Multi-architecture Monte-Carlo (MC) simulation of soft coarse-grained polymeric materials: SOft coarse grained Monte-Carlo Acceleration (SOMA)
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Here, we consider hybrid deterministic-stochastic iterative algorithms for the solution of large, sparse linear systems. Starting from a convergent splitting of the coefficient matrix, we analyze various types of Monte Carlo acceleration schemes applied to the original preconditioned Richardson (stationary) iteration. We expect that these methods will have considerable potential for resiliency to faults when implemented on massively parallel machines. We also establish sufficient conditions for the convergence of the hybrid schemes, and we investigate different types of preconditioners including sparse approximate inverses. Numerical experiments on linear systems arising from the discretization of partial differential equations are presented.
Purpose: To present a new accelerated Monte Carlo code for CT-based dose calculations in high dose rate (HDR) brachytherapy. The new code (HDRMC) accounts for both tissue and nontissue heterogeneities (applicator and contrast medium). Methods: HDRMC uses a fast ray-tracing technique and detailed physics algorithms to transport photons through a 3D mesh of voxels representing the patient anatomy with applicator and contrast medium included. A precalculated phase space file for the{sup 192}Ir source is used as source term. HDRM is calibrated to calculated absolute dose for real plans. A postprocessing technique is used to include the exact density and composition of nontissue heterogeneities in the 3D phantom. Dwell positions and angular orientations of the source are reconstructed using data from the treatment planning system (TPS). Structure contours are also imported from the TPS to recalculate dose-volume histograms. Results: HDRMC was first benchmarked against the MCNP5 code for a single source in homogenous water and for a loaded gynecologic applicator in water. The accuracy of the voxel-based applicator model used in HDRMC was also verified by comparing 3D dose distributions and dose-volume parameters obtained using 1-mm{sup 3} versus 2-mm{sup 3} phantom resolutions. HDRMC can calculate the 3D dose distribution for a typical HDR cervix case with 2-mm resolution in 5 min on a single CPU. Examples of heterogeneity effects for two clinical cases (cervix and esophagus) were demonstrated using HDRMC. The neglect of tissue heterogeneity for the esophageal case leads to the overestimate of CTV D90, CTV D100, and spinal cord maximum dose by 3.2%, 3.9%, and 3.6%, respectively. Conclusions: A fast Monte Carlo code for CT-based dose calculations which does not require a prebuilt applicator model is developed for those HDR brachytherapy treatments that use CT-compatible applicators. Tissue and nontissue heterogeneities should be taken into account in modern HDR brachytherapy planning.
Safe separation of aircraft is a primary objective of any air traffic control system. An accelerated Monte Carlo approach was developed to assess the level of safety provided by a proposed next-generation air traffic control system. It combines features of fault tree and standard Monte Carlo methods. It runs more than one order of magnitude faster than the standard Monte Carlo method while providing risk estimates that only differ by about 10%. It also preserves component-level model fidelity that is difficult to maintain using the standard fault tree method. This balance of speed and fidelity allows sensitivity analysis to be completed in days instead of weeks or months with the standard Monte Carlo method. Results indicate that risk estimates are sensitive to transponder, pilot visual avoidance, and conflict detection failure probabilities.
Purpose: The clinical commissioning of IMRT subject to a magnetic field is challenging. The purpose of this work is to develop a GPU-accelerated Monte Carlo dose calculation platform based on PENELOPE and then use the platform to validate a vendor-provided MRIdian head model toward quality assurance of clinical IMRT treatment plans subject to a 0.35 T magnetic field. Methods: PENELOPE was first translated from FORTRAN to C++ and the result was confirmed to produce equivalent results to the original code. The C++ code was then adapted to CUDA in a workflow optimized for GPU architecture. The original code was expanded to include voxelized transport with Woodcock tracking, faster electron/positron propagation in a magnetic field, and several features that make gPENELOPE highly user-friendly. Moreover, the vendor-provided MRIdian head model was incorporated into the code in an effort to apply gPENELOPE as both an accurate and rapid dose validation system. A set of experimental measurements were performed on the MRIdian system to examine the accuracy of both the head model and gPENELOPE. Ultimately, gPENELOPE was applied toward independent validation of patient doses calculated by MRIdian’s KMC. Results: An acceleration factor of 152 was achieved in comparison to the original single-thread FORTRAN implementation with the original accuracy being preserved. For 16 treatment plans including stomach (4), lung (2), liver (3), adrenal gland (2), pancreas (2), spleen(1), mediastinum (1), and breast (1), the MRIdian dose calculation engine agrees with gPENELOPE with a mean gamma passing rate of 99.1% ± 0.6% (2%/2 mm). Conclusions: A Monte Carlo simulation platform was developed based on a GPU- accelerated version of PENELOPE. This platform was used to validate that both the vendor-provided head model and fast Monte Carlo engine used by the MRIdian system are accurate in modeling radiation transport in a patient using 2%/2 mm gamma criteria. Future applications of this platform will include dose validation and accumulation, IMRT optimization, and dosimetry system modeling for next generation MR-IGRT systems.
