cosmoabc: Likelihood-free inference via Population Monte Carlo Approximate Bayesian Computation
Not Available
Ishida, E. E. O.↗
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Enabling attractive-repulsive potentials in binary-collision-approximation monte-carlo codes for ion-surface interactions
Abstract Binary Collision Approximation (BCA) codes for ion-material interactions, such as SRIM, Tridyn, F-TRIDYN, and SDtrimSP, have historically been limited to screened Coulomb potentials even at low energies due to the difficulty in numerically solving the Distance of Closest Approach (DOCA) problem for attractive-repulsive potentials. Techniques such as direct n-body simulation or modifications to Newton’s method are either prohibitively costly or not guaranteed to work for all potentials. Advanced rootfinding techniques, such as companion matrix solvers, offer a solution. For many attractive-repulsive potentials, however, a companion matrix cannot be used directly, because there is no way to put the associated functions into a monomial basis form. A complementary technique is proxy rootfinding—by finding the best-fit polynomial approximant of a function, the zeros of the approximant can be guaranteed to be close to the zeros of the function. Using the Chebyshev basis and grid offers additional guarantees with regards to the quality of the approximation, the speed of convergence, and the avoidance of Runge’s phenomenon. By finding Chebyshev interpolants and using the Chebyshev-Frobenius companion matrix, the zeros of any real function on a bounded domain can be found. Here we show that using an Adaptive Chebyshev Proxy Rootfinder with Automatic Subdivision (ACPRAS) with appropriate scaling functions, numerical issues presented by attractive-repulsive potentials, including those of scale, can be handled. Using these techniques, we show that it is possible to include any physically reasonable interatomic potential in a BCA code, and to guarantee correctness of the resulting scattering angle calculations.
Materials Science↗
astroABC : An Approximate Bayesian Computation Sequential Monte Carlo sampler for cosmological parameter estimation
Given the complexity of modern cosmological parameter inference where we arefaced with non-Gaussian data and noise, correlated systematics and multi-probecorrelated data sets, the Approximate Bayesian Computation (ABC) method is apromising alternative to traditional Markov Chain Monte Carlo approaches in thecase where the Likelihood is intractable or unknown. The ABC method is called"Likelihood free" as it avoids explicit evaluation of the Likelihood by using aforward model simulation of the data which can include systematics. Weintroduce astroABC, an open source ABC Sequential Monte Carlo (SMC) sampler forparameter estimation. A key challenge in astrophysics is the efficient use oflarge multi-probe datasets to constrain high dimensional, possibly correlatedparameter spaces. With this in mind astroABC allows for massive parallelizationusing MPI, a framework that handles spawning of jobs across multiple nodes. Akey new feature of astroABC is the ability to create MPI groups with differentcommunicators, one for the sampler and several others for the forward modelsimulation, which speeds up sampling time considerably. For smaller jobs thePython multiprocessing option is also available. Other key features include: aSequential Monte Carlo sampler, a method for iteratively adapting tolerancelevels, local covariance estimate using scikit-learn's KDTree, modules forspecifying optimal covariance matrix for a component-wise or multivariatenormal perturbation kernel, output and restart files are backed up everyiteration, user defined metric and simulation methods, a module for specifyingheterogeneous parameter priors including non-standard prior PDFs, a module forspecifying a constant, linear, log or exponential tolerance level,well-documented examples and sample scripts. This code is hosted online athttps://github.com/EliseJ/astroABC
46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
Simulated Stochastic Approximation Annealing for Global Optimization with a Square-Root Cooling Schedule
Simulated annealing has been widely used in the solution of optimization problems. As known by many researchers, the global optima cannot be guaranteed to be located by simulated annealing unless a logarithmic cooling schedule is used. However, the logarithmic cooling schedule is so slow that no one can afford to have such a long CPU time. This paper proposes a new stochastic optimization algorithm, the so-called simulated stochastic approximation annealing algorithm, which is a combination of simulated annealing and the stochastic approximation Monte Carlo algorithm. Under the framework of stochastic approximation Markov chain Monte Carlo, it is shown that the new algorithm can work with a cooling schedule in which the temperature can decrease much faster than in the logarithmic cooling schedule, e.g., a square-root cooling schedule, while guaranteeing the global optima to be reached when the temperature tends to zero. The new algorithm has been tested on a few benchmark optimization problems, including feed-forward neural network training and protein-folding. The numerical results indicate that the new algorithm can significantly outperform simulated annealing and other competitors.
