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Efficient prediction of attosecond two-colour pulses from an X-ray free-electron laser with machine learning

Abstract X-ray free-electron lasers are sources of coherent, high-intensity X-rays with numerous applications in ultra-fast measurements and dynamic structural imaging. Due to the stochastic nature of the self-amplified spontaneous emission process and the difficulty in controlling injection of electrons, output pulses exhibit significant noise and limited temporal coherence. Standard measurement techniques used for characterizing two-coloured X-ray pulses are challenging, as they are either invasive or diagnostically expensive. In this work, we employ machine learning methods such as neural networks and decision trees to predict the central photon energies of pairs of attosecond fundamental and second harmonic pulses using parameters that are easily recorded at the high-repetition rate of a single shot. Using real experimental data, we apply a detailed feature analysis on the input parameters while optimizing the training time of the machine learning methods. Our predictive models are able to make predictions of central photon energy for one of the pulses without measuring the other pulse, thereby leveraging the use of the spectrometer without having to extend its detection window. We anticipate applications in X-ray spectroscopy using XFELs, such as in time-resolved X-ray absorption and photoemission spectroscopy, where improved measurement of input spectra will lead to better experimental outcomes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

GCR Transport in the Brain: Assessment of Self-Shielding, Columnar Damage, and Nuclear Reactions on Cell Inactivation Rates

Radiation shield design is driven by the need to limit radiation risks while optimizing risk reduction with launch mass/expense penalties. Both limitation and optimization objectives require the development of accurate and complete means for evaluating the effectiveness of various shield materials and body-self shielding. For galactic cosmic rays (GCR), biophysical response models indicate that track structure effects lead to substantially different assessments of shielding effectiveness relative to assessments based on LET-dependent quality factors. Methods for assessing risk to the central nervous system (CNS) from heavy ions are poorly understood at this time. High-energy and charge (HZE) ion can produce tissue events resulting in damage to clusters of cells in a columnar fashion, especially for stopping heavy ions. Grahn (1973) and Todd (1986) have discussed a microlesion concept or model of stochastic tissue events in analyzing damage from HZE's. Some tissues, including the CNS, maybe sensitive to microlesion's or stochastic tissue events in a manner not illuminated by either conventional dosimetry or fluence-based risk factors. HZE ions may also produce important lateral damage to adjacent cells. Fluences of high-energy proton and alpha particles in the GCR are many times higher than HZE ions. Behind spacecraft and body self-shielding the ratio of protons, alpha particles, and neutrons to HZE ions increases several-fold from free-space values. Models of GCR damage behind shielding have placed large concern on the role of target fragments produced from tissue atoms. The self-shielding of the brain reduces the number of heavy ions reaching the interior regions by a large amount and the remaining light particle environment (protons, neutrons, deuterons. and alpha particles) may be the greatest concern. Tracks of high-energy proton produce nuclear reactions in tissue, which can deposit doses of more than 1 Gv within 5 - 10 cell layers. Information on rates of cell killing from GCR, including patterns of cell killing from single particle tracks. can provide useful information on expected differences between proton and HZE tracks and clinical experiences with photon irradiation. To model effects on cells in the brain, it is important that transport models accurately describe changes in the GCR due to interactions in the cranium and proximate tissues. We describe calculations of the attenuated GCR particle fluxes at three dose-points in the brain and associated patterns of cell killing using biophysical models. The effects of the brain self-shielding and bone-tissue interface of the skull in modulating the GCR environment are considered. For each brain dose-point, the mass distribution in the surrounding 4(pi) solid angle is characterized using the CAM model to trace 512 rays. The CAM model describes the self-shielding by converting the tissue distribution to mass-equivalent aluminum, and nominal values of spacecraft shielding is considered. Particle transport is performed with the proton, neutron, and heavy-ion transport code HZETRN with the nuclear fragmentation model QMSFRG. The distribution of cells killed along the path of individual GCR ions is modeled using in vitro cell inactivation data for cells with varying sensitivity. Monte Carlo simulations of arrays of inactivated cells are considered for protons and heavy ions and used to describe the absolute number of cell killing events of various magnitude in the brain from the GCR. Included are simulations of positions of inactivated cells from stopping heavy ions and nuclear stars produced by high-energy ions most importantly, protons and neutrons.

