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Mass spectrometric analyses of high performance polymers to assess their radiopurity as ultra low background materials for rare event physics detectors
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Study of radon reduction in gases for rare event search experiments
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Cosmogenic activation of germanium used for tonne-scale rare event search experiments
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Rare Event Sampling Improves Mercury Instability Statistics
Due to the chaotic nature of planetary dynamics, there is a non-zero probability that Mercury's orbit will become unstable in the future. Previous efforts have estimated the probability of this happening between 3 and 5 billion years in the future using a large number of direct numerical simulations with an N-body code, but were not able to obtain accurate estimates before 3 billion years in the future because Mercury instability events are too rare. In this paper we use a new rare-event sampling technique, Quantile Diffusion Monte Carlo (QDMC), to estimate that the probability of a Mercury instability event in the next 2 billion years is approximately 10 –4 in the REBOUND N-body code. We show that QDMC provides unbiased probability estimates at a computational cost of up to 100 times less than direct numerical simulation. QDMC is easy to implement and could be applied to many problems in planetary dynamics in which it is necessary to estimate the probability of a rare event.
Rare Events via Cross-Entropy Population Monte Carlo
Rare events are events that happen with very low frequency. Estimating rare event probabilities using Monte Carlo techniques is computationally expensive, often to the point of intractability, and special methods are required. Importance sampling (IS) is a well known technique that uses a proposal distribution in place of a target distribution to lower the variance of the estimator. Key to the success of IS methods is the choice of a proposal distribution, or the parameters governing the distribution. Adaptive importance sampling improves the parameters of a family or population of proposal distributions iteratively through trials. We present a novel cross-entropy population Monte Carlo algorithm, which adapts the parameters of proposals through the cross-entropy method. The proposed method stands apart from previous work in that we are not optimizing a mixture distribution. Instead, we leverage deterministic mixture weights and optimize the distributions individually through a reinterpretation of the typical derivation of the cross-entropy method. Demonstrations on rare event examples show that the algorithm can outperform existing resampling based population Monte Carlo methods, especially for higher-dimensional problems. Finally, we also demonstrate efficacy on a conjunction analysis problem.
Predicting rare events using neural networks and short-trajectory data
Estimating the likelihood, timing, and nature of events is a major goal of modeling stochastic dynamical systems. When the event is rare in comparison with the timescales of simulation and/or measurement needed to resolve the elemental dynamics, accurate prediction from direct observations becomes challenging. In such cases a more effective approach is to cast statistics of interest as solutions to Feynman-Kac equations (partial differential equations). Here, we develop an approach to solve Feynman-Kac equations by training neural networks on short-trajectory data. Our approach is based on a Markov approximation but otherwise avoids assumptions about the underlying model and dynamics. This makes it applicable to treating complex computational models and observational data. Additionally, we illustrate the advantages of our method using a low-dimensional model that facilitates visualization, and this analysis motivates an adaptive sampling strategy that allows on-the-fly identification of and addition of data to regions important for predicting the statistics of interest. Finally, we demonstrate that we can compute accurate statistics for a 75-dimensional model of sudden stratospheric warming. This system provides a stringent test bed for our method.
Bayesian analysis of rare events
In many areas of engineering and science there is an interest in predicting the probability of rare events, in particular in applications related to safety and security. Increasingly, such predictions are made through computer models of physical systems in an uncertainty quantification framework. Additionally, with advances in IT, monitoring and sensor technology, an increasing amount of data on the performance of the systems is collected. This data can be used to reduce uncertainty, improve the probability estimates and consequently enhance the management of rare events and associated risks. Bayesian analysis is the ideal method to include the data into the probabilistic model. It ensures a consistent probabilistic treatment of uncertainty, which is central in the prediction of rare events, where extrapolation from the domain of observation is common. We present a framework for performing Bayesian updating of rare event probabilities, termed BUS. It is based on a reinterpretation of the classical rejection-sampling approach to Bayesian analysis, which enables the use of established methods for estimating probabilities of rare events. By drawing upon these methods, the framework makes use of their computational efficiency. These methods include the First-Order Reliability Method (FORM), tailored importance sampling (IS) methods and Subset Simulation (SuS). In this contribution, we briefly review these methods in the context of the BUS framework and investigate their applicability to Bayesian analysis of rare events in different settings. We find that, for some applications, FORM can be highly efficient and is surprisingly accurate, enabling Bayesian analysis of rare events with just a few model evaluations. In a general setting, BUS implemented through IS and SuS is more robust and flexible.