Liang, Faming↗
MEASUREMENT AND CALCULATION OF ABSOLUTE SINGLE AND MULTIPLE CHARGE EXCHANGE CROSS SECTIONS FOR Fe {sup q} {sup +} IONS IMPACTING H{sub 2}O
Charge exchange (CE) plays a fundamental role in the collisions of solar- and stellar-wind ions with lunar and planetary exospheres, comets, and circumstellar clouds. Reported herein are absolute cross sections for single, double, triple, and quadruple CE of Fe {sup q} {sup +} (q = 5-13) ions with H{sub 2}O at a collision energy of 7q keV. One measured value of the pentuple CE is also given for Fe {sup 9} {sup +} ions. An electron cyclotron resonance ion source is used to provide currents of the highly charged Fe ions. Absolute data are derived from knowledge of the target gas pressure, target path length, and incident and charge-exchanged ion currents. Experimental cross sections are compared with new results of the n-electron classical trajectory Monte Carlo approximation. The radiative and non-radiative cascades following electron transfers are approximated using scaled hydrogenic transition probabilities and scaled Auger rates. Also given are estimates of cross sections for single capture, and multiple capture followed by autoionization, as derived from the extended overbarrier model. These estimates are based on new theoretical calculations of the vertical ionization potentials of H{sub 2}O up to H{sub 2}O{sup 10+}.
74 ATOMIC AND MOLECULAR PHYSICS↗
Electronic Properties and Magnetocaloric Effect of GdNi{sub 4}Si: Ab Initio Calculations, Mean Field Approximation, and Monte Carlo Simulation
We investigated the magnetic properties and magnetocaloric effect of GdNi{sub 4}Si by using a combination of first-principle density functional theory (DFT) calculations and Monte Carlo Simulation. Ab initio calculations show the stability of the ferromagnetic phase in this material. The Monte Carlo simulations combined with ab initio exchange coupling constants as input parameters lead to discuss the transition temperature, critical exponents, and isothermal entropy changes. The measured critical temperature and the isothermal magnetic entropy changes for a field change of 14T in good agreement with the experimental data.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Efficient Exact and Approximate Kinetic Monte Carlo Algorithms.
Abstract not provided.
Plimpton, Steven J↗
Scalable Bayesian optimization with randomized prior networks
Several fundamental problems in science and engineering consist of global optimization tasks involving unknown high-dimensional (black-box) functions that map a set of controllable variables to the outcomes of an expensive experiment. Bayesian Optimization (BO) techniques are known to be effective in tackling global optimization problems using a relatively small number objective function evaluations, but their performance suffers when dealing with high-dimensional outputs. To overcome the major challenge of dimensionality, here we propose a deep learning framework for BO and sequential decision making based on bootstrapped ensembles of neural architectures with randomized priors. Using appropriate architecture choices, we show that the proposed framework can approximate functional relationships between design variables and quantities of interest, even in cases where the latter take values in high-dimensional vector spaces or even infinite-dimensional function spaces. In the context of BO, we augmented the proposed probabilistic surrogates with re-parameterized Monte Carlo approximations of multiple-point (parallel) acquisition functions, as well as methodological extensions for accommodating black-box constraints and multi-fidelity information sources. We test the proposed framework against state-of-the-art methods for BO and demonstrate superior performance across several challenging tasks with high-dimensional outputs, including a constrained multi-fidelity optimization task involving shape optimization of rotor blades in turbo-machinery.