Shavers, M. R.↗

Role of Interactions and Correlations on Collective Dynamics of Molecular Motors Along Parallel Filaments

Cytoskeletal motors known as motor proteins are molecules that drive cellular transport along several parallel cytoskeletal filaments and support many biological processes. Experimental evidences suggest that they interact with the nearest molecules of their filament while performing any mechanical work. These interactions modify the microscopic level properties of motor proteins. In this work, a new version of two-channel totally asymmetric simple exclusion process, that incorporates the intra-channel interactions in a thermodynamically consistent way, is proposed. As the existing approaches for multi-channel systems deviate from analyzing the combined effect of inter and intra-channel interactions, a new approach known as modified vertical cluster mean field is developed. The approach along with Monte Carlo simulations successfully encounters some correlations and computes the complex dynamic properties of the system. Role of symmetry of interactions and inter-channel coupling is observed on the phase diagrams, maximal particle current and its corresponding optimal interaction strength. Surprisingly, for all values of coupling rate and most of the interaction splittings, the optimal interaction strength corresponding to maximal current belongs to the case of weak repulsive interactions. Moreover, for weak interaction splittings and with an increase in the coupling rate, the optimal interaction strength tends towards the known experimental results. The effect of coupling as well as interaction energy is also measured for correlations. They are found to be short-range and weaker for repulsive and weak attractive interactions while they are long-range and stronger for large attractions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Wildfire Segmentation From Remotely Sensed Data Using Quantum-Compatible Conditional Vector Quantized-Variational Autoencoders

Wildfires represent a critical environmental hazard with multifaceted implications for ecosystems, communities, and public health [1]. The escalating frequency and intensity of wildfires globally have intensified the urgency for robust segmentation methodologies to facilitate effective mitigation, response, and recovery strategies [2]. Accurate wildfire segmentation is pivotal for delineating fire boundaries, assessing progression patterns, and prioritizing resource allocation during emergency scenarios. Furthermore, precise segmentation enables stakeholders, including policymakers, environmental scientists, and emergency responders, to formulate evidence-based strategies, thereby minimizing socio-economic disruptions and ecological degradation. Consequently, advancing wildfire segmentation techniques through innovative technological interventions remains a paramount research imperative. Although foundational in wildfire segmentation, traditional deterministic models exhibit inherent limitations that compromise their efficacy in dynamic and uncertain environments. These models often operate on rigid algorithms prioritizing deterministic classifications, thereby overlooking the inherent complexities and uncertainties associated with wildfire behavior and satellite data variability. Such deterministic frameworks tend to produce oversimplified representations that fail to capture the intricate nuances of evolving fire dynamics, spatial heterogeneity, and environmental interactions [1]. Consequently, the deterministic approach’s propensity for uncertainty collapsing [1, 3] hampers the accuracy, reliability, and applicability of segmentation outcomes in real-world scenarios. Contrastingly, stochastic models offer a more nuanced and adaptable framework for wildfire segmentation. By integrating probabilistic elements into the modeling paradigm, stochastic approaches, particularly probabilistic approaches such as variational auto encoders (VAEs) [4], facilitate comprehensive uncertainty assessment, enabling researchers to quantify and incorporate uncertainties into segmentation outcomes effectively. This probabilistic nature empowers stochastic models to encapsulate variability, account for data inconsistencies, and adapt to evolving environmental conditions, enhancing segmentation accuracy, reliability, and robustness. Embracing stochastic methodologies thus catalyzes advancements in wildfire science by fostering a more holistic, adaptive, and resilient segmentation framework. Despite VAEs demonstrating significant promise in various applications, they come with inherent limitations that have garnered attention within the machine learning community. One of the primary drawbacks lies in their reliance on static priors, which essentially assume a fixed distribution for latent variables, thereby limiting the model’s flexibility to capture complex data structures effectively [5]. This static nature leads to suboptimal representations, especially when dealing with complex and high-dimensional data. Additionally, VAEs often struggle with generating sharp and realistic samples, a phenomenon commonly referred to as mode collapse [5, 7, 6]. Furthermore, the optimization process in VAEs, which involves balancing the reconstruction loss and the regularization term, can sometimes be challenging to fine-tune [7]. In recent efforts to address these shortcomings, alternative approaches like Vector Quantized Variational Auto encoders(VQ-VAEs) [7], address the challenges by incorporating discrete latent variables and leveraging techniques that enhance the quality and diversity of generated samples while maintaining efficient training dynamics. VQ-VAEs propose a dynamic prior distribution generation mechanism that diverges from the static priors commonly associated with traditional VAEs. This dynamic approach allows for more adaptive and context-aware latent variable representations, thereby potentially capturing complex data structures more effectively. Unlike autoregressive prior models such as PixelCNN, which, despite their ability to model dependencies across data dimensions, suffer from significant computational inefficiencies and lack flexibility in handling diverse datasets. In our work, we propose to use a generative quantum-compatible approach to help alleviate the shortcomings of autoregressive prior model in VQ-VAEs. Restricted Boltzmann Machines (RBMs) are a viable alternative prior model that can learn prior distributions in a faster and more flexible manner. In this research endeavor, we meticulously curate a state-of-the-art dataset leveraging satellite MODIS data in conjunction with VIIRS fire masks, derived from Fire Radiative Power (FRP), thereby encapsulating diverse wildfire scenarios and environmental contexts. We developed a conditional VQ-VAE architecture with the RBM prior model that is trained in a supervised manner for segmenting wildfire masks. This innovative approach synergistically harnesses deep learning capabilities, enabling the generation of segmentation maps characterized by heightened precision, granularity, and contextual relevance. Furthermore, replacing the autoregressive prior learning method proposed by the original VQ-VAE with a prior density approximation via quantum-compatible RBM facilitates expedited inference processes, augments flexibility in prior sampling, optimizes computational efficiency and establishes a groundbreaking benchmark in wildfire segmentation methodologies.