Contour forward flux sampling: Sampling rare events along multiple collective variables
Many rare event transitions involve multiple collective variables (CVs), and the most appropriate combination of CVs is generally unknown a priori. As such, we introduce a new method, contour forward flux sampling (cFFS), to study rare events with multiple CVs simultaneously. cFFS places nonlinear interfaces on-the-fly from the collective progress of the simulations, without any prior knowledge of the energy landscape or appropriate combination of CVs. We demonstrate cFFS on analytical potential energy surfaces and a conformational change in alanine dipeptide.
Sampling Rare Events in Aqueous Systems Using Molecular Simulations
Birth of a new distinct phase is a phenomenon encountered in a myriad of processes, and has wide ranging consequences in material processing, biological self-assembly, separations and several other processes. Several phase transitions are nucleation driven. The nucleation events occur over nanosecond timescales and involve hundreds to thousands of molecules. These length and timescales are difficult to access in experiments, thereby making experimental studies of nucleation challenging. On the other hand, molecular simulations sample the nanosecond and nanometer scales making them ideal to study nucleation. However, nucleation is a rare event, meaning that the waiting time to observe one nucleation event is significant. This makes simulation studies of rare events challenging. The project focused on a multi-pronged approach to address such challenges to develop the next generation rare event sampling methods for molecular simulations. The key outcomes of our work include developing more effective methods for sampling rare events, utilizing machine learning to better elucidate nucleation mechanisms, development of software for easy implementation of the methodologies, and applications of the methods to realistic systems to push the method applicability beyond model systems. Overall, this work has enabled pushing the frontiers of molecular simulations to study rare events with a focus on nucleation in aqueous solutions.
Risk Assessment of Rare Events in Probabilistic Power Flow via Hybrid Multi-Surrogate Method
The risks associated with rare events threatening the security of power system operation are of paramount importance to power system planners and operators. To analyze the risks caused by high-impact, low-frequency rare events, an immensely large number of samples are typically required for the Monte-Carlo (MC) method on the high-fidelity power system model to achieve a sufficient accuracy, thereby rendering this approach computationally prohibitive. To handle this problem efficiently, it is desirable to construct a surrogate model for the power system response. However, the straightforward MC sampling of the low-fidelity surrogate can lead to biased results in the low-probability tail regions that are vital to risk assessment. Moreover, a single surrogate is unable to handle the topology uncertainties caused by random branch outages. To overcome these issues, we propose a hybrid multi-surrogate (HMS) method based on the polynomial chaos expansion (PCE) with low-probability tail events reevaluated by the high-fidelity model through a probabilistic analysis. This method improves the computational efficiency of the MC method for rare-event risk assessment by leveraging multi-fidelity models while retaining the desired accuracy. Simulations conducted in three test systems verify the excellent performances of the HMS method.
KamNet: An integrated spatiotemporal deep neural network for rare event searches in KamLAND-Zen
Rare event searches allow us to search for new physics at energy scales inaccessible with other means by leveraging specialized large-mass detectors. Machine learning provides a new tool to maximize the information provided by these detectors. The information is sparse, which forces these algorithms to start from the lowest level data and exploit all symmetries in the detector to produce results. In this work we present KamNet, which harnesses breakthroughs in geometric deep learning and spatiotemporal data analysis to maximize the physics reach of KamLAND-Zen, a kiloton scale spherical liquid scintillator detector searching for 0νββ. Using a simplified background model for KamLAND, we show that KamNet outperforms a conventional convolutional neural network (CNN) on benchmarking Monte Carlo simulations with an increasing level of robustness. Using simulated data, we then demonstrate KamNet's ability to increase KamLAND-Zen's sensitivity to 0νββ and 2νββ decay to excited states. A key component of this work is the addition of an attention mechanism to elucidate the underlying physics KamNet is using for the background rejection.