97 MATHEMATICS AND COMPUTING↗
Diagram of states and morphologies of flexible-semiflexible copolymer chains: A Monte Carlo simulation
A single copolymer chain consisting of multiple flexible (F) and semiflexible (S) blocks has been studied using a continuum bead-spring model by Stochastic Approximation Monte Carlo simulations, which determine the density of states of the model. The only difference between F and S blocks is the intramolecular bending potential, all non-bonded interactions are equal. The state diagrams for this class of models display multiple nematic phases in the collapsed state, characterized through a demixing of the blocks of different stiffness and orientational ordering of the stiff blocks. We observe dumbbell-like morphologies, lamellar phases, and for the larger block lengths also Saturn-like structures with a core of flexible segments and the stiff segments forming a ring around the core.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Model selection and parameter estimation in tumor growth models using approximate Bayesian computation-ABC
Cancer is one of the most fatal diseases in the world. Governments and researchers from various areas have continuously concentrated efforts to better understand the disease and propose diagnostic and treatment techniques. The use of mathematical models of tumor growth is of great importance for the development of such techniques. Due to the variety of models nowadays available in the literature, the problems of model selection and parameter estimation come into picture, aiming at suitably predicting the patient’s status of the disease. As the available data on dependent variables of existing models might not justify the use of common likelihood functions, approximate Bayesian computation (ABC) becomes a very attractive tool for model selection and model calibration (parameter estimation) in tumor growth models. In the present study, a Monte Carlo approximate Bayesian computation (ABC) algorithm is applied to select among competing models of tumor growth, with and without chemotherapy treatment. Simulated measurements are used in this work. The results obtained show that the algorithm correctly selects the model and estimates the parameters used to generate the simulated measurements.
60 APPLIED LIFE SCIENCES↗
Integration of multiple coinflip devices for high-quality random sampling
Artificial intelligence, scientific computing, and probabilistic computing use random sampling to approximate solutions to various problems, with larger models requiring a substantial quantity of random numbers. To generate the required vast quantity of random numbers at high rates, we explore so-called “coinflip” devices, which are stochastic microelectronic devices ideally capable of independently generating random bits with a tunable weight at a high rate. However, coinflip devices are inherently analog and demonstrate nonidealities, like temperature dependence and drift, that can introduce determinism into the outputs. We present important considerations for building systems of multiple coinflip devices to produce high-quality bitstreams with low error and little dependency on previous bits. Using tunnel diodes as coinflip devices, we implement a control loop to adapt to temperature dependence and generate fair bitstreams with each device. While this can lead to dependencies between bits in a single bitstream, we demonstrate that combining results generated in parallel with individual tunnel diodes can produce fair and unpredictable bitstreams. The suitability of these bitstreams for use in probabilistic computing is then demonstrated through a Monte Carlo approximation of π.
Taylor, Brady Garland [Sandia National Laboratorie↗
Orbital structure of the effective pairing interaction in the high-temperature superconducting cuprates
The nature of the effective interaction responsible for pairing in the high-temperature superconducting cuprates remains unsettled. This question has been studied extensively using the simplified single-band Hubbard model, which does not explicitly consider the orbital degrees of freedom of the relevant CuO 2 planes. Here, we use a dynamical cluster quantum Monte Carlo approximation to study the orbital structure of the pairing interaction in the three-band Hubbard model, which treats the orbital degrees of freedom explicitly. We find that the interaction predominately acts between neighboring copper orbitals, but with significant additional weight appearing on the surrounding bonding molecular oxygen orbitals. By explicitly comparing these results to those from the simpler single-band Hubbard model, our study provides strong support for the single-band framework for describing superconductivity in the cuprates.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Uncertainty quantification in multivariable regression for material property prediction with Bayesian neural networks
With the increased use of data-driven approaches and machine learning-based methods in material science, the importance of reliable uncertainty quantification (UQ) of the predicted variables for informed decision-making cannot be overstated. UQ in material property prediction poses unique challenges, including multi-scale and multi-physics nature of materials, intricate interactions between numerous factors, limited availability of large curated datasets, etc. In this work, we introduce a physics-informed Bayesian Neural Networks (BNNs) approach for UQ, which integrates knowledge from governing laws in materials to guide the models toward physically consistent predictions. To evaluate the approach, we present case studies for predicting the creep rupture life of steel alloys. Experimental validation with three datasets of creep tests demonstrates that this method produces point predictions and uncertainty estimations that are competitive or exceed the performance of conventional UQ methods such as Gaussian Process Regression. Additionally, we evaluate the suitability of employing UQ in an active learning scenario and report competitive performance. The most promising framework for creep life prediction is BNNs based on Markov Chain Monte Carlo approximation of the posterior distribution of network parameters, as it provided more reliable results in comparison to BNNs based on variational inference approximation or related NNs with probabilistic outputs.
