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The intricate interactions between data sampling, model selection and the inherent randomness in complex systems strongly emphasize the need for a rigorous characterization of ML algorithms. In conventional statistics, uncertainty quantification (UQ) provides this characterization by measuring how accurately a model reflects the physical reality and by studying the impact of different error sources on the prediction.
Refractory complex concentrated alloys (RCCAs) have drawn increasing attention recently owing to their balanced mechanical properties, including excellent creep resistance, ductility, and oxidation resistance. The mechanical and thermal properties of RCCAs are directly linked with the elastic constants. However, it is time consuming and expensive to obtain the elastic constants of RCCAs with conventional trial-and-error experiments. The elastic constants of RCCAs are predicted using a combination of density functional theory simulation data and machine learning (ML) algorithms in this study. The elastic constants of several RCCAs are predicted using the random forest regressor, gradient boosting regressor (GBR), and XGBoost regression models. Based on performance metrics R-squared, mean average error and root mean square error, the GBR model was found to be most promising in predicting the elastic constant of RCCAs among the three ML models. Additionally, GBR model accuracy was verified using the other four RHEAs dataset which was never seen by the GBR model, and reasonable agreements between ML prediction and available results were found. The present findings show that the GBR model can be used to predict the elastic constant of new RHEAs more accurately without performing any expensive computational and experimental work.
A new algorithm for molecular dynamics (MD) simulations is developed to optimize plasma particle distributions at given initial temperatures. By combining velocity scaling and reassignment, the method effectively eliminates the initial rise and oscillation in temperatures observed with randomly distributed positions. These rises and oscillations are undesired numerical artifacts observed in conventional plasma MD simulations, arising from unoptimized particle positions. The algorithm demonstrates temperature relaxation without initial rises or oscillations, as well as precise flow velocity relaxation, enabling accurate measurement of relaxation times. The code is accelerated using graphics processing units for parallel processing, enhancing the study of plasma dynamics. The proposed method for distributing physically valid particles in MD simulations enables accurate studies of intrinsic collision processes in plasmas, including the dynamics of strongly coupled plasmas, plasma–wave interactions, and transport phenomena in magnetized plasmas. The paper concludes with a discussion of potential applications and future enhancements to the algorithm.
We propose a new statistical ensemble of toric bases for elliptic Calabi-Yaus used in F-theory models, by focusing on only the convex hull of the base, i.e., the base polytope. This physically motivated coarse-graining greatly simplifies the combinatorial complexity of the part of the 4d F-theory landscape with toric bases. We develop a Monte Carlo approach that randomly samples the base polytopes within fixed boxes, with proper statistical weights. We first apply the algorithm to the set of 2d base polytopes, generating an enlarged set of toric 2d bases that include certain types of codimension-two (4,6) points, and we validate our approach against exact numbers. We then explore the set of 3d base polytopes which fit in a set of “maximal” 3d boxes, and estimate the total number of inequivalent 3d base polytopes to be 10 85 –10 90 . We provide statistical data such as the distribution of non-Higgsable gauge groups on these bases. Amusingly, a similar method can also be applied to generate reflexive polytopes in various dimensions. In both the reflexive and base polytope cases, the number of relevant polytopes obeys a Gaussian distribution as a function of the number of vertices, which can be understood in terms of other results on random polytopes in the math literature.
Probabilistic and Bayesian neural networks have long been proposed as a method to incorporate uncertainty about the world (both in training data and operation) into artificial intelligence applications. One approach to making a neural network probabilistic is to leverage a Monte Carlo sampling approach that samples a trained network while incorporating noise. Such sampling approaches for neural networks have not been extensively studied due to the prohibitive requirement of many computationally expensive samples. While the development of future microelectronics platforms that make this sampling more efficient is an attractive option, it has not been immediately clear how to sample a neural network and what the quality of random number generation should be. This research aimed to start addressing these two fundamental questions by examining basic “off the shelf” neural networks can be sampled through a few different mechanisms (including synapse “dropout” and neuron “dropout”) and examine how these sampling approaches can be evaluated both in terms of evaluating algorithm effectiveness and the required quality of random numbers.
