Lee’s derivation. The second is to establish the origin of the equation used by the laboratories. The third is to elucidate the fixed point technique formulated by Mokhtar-Kharroubi for solving the Pál-Bell equation. The fourth is to derive the α eigenvalue that is associated with a time dependent Pál-Bell equation. The fifth is to show in Appendix A that the non-linear fission operator of the Pál-Bell equation is descended from the operator of the Galton-Watson process of stochastic theory. The sixth is to describe in Appendix B a second order positivity preserving technique that accelerates the convergence of the first order fixed point method developed by Mokhtar-Kharroubi.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
The Dynamics of Interstellar Asteroids and Comets within the Galaxy: An Assessment of Local Candidate Source Regions for 1I/’Oumuamua and 2I/Borisov
The low velocity of interstellar asteroid 1I/’Oumuamua with respect to our galaxy’s local standard of rest implies that it is young. Adopting the young age hypothesis, we assess possible origin systems for this interstellar asteroid and for 2I/Borisov, though the latter’s higher speed means it is unlikely to be young. First, their past trajectories are modeled under gravitational scattering by galactic components (“disk heating”) to assess how far back one can trace them. The stochastic nature of disk heating means that a back integration can only expect to be accurate to within 15 pc and 2 km s{sup −1} at −10 Myr, dropping steeply to 400 pc and 10 km s{sup −1} at −100 Myr, sharply limiting our ability to determine a precise origin. Nevertheless, we show that ’Oumuamua’s origin system likely is currently within 1 kpc of Earth, in the local Orion Arm. Second, we back integrate ’Oumuamua’s trajectory in order to assess source regions, emphasizing young systems and moving groups. Though disk heating allows for only a statistical link to source regions, ’Oumuamua passed through a considerable subset of the Carina and Columba moving groups when those groups were forming. This makes them perhaps the most plausible source region, if ’Oumuamua was ejected during planet formation or via intra-cluster interactions. We find three stars in the Ursa Major group, one brown dwarf, and seven other stars to have plausible encounters with 2I/Borisov, within 2 pc and 30 km s{sup −1}. These encounters’ high relative speeds mean none are likely to be the home of 2I/Borisov.
79 ASTRONOMY AND ASTROPHYSICS↗
On the Accuracy of the ALMA Flux Calibration in the Time Domain and across Spectral Windows
A diverse array of science goals requires accurate flux calibration of observations with the Atacama Large Millimeter/submillimeter array (ALMA); however, this goal remains challenging due to the stochastic time-variability of the “grid” quasars ALMA uses for calibration. In this work, we use 343.5 GHz (Band 7) ALMA Atacama Compact Array observations of four bright and stable young stellar objects over seven epochs to independently assess the accuracy of the ALMA flux calibration and to refine the relative calibration across epochs. The use of these four extra calibrators allows us to achieve an unprecedented relative ALMA calibration accuracy of ~3%. On the other hand, when the observatory calibrator catalog is not up to date, the Band 7 data calibrated by the ALMA pipeline may have a flux calibration poorer than the nominal 10%, which can be exacerbated by weather-related phase decorrelation when self-calibration of the science target is either not possible or not attempted. We also uncover a relative flux calibration uncertainty between spectral windows of 0.8%, implying that measuring spectral indices within a single ALMA band is likely highly uncertain. We thus recommend various methods for science goals requiring high flux accuracy and robust calibration, in particular, the observation of additional calibrators combined with a relative calibration strategy, and observation of solar system objects for high absolute accuracy.
79 ASTRONOMY AND ASTROPHYSICS↗