36 MATERIALS SCIENCE↗
tSFM 1.0: tRNA Structure–Function Mapper
Structure-conditioned information statistics have proven useful to predict and visualize tRNA Class-Informative Features (CIFs) and their evolutionary divergences. Although permutation P-values can quantify the significance of CIF divergences between two taxa, their naive Monte Carlo approximation is slow and inaccurate. The Peaks-over-Threshold approach of Knijnenburg et al. (2009) promises improvements to both speed and accuracy of permutation P-values, but has no publicly available API. Here, we present tRNA Structure–Function Mapper (tSFM) v1.0, an open-source, multi-threaded application that efficiently computes, visualizes and assesses significance of single- and paired-site CIFs and their evolutionary divergences for any RNA, protein, gene or genomic element sequence family. Multiple estimators of permutation P-values for CIF evolutionary divergences are provided along with confidence intervals. tSFM is implemented in Python 3 with compiled C extensions and is freely available through GitHub (https://github.com/tlawrence3/tSFM) and PyPI.
59 BASIC BIOLOGICAL SCIENCES↗
Pair structure and the pairing interaction in a bilayer Hubbard model for unconventional superconductivity
The bilayer Hubbard model with an intralayer hopping t and an interlayer hopping t{sub {lambda}} provides an interesting testing ground for several aspects of what has been called unconventional superconductivity. One can study the type of pair structures which arise when there are multiple Fermi surfaces. One can also examine the pairing for a system in which the structure of the spin-fluctuation spectral weight can be changed. Using a dynamic cluster quantum Monte Carlo approximation, we find that near half filling, if the splitting between the bonding and antibonding bands t{sub {lambda}}/t is small, the gap has B{sub 1g} (d{sub x{sup 2}-y{sup 2}}-wave) symmetry, but when the splitting becomes larger, A{sub 1g} (s{sup {+-}}-wave) pairing is favored. We also find that in the s{sup {+-}} pairing region, the pairing is driven by interlayer spin fluctuations and that T{sub c} is enhanced.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Coexistence of strong nematic and superconducting correlations in a two-dimensional Hubbard model
Not Available
Su, Shi-Quan↗
The Role of Scale and Model Bias in ADAPT's Photospheric Estimation
The Air Force Assimilative Photospheric flux Transport model (ADAPT), is a magnetic flux propagation based on Worden-Harvey (WH) model. ADAPT would be used to provide a global photospheric map of the Earth. A data assimilation method based on the Ensemble Kalman Filter (EnKF), a method of Monte Carlo approximation tied with Kalman filtering, is used in calculating the ADAPT models.
58 GEOSCIENCES↗
Beyond chemical accuracy: The pseudopotential approximation in diffusion Monte Carlo calculations of the HCP to BCC phase transition in beryllium.
Motivated by the disagreement between recent diffusion Monte Carlo calculations of the phase transition pressure between the ambient and beta-Sn phases of silicon and experiments, we present a study of the HCP to BCC phase transition in beryllium. This lighter element provides an opportunity for directly testing many of the approximations required for calculations on silicon and may suggest a path towards increasing the practical accuracy of diffusion Monte Carlo calculations of solids in general. We demonstrate that the single largest approximation in these calculations is the pseudopotential approximation and after removing this we find excellent agreement with experiment for the ambient HCP phase and results similar to careful calculations using density functional theory for the phase transition pressure.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