Cross-entropy (XE) measure is a widely used benchmark to demonstrate quantum computational advantage from sampling problems, such as random circuit sampling using superconducting qubits and boson sampling (BS). We present a heuristic classical algorithm that attains a better XE than the current BS experiments in a verifiable regime and is likely to attain a better XE score than the near-future BS experiments in a reasonable running time. The key idea behind the algorithm is that there exist distributions that correlate with the ideal BS probability distribution and that can be efficiently computed. The correlation and the computability of the distribution enable us to postselect heavy outcomes of the ideal probability distribution without computing the ideal probability, which essentially leads to a large XE. Our method scores a better XE than the recent Gaussian BS experiments when implemented at intermediate, verifiable system sizes. Much like current state-of-the-art experiments, we cannot verify that our spoofer works for quantum-advantage-size systems. However, we demonstrate that our approach works for much larger system sizes in fermion sampling, where we can efficiently compute output probabilities. Finally, we provide analytic evidence that the classical algorithm is likely to spoof noisy BS efficiently.
Networking of microgrids can provide the operational flexibility needed for the increasing number of DERs deployed at the distribution level and supporting end-use demand when there is loss of the bulk power system. But, networked microgrids are vulnerable to cyber-physical attacks and faults due to the complex interconnections. As such, it is necessary To design resilient control systems to support the operations of networked microgrids in responses to cyber-physical attacks and faults. This paper introduces a resilient communication scheme for interconnecting multiple microgrids to support critical demand, in which the interconnection decision can be made distributedly by each microgrid controller even in the presence of cyberattacks to some communication links or microgrid controllers. This scheme blends a randomized peer-to-peer communication network for exchanging information among controllers and resilient consensus algorithms for achieving reliable interconnection agreement. The network of 6 microgrids divided from a modified 123-node test distribution feeder is used to demonstrate the effectiveness of the proposed resilient communication scheme.
The increasing adoption of distributed energy resources (DERs) over the last decade warrants a reconsideration of control of generation resources. This paper proposes a distributed Automatic Generation Control (AGC) using transmission-and-distribution (T&D) dynamic co-simulation framework for the efficient DPV frequency regulation services. The co-simulation framework allows AGC units to exchange the information for distributed AGC, based on their adopted communication network topology. As a result, a cost-effective automatic generation control is achieved with DPV and conventional generators. The proposed distributed AGC is based on the gossip algorithm in which the neighboring AGC units share the relevant local information with each other and updates their share of AGC regulation signal. Distributed photovoltaics (DPV) unit contribute to AGC response based on their headroom capacity via DER aggregators. The algorithm is tested on IEEE-14 bus transmission system under conditions of generation failure and random load variation to observe effective frequency regulations service offered by DPVs and other AGC units. The study shows that DPV can effectively participate in AGC with the proposed distributed control framework.
The prototype quantum random number (random bit) generator (QRNG) consists of one photon at a time falling on a 50:50 beam splitter followed by random detection in one or the other output beams due to the irreducible probabilistic nature of quantum mechanics. Due to the difficulties in producing single photons on demand, in practice, pulses of weak coherent (laser) light are used. In this paper, we take a different approach, one that uses moderate coherent light. It is shown that a QRNG can be implemented by performing photon-number parity measurements. For moderate coherent light, the probabilities of obtaining even or odd parity in photon counts are 0.5 each. Photon counting with single-photon resolution can be performed through use of a cascade of beam splitters and single-photon detectors, as was done recently in a photon-number parity-based interferometry experiment involving coherent light. We highlight the point that unlike most quantum-based random number generators, our proposal does not require the use of classical de-biasing algorithms or post-processing of the generated bit sequence.
This report describes research conducted to use data science and machine learning methods to distinguish targeted genome editing versus natural mutation and sequencer machine noise. Genome editing capabilities have been around for more than 20 years, and the efficiencies of these techniques has improved dramatically in the last 5+ years, notably with the rise of CRISPR-Cas technology. Whether or not a specific genome has been the target of an edit is concern for U.S. national security. The research detailed in this report provides first steps to address this concern. A large amount of data is necessary in our research, thus we invested considerable time collecting and processing it. We use an ensemble of decision tree and deep neural network machine learning methods as well as anomaly detection to detect genome edits given either whole exome or genome DNA reads. The edit detection results we obtained with our algorithms tested against samples held out during training of our methods are significantly better than random guessing, achieving high F1 and recall scores as well as with precision overall.
