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Results for “Monte Carlo approximation”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

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↗
DOE OSTI2023

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↗
DOE OSTI2025

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↗
DOE OSTI2024

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↗
NASA NTRS1991

Conditional Probability And The Sparse Distributed Memory

Report presents conditional-probability interpretation of Kanerva's sparse distributed memory (SDM). SDM is conceptual digital electronic memory in which addresses chosen sparsely in space of many dimensions and content of memory at each address positive or negative integer written (incremented or decremented) or read according to special rules. Contents of SDM constitute Monte Carlo approximation to multidimensional conditional-probability integral.

Anderson, Charles H.↗
NASA NTRS2003

Energetics of Single Substitutional Impurities in NiTi

Shape-memory alloys are of considerable current interest, with applications ranging from stents to Mars rover components. In this work, we present results on the energetics of single substitutional impurities in B2 NiTi. Specifically, energies of Pd, Pt, Zr and Hf impurities at both Ni and Ti sites are computed. All energies are computed using the CASTEP ab initio code, and, for comparison, using the quantum approximate energy method of Bozzolo, Ferrante and Smith. Atomistic relaxation in the vicinity of the impurities is investigated via quantum approximate Monte Carlo simulation, and in cases where the relaxation is found to be important, the resulting relaxations are applied to the ab initio calculations. We compare our results with available experimental work.

Good, Brian S.↗
DOE OSTI2024

Density scaling approximation for Monte-Carlo simulations of radioactive plumes

The release of radioactive gas into the atmosphere can diffuse into large volumes of air downwind from the point of release. The extent of radioactivity can cover thousands of cubic meters of air. For such large volumes, the weather models used to predict the down-wind distribution of the plume and the radiation transport models used to predict the radiation reaching ground-level from the plume can take tens of hours of computer time on multi-node institutional High-Performance Computing facilities. In this paper we focus on the radiation transport aspect of plume modeling. Here, we describe a phenomenological method for approximating the amounts of radiation that reach ground level from large volumes of a static radioactive plume that can be calculated on a stand-alone personal computer in much shorter computation times than those usually needed for such large volume evaluations. We refer to this method as the Density Scaling Approximation (DSA). Its ability to approximate ground-level count rates of large plumes comes from using a small-plume volume with a scaled-up value of air density to simulate the same number of scatterings that occur during transport in larger plume volumes at normal air density. We demonstrate the DSA by using a 100 m-diameter air-filled hemispherical dome geometry with a uniform volumetric activity of 135 Xe gas throughout the air-filled volume. The DSA for a larger dome diameter is obtained by evaluating the 100 m dome with an air density scaled up by the linear ratio of the larger diameter to the 100 m diameter. We find that this approximation works well for dome diameters up to 1200 m – the largest diameter studied and a size more than sufficient for accounting for all the radiation from 135 Xe. Moreover, most of our DSA results can be calculated over 500 times faster than corresponding full-sized geometry with normal air density. To help evaluate the accuracy of the DSA and gain insight into how well it can reproduce different regions of the spectra, we use three, easily understood regions of interest to compare the DSA results to the full-sized geometry at normal air density results. These regions are the full-energy peak, the region of single-Compton scattering, and the region of multiple-Compton scattering. We show how the dominance of the Compton scattering mechanism determines this division and thus provides insight into how Compton scattering is manifested in spectra from photon scattering through air in general, and how well the DSA approximation works.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2024

Beyond Single-Reference Fixed-Node Approximation in Ab Initio Diffusion Monte Carlo Using Antisymmetrized Geminal Power Applied to Systems with Hundreds of Electrons

Diffusion Monte Carlo (DMC) is an exact technique to project out the ground state (GS) of a Hamiltonian. Since the GS is always bosonic, in Fermionic systems, the projection needs to be carried out while imposing antisymmetric constraints, which is a nondeterministic polynomial hard problem. In practice, therefore, the application of DMC on electronic structure problems is made by employing the fixed-node (FN) approximation, consisting of performing DMC with the constraint of having a fixed, predefined nodal surface. How do we get the nodal surface? The typical approach, applied in systems having up to hundreds or even thousands of electrons, is to obtain the nodal surface from a preliminary mean-field approach (typically, a density functional theory calculation) used to obtain a single Slater determinant. This is known as single reference. In this paper, we propose a new approach, applicable to systems as large as the C 60 fullerene, which improves the nodes by going beyond the single reference. In practice, we employ an implicitly multireference ansatz (antisymmetrized geminal power wave function constraint with molecular orbitals), initialized on the preliminary mean-field approach, which is relaxed by optimizing a few parameters of the wave function determining the nodal surface by minimizing the FN-DMC energy. We highlight the improvements of the proposed approach over the standard single-reference method on several examples and, where feasible, the computational gain over the standard multireference ansatz, which makes the methods applicable to large systems. We also show that physical properties relying on relative energies, such as binding energies, are affordable and reliable within the proposed scheme.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Interlayer pairing in bilayer nickelates