quantum machine learning↗

Possible role of interference, protein noise, and sink effects in nonphotochemical quenching in photosynthetic complexes

Here, we analyze theoretically a simple and consistent quantum mechanical model that reveals the possible role of quantum interference, protein noise, and sink effects in the nonphotochemical quenching (NPQ) in light-harvesting complexes (LHCs). The model consists of a network of five interconnected sites (excitonic states of light-sensitive molecules) responsible for the NPQ mechanism. The model also includes the “damaging” and the dissipative channels. The damaging channel is responsible for production of singlet oxygen and other destructive outcomes. In this model, both damaging and “dissipative” charge transfer channels are described by discrete electron energy levels attached to their sinks, that mimic the continuum part of electron energy spectrum. All five excitonic sites interact with the protein environment that is modeled using a stochastic process. Our approach allowed us to derive the exact and closed system of linear ordinary differential equations for the reduced density matrix and its first momentums. Moreover, these equations are solved numerically including for strong interactions between the light-sensitive molecules and protein environment. As an example, we apply our model to demonstrate possible contributions of quantum interference, protein noise, and sink effects in the NPQ mechanism in the CP29 minor LHC. The numerical simulations show that using proper combination of quantum interference effects, properties of noise, and sinks, one can significantly suppress the damaging channel. Finally, our findings demonstrate the possible role of interference, protein noise, and sink effects for modeling, engineering, and optimizing the performance of the NPQ processes in both natural and artificial light-harvesting complexes.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Spatial Graph Attention and Curiosity-driven Policy for Antiviral Drug Discovery

We developed Distilled Graph Attention Policy Network (DGAPN), a reinforcement learning model to generate novel graph-structured chemical representations that optimize user-defined objectives by efficiently navigating a physically constrained domain. The framework is examined on the task of generating molecules that are designed to bind, noncovalently, to functional sites of SARS-CoV-2 proteins. We present a spatial Graph Attention (sGAT) mechanism that leverages self-attention over both node and edge attributes as well as encoding the spatial structure --- this capability is of considerable interest in synthetic biology and drug discovery. An attentional policy network is introduced to learn the decision rules for a dynamic, fragment-based chemical environment, and state-of-the-art policy gradient techniques are employed to train the network with stability. Exploration is driven by the stochasticity of the action space design and the innovation reward bonuses learned and proposed by random network distillation. In experiments, our framework achieved outstanding results compared to state-of-the-art algorithms, while reducing the complexity of paths to chemical synthesis.