Scalable Risk Assessment of Rare Events in Power Systems With Uncertain Wind Generation and Loads
Risk assessment of rare events has become increasingly important in power system planning and operation with the increasing integration of renewable energy and the presence of system uncertainties. However, quantifying the risk posed by rare events via the traditional method, i.e., Monte Carlo sampling (MCS), incurs substantial computational expense stemming from the vast ensemble of power flow simulations. To accelerate the assessment, this paper proposes a Deep Neural Network (DNN)-kernelized vector-valued Gaussian Process (VVGP) approach with excellent computational efficiency while maintaining high accuracy. Consequently, serving as a surrogate model for the power flow solver, the DNN-kernelized VVGP enables significantly faster but accurate risk assessment compared to the power flow solver. The developed surrogate model evaluates low-order N - k events that contain more than 90% instances by adeptly capturing the topological features while the high-order N - k events are assessed via a power flow solver, thereby striking a balance between computational efficiency and uncertainty quantification accuracy. Moreover, the model incorporates a Support Vector Machine (SVM) classifier to resample concerning low-probability tail events to counteract the biases potentially introduced during the DNN-kernelized VVGP evaluations. Simulations conducted on the modified IEEE 24-bus, 118-bus, and European 1354-bus systems demonstrate that the proposed method maintains the accuracy benchmark set by MCS while significantly reducing computational demands in large-scale power systems as compared to other state-of-the-art methods.
Rare events and Griffiths phases in topological quantum error correction
The performance of quantum error correcting (QEC) codes is often studied under the assumption of spatiotemporally uniform error rates. On the other hand, experimental implementations almost always produce heterogeneous error rates, in either space or time, as a result of effects such as imperfect fabrication and/or cosmic rays. It is therefore important to understand if and how their presence can affect the performance of QEC in qualitative ways. Here, in this work, we study the effects of nonuniform error rates in the representative examples of the 1D repetition code and the 2D toric code, focusing on when they have extended spatiotemporal correlations; these may arise, for instance, from rare events (such as cosmic rays) that temporarily elevate error rates over the entire code patch. These effects can be described in the corresponding statistical mechanics models for decoding, where long-range correlations in the error rates lead to extended rare regions of weaker coupling. For the 1D repetition code where the rare regions are linear, we find two distinct decodable phases: a conventional ordered phase in which logical failure rates decay exponentially with the code distance, and a rare-region dominated Griffiths phase in which failure rates are parametrically larger and decay as a stretched exponential. In particular, the latter phase is present when the error rates in the rare regions are above the bulk threshold. For the 2D toric code where the rare regions are planar, we find no decodable Griffiths phase: rare events which boost error rates above the bulk threshold lead to an asymptotic loss of threshold and failure to decode. Unpacking the failure mechanism implies that techniques for suppressing extended sequences of repeated rare events (which, without intervention, will be statistically present with high probability) will be crucial for QEC with the toric code.
Low-diffusion Xe-He gas mixtures for rare-event detection: electroluminescence yield
High pressure xenon Time Projection Chambers (TPC) based on secondary scintillation (electroluminescence) signal amplification are being proposed for rare event detection such as directional dark matter, double electron capture and double beta decay detection. The discrimination of the rare event through the topological signature of primary ionisation trails is a major asset for this type of TPC when compared to single liquid or double-phase TPCs, limited mainly by the high electron diffusion in pure xenon. Helium admixtures with xenon can be an attractive solution to reduce the electron diffusion significantly, improving the discrimination efficiency of these optical TPCs. We have measured the electroluminescence (EL) yield of Xe-He mixtures, in the range of 0 to 30% He and demonstrated the small impact on the EL yield of the addition of helium to pure xenon. For a typical reduced electric field of 2.5 kV/cm/bar in the scintillation region, the EL yield is lowered by ~ 2%, 3%, 6% and 10% for 10%, 15%, 20% and 30% of helium concentration, respectively. This decrease is less than what has been obtained from the most recent simulation framework in the literature. The impact of the addition of helium on EL statistical fluctuations is negligible, within the experimental uncertainties. The present results are an important benchmark for the simulation tools to be applied to future optical TPCs based on Xe-He mixtures.