A system or method for encryption of data includes a light source, a random optical element and a light detection element. The light source is arranged to transmit an input data signal to the random optical element. The light source is incident on the random optical element such that the input data signal is randomly scattered by the random optical element to generate an image at on the detector disposed at an output of the random optical element. The image received by the detector is applied to a compressive sensing algorithm to generate a transfer function. The transfer function defines a relationship between the input data signal and the image to enable estimation and reconstruction of the input data signal.
Manipulating matter with a scanning tunneling microscope (STM) enables the creation of atomically defined artificial structures that host designer quantum states. However, the time-consuming nature of the manipulation process, coupled with the sensitivity of the STM tip, constrains the exploration of diverse configurations and limits the size of the designed features. In this study, we present a reinforcement learning (RL)-based framework for creating artificial structures by spatially manipulating carbon monoxide (CO) molecules on a copper substrate by using the STM tip. The automated workflow combines molecule detection and manipulation, employing deep-learning-based object detection to locate CO molecules and linear assignment algorithms to allocate these molecules to designated target sites. We initially perform molecule maneuvering based on randomized parameter sampling for sample bias, tunneling current set point, and manipulation speed. This data set is then structured into an action trajectory used to train an RL agent. The model is subsequently deployed on the STM for real-time fine-tuning of the manipulation parameters during structure construction. Our approach incorporates path-planning protocols coupled with active drift compensation to enable atomically precise fabrication of structures with significantly reduced human input while realizing larger-scale artificial lattices with the desired electronic properties. Furthermore, using our approach, we demonstrate the automated construction of an extended artificial graphene lattice and confirm the existence of a characteristic Dirac point in its electronic structure. Further challenges regarding the RL-based structural assembly scalability are discussed.
The Katz centrality of a node in a complex network is a measure of the node’s importance as far as the flow of information across the network is concerned. For ensembles of locally tree-like undirected random graphs, this observable is a random variable. Its full probability distribution is of interest but difficult to handle analytically because of its “global” character and its definition in terms of a matrix inverse. Leveraging a fast Gaussian Belief Propagation-Cavity algorithm to solve linear systems on tree-like structures, we show that i) the Katz centrality of a single instance can be computed recursively in a very fast way, and ii) the probability P ( K ) that a random node in the ensemble of undirected random graphs has centrality K satisfies a set of recursive distributional equations, which can be analytically characterized and efficiently solved using a population dynamics algorithm. We test our solution on ensembles of Erdős-Rényi and Scale Free networks in the locally tree-like regime, with excellent agreement. The analytical distribution of centrality for the configuration model conditioned on the degree of each node can be employed as a benchmark to identify nodes of empirical networks with over- and underexpressed centrality relative to a null baseline. We also provide an approximate formula based on a rank- 1 projection that works well if the network is not too sparse, and we argue that an extension of our method could be efficiently extended to tackle analytical distributions of other centrality measures such as PageRank for directed networks in a transparent and user-friendly way.
Introduction Accurately predicting the competitive performance of elite athletes is an essential prerequisite for formulating competitive strategies. Women’s all-around speed skating event consists of four individual subevents, and the competition system is complex and challenging to make accurate predictions on their performance. Objective The present study aims to explore the feasibility and effectiveness of machine learning algorithms for predicting the performance of women’s all-around speed skating event and provide effective training and competition strategies. Methods The data, consisting of 16 seasons of world-class women’s all-around speed skating competition results, used in the present study came from the International Skating Union (ISU). According to the competition rules, distinct features are filtered using lasso regression, and a 5,000 m race model and a medal model are built using a fivefold cross-validation method. Results The results showed that the support vector machine model was the most stable among the 5,000 m race and the medal models, with the highest AUC (0.86, 0.81, respectively). Furthermore, 3,000 m points are the main characteristic factors that decide whether an athlete can qualify for the final. The 11th lap of the 5,000 m, the second lap of the 500 m, and the fourth lap of the 1,500 m are the main characteristic factors that affect the athlete’s ability to win medals. Conclusion Compared with logistic regression, random forest, K-nearest neighbor, naive Bayes, neural network, support vector machine is a more viable algorithm to establish the performance prediction model of women’s all-around speed skating event; excellent performance in the 3,000 m event can facilitate athletes to advance to the final, and athletes with outstanding performance in the 500 m event are more likely competitive for medals.