Wu, Yulun↗

SPATIAL GRAPH ATTENTION AND CURIOSITY-DRIVEN POLICY FOR ANTIVIRAL DRUG DISCOVERY

We developed Distilled Graph Attention Policy Network (DGAPN), a reinforcement learning model to generate novel graph-structured chemical representations that optimize user-defined objectives by efficiently navigating a physically constrained domain. The framework is examined on the task of generating molecules that are designed to bind, noncovalently, to functional sites of SARS-CoV-2 proteins. We present a spatial Graph Attention (sGAT) mechanism that leverages self-attention over both node and edge attributes as well as encoding the spatial structure - this capability is of considerable interest in synthetic biology and drug discovery. An attentional policy network is introduced to learn the decision rules for a dynamic, fragment-based chemical environment, and state-of-the-art policy gradient techniques are employed to train the network with stability. Exploration is driven by the stochasticity of the action space design and the innovation reward bonuses learned and proposed by random network distillation. In experiments, our framework achieved outstanding results compared to state-of-the-art algorithms, while reducing the complexity of paths to chemical synthesis.

Wu, Y↗

An improved multilevel Monte Carlo method for estimating probability distribution functions in stochastic oil reservoir simulations

In this paper, we develop an improved multilevel Monte Carlo (MLMC) method for estimating cumulative distribution functions (CDFs) of a quantity of interest, coming from numerical approximation of large-scale stochastic subsurface simulations. Compared with Monte Carlo (MC) methods, that require a significantly large number of high-fidelity model executions to achieve a prescribed accuracy when computing statistical expectations, MLMC methods were originally proposed to significantly reduce the computational cost with the use of multifidelity approximations. The improved performance of the MLMC methods depends strongly on the decay of the variance of the integrand as the level increases. However, the main challenge in estimating CDFs is that the integrand is a discontinuous indicator function whose variance decays slowly. To address this difficult task, we approximate the integrand using a smoothing function that accelerates the decay of the variance. In addition, we design a novel a posteriori optimization strategy to calibrate the smoothing function, so as to balance the computational gain and the approximation error. The combined proposed techniques are integrated into a very general and practical algorithm that can be applied to a wide range of subsurface problems for high-dimensional uncertainty quantification, such as a fine-grid oil reservoir model considered in this effort. The numerical results reveal that with the use of the calibrated smoothing function, the improved MLMC technique significantly reduces the computational complexity compared to the standard MC approach. Finally, we discuss several factors that affect the performance of the MLMC method and provide guidance for effective and efficient usage in practice.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Demonstration of Optimal Benchmark Selection Website and Validation of the q c Coverage Metric Using HEU-SOL-THERM-013-003 Experiment

In the work documented in this interim report, the experiment selection toolkit web site was demonstrated and q C coverage metric methodology was validated for IEU-MET-FAST-002-001, MIX-COMP-THERM 004-004, and HEU-SOL-THERM-013-003 experiments. 𝑞 𝐶 is an information-theoretic measure based on mutual information that quantifies the ability of candidate benchmark experiments to reduce the bias and uncertainty of a target criticality safety application. The metric and an accompanying open-source Python toolkit with a web-based interface were tested against a benchmark set of 425 experiments drawn from the International Criticality Safety Benchmark Evaluation Project Handbook. The interface is hosted at https://edim.covdef.com. It accepts sensitivity data files produced by the TSUNAMI-IP module of the SCALE code system and supports both (i) deterministic analysis using the ENDF/B-VII.0 covariance library and (ii) stochastic analysis based on user-supplied keff samples. Demonstrations on representative applications across a range of material composition, spectrum, and form show that q C -guided benchmark selection achieves greater uncertainty reduction with fewer experiments and yields more stable posterior bias and uncertainty estimates than traditional similarity coefficient ( c k )–based selection, while also capturing valuable low-ck experiments that one-to-one metrics overlook.