The discovery of T c ~ 80 K superconductivity in pressurized La 3 Ni 2 O 7 has launched a new platform to study high-temperature superconductivity. Using non-perturbative dynamic cluster approximation quantum Monte Carlo calculations, we characterize the magnetic and superconducting pairing behavior of a realistic bilayer two-orbital Hubbard-Hund model of this system that describes the relevant Ni e g states with physically relevant interaction strengths. We find a leading s ± superconducting instability in this model at a temperature T ~ 100 K close to the experimentally observed T c . Analyzing the orbital and spatial structure of the effective pairing interaction giving rise to this state reveals that the interaction predominantly acts between local interlayer pairs of the $d_{3z^2-r^2}$ orbital. By correlating the strength of the interaction with that of the magnetic spin fluctuations we show that it is driven by strong interlayer spin-fluctuations arising from the $d_{3z^2-r^2}$ orbital. These results provide first-time non-perturbative evidence supporting the picture that a simple single-orbital bilayer Hubbard model for the Ni $d_{3z^2-r^2}$ orbital provides an excellent low-energy effective description of the superconducting behavior of La 3 Ni 2 O 7 .

Maier, Thomas A. [Oak Ridge National Laboratory (O↗
NASA NTRS1986

Monte Carlo turbulence simulation using rational approximations to von Karman spectra

Turbulence simulation is computationally much simpler using rational spectra, but turbulence falls off as f exp -5/3 in frequency ranges of interest to aircraft response and as predicted by von Karman's model. Rational approximations to von Karman spectra should satisfy three requirements: (1) the rational spectra should provide a good approximation to the von Karman spectra in the frequency range of interest; (2) for stability, the resulting rational transfer function should have all its poles in the left half-plane; and (3) at high frequencies, the rational spectra must fall off as an integer power of frequency, and since the -2 power is closest to the -5/3 power, the rational approximation should roll off as the -2 power at high frequencies. Rational approximations to von Karman spectra that satisfy these three criteria are presented, along with spectra from simulated turbulence. Agreement between the spectra of the simulated turbulence and von Karman spectra is excellent.

Campbell, C. W.↗
NASA NTRS2016

Optics of Water Microdroplets with Soot Inclusions: Exact Versus Approximate Results

We use the recently generalized version of the multi-sphere superposition T-matrix method (STMM) to compute the scattering and absorption properties of microscopic water droplets contaminated by black carbon. The soot material is assumed to be randomly distributed throughout the droplet interior in the form of numerous small spherical inclusions. Our numerically-exact STMM results are compared with approximate ones obtained using the Maxwell-Garnett effective-medium approximation (MGA) and the Monte Carlo ray-tracing approximation (MCRTA). We show that the popular MGA can be used to calculate the droplet optical cross sections, single-scattering albedo, and asymmetry parameter provided that the soot inclusions are quasi-uniformly distributed throughout the droplet interior, but can fail in computations of the elements of the scattering matrix depending on the volume fraction of soot inclusions. The integral radiative characteristics computed with the MCRTA can deviate more significantly from their exact STMM counterparts, while accurate MCRTA computations of the phase function require droplet size parameters substantially exceeding 60.

cloud droplets↗
NASA NTRSDate not supplied

Improving Multi-Model Trajectory Simulation Estimators using Model Selection and Tuning

Multi-model Monte Carlo methods have been demonstrated to be an efficient and accurate alternative to standard Monte Carlo (MC) in the model-based propagation of uncertainty in entry, descent, and landing (EDL) applications. These multi-model MC methods fuse predictions from low-fidelity models with the high-fidelity EDL model of interest to produce unbiased statistics with a fraction of the computational cost. The accuracy and efficiency of the multi-model MC methods are dependent upon the magnitude of correlations of the low-fidelity models with the high-fidelity model, but also upon the correlation among the low-fidelity models, and their relative computational cost. Because of this layer of complexity, the question of how to optimally select the set of low-fidelity models has remained open. In this work, methods for optimal model construction and tuning are investigated as a means to increase the speed and precision of trajectory simulation for EDL. Specifically, the focus is on the inclusion of low-fidelity model tuning within the sample allocation optimization that accompanies multi-model MC methods. Preliminary results indicate that low-fidelity model tuning can significantly improve efficiency and precision of trajectory simulations and provide an increased edge to multi-model MC methods when compared to standard MC. The challenges and potential benefits to exploring a fully iterative and comprehensive optimization strategy in future work are highlighted.

uncertainty quantification↗
NASA NTRS1972

Evaluation of Jacobian determinants by Monte Carlo methods - Application to the quasiclassical approximation in molecular scattering.

Sampling techniques have been used previously to evaluate Jacobian determinants that occur in classical mechanical descriptions of molecular scattering. These determinants also occur in the quasiclassical approximation. A new technique is described which can be used to evaluate Jacobian determinants which occur in either description. This method is expected to be valuable in the study of reactive scattering using the quasiclassical approximation.

La Budde, R. A.↗