Extended temperature-accelerated dynamics: Enabling long-time full-scale modeling of large rare-event systems
A new method, the Extended Temperature-Accelerated Dynamics (XTAD), is introduced for modeling long-timescale evolution of large rare-event systems. The method is based on the Temperature-Accelerated Dynamics approach [M. Sørensen and A. Voter, J. Chem. Phys. 112, 9599 (2000)], but uses full-scale parallel molecular dynamics simulations to probe a potential energy surface of an entire system, combined with the adaptive on-the-fly system decomposition for analyzing the energetics of rare events. The method removes limitations on a feasible system size and enables to handle simultaneous diffusion events, including both large-scale concerted and local transitions. Due to the intrinsically parallel algorithm, XTAD not only allows studies of various diffusion mechanisms in solid state physics, but also opens the avenue for atomistic simulations of a range of technologically relevant processes in material science, such as thin film growth on nano- and microstructured surfaces.
Charge Trap Analysis in a SENSEI Skipper-CCD: Understanding Low-Energy Backgrounds in Rare-Event Searches
Skipper Charge-Coupled Devices (Skipper-CCDs) are ultra-low-threshold detectors capable of detecting energy deposits in silicon at the eV scale. Increasingly used in rare-event searches, one of the major challenges in these experiments is mitigating low-energy backgrounds. In this work, we present results on trap characterization in a silicon Skipper-CCD produced in the same fabrication run as the SENSEI experiment at SNOLAB. Lattice defects contribute to backgrounds in rare-event searches through single-electron charge trapping. To investigate this, we employ the charge-pumping technique at different temperatures to identify dipoles produced by traps in the CCD channel. We fully characterize a fraction of these traps and use this information to extrapolate their contribution to the single-electron background in SENSEI. We find that this subpopulation of traps does not contribute significantly but more work is needed to assess the impact of the traps that can not be characterized.
Performance study of charcoal-based radon reduction systems for ultraclean rare event detectors
The continuous emanation of radon due to trace amounts of uranium and thorium in detector materials introduces radon to the active detection volume of low-background rare event search detectors. 222 Rn produces a particularly problematic background in the physics region of interest by the "naked" beta decay of its 214 Pb daughter nucleus. While charcoal-based adsorption traps are expected to be effective for radon reduction in auxiliary circulation loops that service the warm components of current ton-scale detectors at slow flow rates (0.5-2 SLPM), radon reduction in the entire circulation loop at high flow rates $\mathcal{O}$(100s SLPM) is necessary to reach high sensitivity in future generation experiments. In this article we explore radon dynamics with a charcoal-based radon reduction system in the main circulation loop of time projection chamber detectors. Here, we find that even for perfect radon traps, circulation speeds of 2,000 SLPM are needed to reduce radon concentration in a 10 ton detector by 90%. This is faster by a factor of four than the highest circulation speeds currently achieved in dark matter detectors. We further find that the effectiveness of vacuum swing adsorption systems, which have been employed very successfully at reducing atmospheric radon levels in clean-rooms, is limited by the intrinsic radon activity of the charcoal adsorbent in ultra-low radon environments. Adsorbents with significantly lower intrinsic radon activity than in currently available activated charcoals would be necessary to build effective vacuum swing adsorption systems operated at room temperature for rare event search experiments. If such VSA systems are cooled to about 190 K, this requirement relaxes drastically.