Abdel-khalik, Hany S. [Indiana Univ.-Purdue Univ. ↗

An Improved Discrete Least-Squares/Reduced-Basis Method for Parameterized Elliptic PDEs

It is shown that the computational efficiency of the discrete least-squares (DLS) approximation of solutions of stochastic elliptic PDEs is improved by incorporating a reduced-basis method into the DLS framework. In particular, we consider stochastic elliptic PDEs with an affine dependence on the random variable. The goal is to recover the entire solution map from the parameter space to the finite element space. To this end, first, a reduced-basis solution using a weak greedy algorithm is constructed, then a DLS approximation is determined by evaluating the reduced-basis approximation instead of the full finite element approximation. The main advantage of the new approach is that one only need apply the DLS operator to the coefficients of the reduced-basis expansion, resulting in huge savings in both the storage of the DLS coefficients and the online cost of evaluating the DLS approximation. In addition, the recently developed quasi-optimal polynomial space is also adopted in the new approach, resulting in superior convergence rates for a wider class of problems than previous analyzed. Numerical experiments are provided that illustrate the theoretical results.

97 MATHEMATICS AND COMPUTING↗

Projection pursuit adaptation on polynomial chaos expansions

Here, the present work addresses the issue of accurate stochastic approximations in high-dimensional parametric space using tools from uncertainty quantification (UQ). The basis adaptation method and its accelerated algorithm in polynomial chaos expansions (PCE) were recently proposed to construct low-dimensional approximations adapted to specific quantities of interest (QoI). The present paper addresses one difficulty with these adaptations, namely their reliance on quadrature point sampling, which limits the reusability of potentially expensive samples. Projection pursuit (PP) is a statistical tool to find the “interesting” projections in high-dimensional data and thus bypass the curse-of-dimensionality. In the present work, we combine the fundamental ideas of basis adaptation and projection pursuit regression (PPR) to propose a novel method to simultaneously learn the optimal low-dimensional spaces and PCE representation from given data. While this projection pursuit adaptation (PPA) can be entirely data-driven, the constructed approximation exhibits mean-square convergence to the solution of an underlying governing equation and thus captures the supports and probability distributions associated with the physics constraints. The proposed approach is demonstrated on a borehole problem and a structural dynamics problem, demonstrating the versatility of the method and its ability to discover low-dimensional manifolds with high accuracy with limited data. In addition, the method can learn surrogate models for different quantities of interest while reusing the same data set.

97 MATHEMATICS AND COMPUTING↗

Detective quantum efficiency of photon-counting x-ray detectors

Purpose: Single-photon-counting (SPC) x-ray imaging has the potential to improve image quality and enable novel energy-dependent imaging methods. Similar to conventional detectors, optimizing image SPC quality will require systems that produce the highest possible detective quantum efficiency (DQE). This paper builds on the cascaded-systems analysis (CSA) framework to develop a comprehensive description of the DQE of SPC detectors that implement adaptive binning. Methods: The DQE of SPC systems can be described using the CSA approach by propagating the probability density function (PDF) of the number of image-forming quanta through simple quantum processes. New relationships are developed to describe PDF transfer through serial and parallel cascades to accommodate scatter reabsorption. Results are applied to hypothetical silicon and selenium-based flat-panel SPC detectors including the effects of reabsorption of characteristic/scatter photons from photoelectric and Compton interactions, stochastic conversion of x-ray energy to secondary quanta, depth-dependent charge collection, and electronic noise. Results are compared with a Monte Carlo study. Results: Depth-dependent collection efficiency can result in substantial broadening of photopeaks that in turn may result in reduced DQE at lower x-ray energies (20–45 keV). Double-counting interaction events caused by reabsorption of characteristic/scatter photons may result in falsely inflated image signal-to-noise ratio and potential overestimation of the DQE. Conclusions: The CSA approach is extended to describe signal and noise propagation through photoelectric and Compton interactions in SPC detectors, including the effects of escape and reabsorption of emission/scatter photons. High-performance SPC systems can be achieved but only for certain combinations of secondary conversion gain, depth-dependent collection efficiency, electronic noise, and reabsorption characteristics.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Cosmic heavy ion tracks in mesoscopic biological test objects