Abstract We describe and analyze an error mitigation technique that uses multiple pairs of parity checks to detect the presence of errors. Each pair of checks uses one ancilla qubit to detect a component of the error operator and represents one layer of the technique. We build on the results on extended flag gadgets and put it on a firm theoretical foundation. We prove that this technique can recover the noiseless state under the assumption of noise not affecting the checks. The method does not incur any encoding overhead and instead chooses the checks based on the input circuit. We provide an algorithm for obtaining such checks for an arbitrary target circuit. Since the method applies to any circuit and input state, it can be easily combined with other error mitigation techniques. We evaluate the performance of the proposed methods using extensive numerical simulations on 1850 random input circuits composed of Clifford gates and non-Clifford single-qubit rotations, a class of circuits encompassing most commonly considered variational algorithm circuits. We observe average improvements in fidelity of 34 percentage points with six layers of checks.
Abstract Spatial prediction is commonly achieved under the assumption of a Gaussian random field by obtaining maximum likelihood estimates of parameters, and then using the kriging equations to arrive at predicted values. For massive datasets, fixed rank kriging using the expectation–maximization algorithm for estimation has been proposed as an alternative to the usual but computationally prohibitive kriging method. The method reduces computation cost of estimation by redefining the spatial process as a linear combination of basis functions and spatial random effects. A disadvantage of this method is that it imposes constraints on the relationship between the observed locations and the knots. We develop an alternative method that utilizes the spatial mixed effects model, but allows for additional flexibility by estimating the range of the spatial dependence between the observations and the knots via an alternating expectation conditional maximization algorithm. Experiments show that our methodology improves estimation without sacrificing prediction accuracy while also minimizing the additional computational burden of extra parameter estimation. The methodology is applied to a temperature dataset archived by the United States National Climate Data Center, with improved results over previous methodology.
In engineering examples, one often encounters the need to sample from unnormalized distributions with complex shapes that may also be implicitly defined through a physical or numerical simulation model, making it computationally expensive to evaluate the associated density function. For such cases, MCMC has proven to be an invaluable tool. Random-walk Metropolis Methods (also known as Metropolis-Hastings (MH)), in particular, are highly popular for their simplicity, flexibility, and ease of implementation. However, most MH algorithms suffer from significant limitations when attempting to sample from distributions with multiple modes (particularly disconnected ones). Here, in this paper, we present Intrepid MCMC - a novel MH scheme that utilizes a simple coordinate transformation to significantly improve the mode-finding ability and convergence rate to the target distribution of random-walk Markov chains while retaining most of the simplicity of the vanilla MH paradigm. Through multiple examples, we showcase the improvement in the performance of Intrepid MCMC over vanilla MH for a wide variety of target distribution shapes. We also provide an analysis of the mixing behavior of the Intrepid Markov chain, as well as the efficiency of our algorithm for increasing dimensions. A thorough discussion is presented on the practical implementation of the Intrepid MCMC algorithm. Finally, its utility is highlighted through a Bayesian parameter inference problem for a two-degree-of-freedom oscillator under free vibration.
Quantum embedding theories are promising approaches to investigate strongly correlated electronic states of active regions of large-scale molecular or condensed systems. Notable examples are spin defects in semiconductors and insulators. We present a detailed derivation of a quantum embedding theory recently introduced, which is based on the definition of effective Hamiltonians. The effect of the environment on a chosen active space is accounted for through screened Coulomb interactions evaluated using density functional theory. Importantly, the random phase approximation is not required, and the evaluation of virtual electronic orbitals is circumvented with algorithms previously developed in the context of calculations based on many-body perturbation theory. In addition, we generalize the quantum embedding theory to active spaces composed of orbitals that are not eigenstates of Kohn–Sham Hamiltonians. Finally, we report results for spin defects in semiconductors.