Since more than 20 years ago, when the National Academy of Sciences and the National Research Council of the U.S.A. released their report on 'HZE particle effects in manned spaced flight', it has been emphasized how difficult - if not even impossible - it is to assess their radiobiological impact on man from conventional studies where biological test organisms are stochastically exposed to 'large' fluences of heavy ions. An alternative, competing approach had been realized in the BIOSTACK experiments, where the effects of single cosmic as well as accelerator - heavy ions on individual biological test organisms could be investigated. Although presented from the beginning as the preferable approach for terrestrial investigations with accelerator heavy ions too ('The BIOSTACK as an approach to high LET radiation research'), only recently this insight is gaining more widespread recognition. In space flight experiments, additional constraints imposed by the infrastructure of the vehicle or satellite further impede such investigations. Restrictions concern the physical detector systems needed for the registration of the cosmic heavy ions' trajectories as well as the biological systems eligible as test organisms. Such optimized procedures and techniques were developed for the investigations on chromosome aberrations induced by cosmic heavy ions in cells of the stem meristem of lettuce seeds (Lactuca sativa) and for the investigation of the radiobiological response of Wolffia arriza, which is the smallest flowering (water) plant. The biological effects were studied by the coworkers of the Russian Institute of Biomedical Problems (IBMP) which in cooperation with the European Space Agency ESA organized the exposure in the Biosatellites of the Cosmos series. Since biological investigations and physical measurements of particle tracks had to be performed in laboratories widely separated, the preferred fixed contact between biological test objects and the particle detectors until the geometrical correlation between tracks and organisms has been established could not be maintained. This gave rise to half a dozen of coordinate systems for different measurements which finally had to be related to a single stack reference system.

Facius, R.↗

An indirect approach to optimize the reaction rates of thermal NO formation for diesel engines

With stringent emission regulations, it has become more important for modern diesel engine manufacturers to accurately predict engine-out nitrogen oxide (NO x ) emissions across a wide range of operating conditions. Thermal NO is the major source of engine-out NO x in modern diesel engines. For thermal NO formation, several earlier studies have recommended the forward and reverse reaction rate coefficients of the rate-limiting reaction (O + N 2 ⇌ NO + N). However, due to deficiencies in sub-models and inadequacies of reduced chemical mechanisms to represent diesel combustion, these recommended values more often than not need to be adjusted in reduced order combustion models to accurately predict engine-out NO x . Hence, in this work a systematic and computationally efficient approach has been proposed to streamline the process of determining the optimum reaction rate coefficients. Here, to develop the optimization approach, four different production diesel engines with different operating conditions in terms of speed, load, and exhaust-gas recirculation have been considered. Numerical simulations have been performed using a detailed zero-dimensional velocity-composition-frequency transported probability density function (0D-VCF-tPDF) model that uses hundreds of notional particles to capture in-cylinder stratification. Four different combinations of hydrocarbon and NO x chemical mechanisms were used to represent chemistry. It was found that for the rate-limiting reaction, the pre-exponent factors (A f1 , A r1 ) and activation energies (E A,f1 , E A,r1 ) of the forward and reverse reaction rates follow a linear band in A f1 - E A,f1 and A r1 - E A,r1 space where predicted engine-out NO x match the measured values closely. By encompassing such bands from different engines and considering constraints on activation energies, a reduced search domain of pre-exponent factors and activation energies was constructed that is expected to be applicable to any diesel engine. Eventually, computationally efficient three-line and one-line search approaches were proposed to determine the optimum values of the pre-exponent factors and activation energies that led to a minimum error between measured and predicted engine-out NO x . Finally, these three-line and one-line NO x optimization approaches were applied to a fifth production diesel engine for which the 0D-VCF-tPDF model showed a very good predictive performance in terms of predicting peak pressure, 50% burn rate, and engine-out NO x when compared to measured and 3D-CFD values.

33 ADVANCED PROPULSION SYSTEMS↗

An automated approach to the alignment of compound refractive lenses

Compound refractive lenses (CRLs) are established X-ray focusing optics, and are thus a key element of many beamlines at X-ray facilities, used to either to focus a beam or image a sample. While CRLs are quite established, the stack of single lens elements affords a very small numerical aperture because of the thick lens profile, making them far more difficult to align than classical optical lenses that obey the thin-lens approximation. This means that the alignment must be very precise and is highly sensitive to changes to the incident beam; aligning CRLs is thus typically treated as a time-consuming manual process. Many groups circumvent day-to-day realignment by using engineering controls (e.g. mounting optics) that sacrifice some of the beam’s focusing characteristics, i.e. spot size, or resolution. While these choices minimize setup time, there are clear disadvantages. This work presents a new automated approach to align CRLs using a simple alignment apparatus that is easy to adapt and install at different types of X-ray experiments or facilities. Our approach builds on recent CRL modeling efforts, using an approach based on the Stochastic Nelder-Mead (SNM) simplex method. We demonstrate the efficacy of this method by numerical simulation and then extend this test to real experiments conducted at the Advanced Photon Source to confirm its performance with a synchrotron X-ray beam. This work provides an opportunity to automate key instrumentation at X-ray facilities.

97 MATHEMATICS AND COMPUTING↗

Algorithm to solve a chance-constrained network capacity design problem with stochastic demands and finite support

Here, we consider the problem of determining the capacity to assign to each arc in a given network, subject to uncertainty in the supply and/or demand of each node. This design problem underlies many real-world applications, such as the design of power transmission and telecommunications networks. We first consider the case where a set of supply/demand scenarios are provided, and we must determine the minimum-cost set of arc capacities such that a feasible flow exists for each scenario. We briefly review existing theoretical approaches to solving this problem and explore implementation strategies to reduce run times. With this as a foundation, our primary focus is on a chance-constrained version of the problem in which α% of the scenarios must be feasible under the chosen capacity, where α is a user-defined parameter and the specific scenarios to be satisfied are not predetermined. We describe an algorithm which utilizes a separation routine for identifying violated cut-sets which can solve the problem to optimality, and we present computational results. We also present a novel greedy algorithm, our primary contribution, which can be used to solve for a high quality heuristic solution. We present computational analysis to evaluate the performance of our proposed approaches.

97 MATHEMATICS AND COMPUTING↗

Training neural networks using Metropolis Monte Carlo and an adaptive variant

Abstract We examine the zero-temperature Metropolis Monte Carlo (MC) algorithm as a tool for training a neural network by minimizing a loss function. We find that, as expected on theoretical grounds and shown empirically by other authors, Metropolis MC can train a neural net with an accuracy comparable to that of gradient descent (GD), if not necessarily as quickly. The Metropolis algorithm does not fail automatically when the number of parameters of a neural network is large. It can fail when a neural network’s structure or neuron activations are strongly heterogenous, and we introduce an adaptive Monte Carlo algorithm (aMC) to overcome these limitations. The intrinsic stochasticity and numerical stability of the MC method allow aMC to train deep neural networks and recurrent neural networks in which the gradient is too small or too large to allow training by GD. MC methods offer a complement to gradient-based methods for training neural networks, allowing access to a distinct set of network architectures and principles.

97 MATHEMATICS AND COMPUTING↗

Occupancy-Based HVAC Control with Short-Term Occupancy Prediction Algorithms for Energy-Efficient Buildings

This study aims to develop a concrete occupancy prediction as well as an optimal occupancy-based control solution for improving the efficiency of Heating, Ventilation, and Air-Conditioning (HVAC) systems. Accurate occupancy prediction is a key enabler for demand-based HVAC control so as to ensure HVAC is not run needlessly when when a room/zone is unoccupied. In this paper, we propose simple yet effective algorithms to predict occupancy alongside an algorithm for automatically assigning temperature set-points. Utilizing past occupancy observations, we introduce three different techniques for occupancy prediction. Firstly, we propose an identification-based approach, which identifies the model via Expectation Maximization (EM) algorithm. Secondly, we study a novel finite state automata (FSA) which can be reconstructed by a general systems problem solver (GSPS). Thirdly, we introduce an alternative stochastic model based on uncertain basis functions. The results show that all the proposed occupancy prediction techniques could achieve around 70% accuracy. Then, we have proposed a scheme to adaptively adjust the temperature set-points according to a novel temperature set algorithm with customers’ different discomfort tolerance indexes. By cooperating with the temperature set algorithm, our occupancy-based HVAC control shows 20% energy saving while still maintaining building comfort requirements.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