Accurate solution of the k-eigenvalue form of the Boltzmann radiation transport equation is required in many application areas, including nuclear reactor analysis and criticality safety. Monte Carlo calculations are free of the discretization errors inherent to deterministic methods and therefore offer the most accurate solutions. However, converging the fission source can be difficult for many problems, resulting in either a substantial computational overhead or potential inaccuracies that negate many of the benefits of using Monte Carlo methods. Difficulty in converging the fission source occurs for two distinct reasons. The first is the existence of a high dominance ratio in the problem (i.e. the largest and second largest eigenvalues have approximately the same magnitude). The second difficulty arises due to undersampling of the fission source because an insufficient number of particle histories are simulated. The first difficulty is shared by deterministic solvers when using power iteration, while the second difficulty is unique to Monte Carlo solvers. In practice, both difficulties may be present in the same problem, compounding the difficulty in achieving a converged distribution. In this paper, we consider a new approach to accelerate the convergence of the fission source based on combining the use of fission matrix methods with kernel density estimators (KDEs). It has been observed that deterministic fission matrix methods show the potential to accelerate the convergence of the fission source in Monte Carlo criticality calculations but may introduce significant additional noise for difficult problems. In this paper, we have demonstrated the use of a KDE approach in combination with the fission matrix acceleration. Although the addition of the KDE initially slows the convergence of the fission matrix acceleration, it decreases the magnitude of the noise while still offering significantly improved convergence relative to analog Monte Carlo. (authors)
Purpose: To develop an accurate and fast Monte Carlo (MC) method of simulating CT that is capable of correlating dose with image quality using voxelized phantoms. Methods: A realistic voxelized phantom based on patient CT data, XCAT, was used with a GPU accelerated MC code for helical MDCT. Simulations were done with both uniform density organs and with textured organs. The organ doses were validated using previous experimentally validated simulations of the same phantom under the same conditions. Images acquired by tracking photons through the phantom with MC require lengthy computation times due to the large number of photon histories necessary for accurate representation of noise. A substantial speed up of the process was attained by using a low number of photon histories with kernel denoising of the projections from the scattered photons. These FBP reconstructed images were validated against those that were acquired in simulations using many photon histories by ensuring a minimal normalized root mean square error. Results: Organ doses simulated in the XCAT phantom are within 10% of the reference values. Corresponding images attained using projection kernel smoothing were attained with 3 orders of magnitude less computation time compared to a reference simulation using many photon histories. Conclusion: Combining GPU acceleration with kernel denoising of scattered photon projections in MC simulations allows organ dose and corresponding image quality to be attained with reasonable accuracy and substantially reduced computation time than is possible with standard simulation approaches.
Accurate determination of thermodynamic properties of petroleum reservoir fluids is of great interest to many applications, especially in petroleum engineering and chemical engineering. Molecular simulation has many appealing features, especially its requirement of fewer tuned parameters but yet better predicting capability; however it is well known that molecular simulation is very CPU expensive, as compared to equation of state approaches. We have recently introduced an efficient thermodynamically consistent technique to regenerate rapidly Monte Carlo Markov Chains (MCMCs) at different thermodynamic conditions from the existing data points that have been pre-computed with expensive classical simulation. This technique can speed up the simulation more than a million times, making the regenerated molecular simulation almost as fast as equation of state approaches. In this paper, this technique is first briefly reviewed and then numerically investigated in its capability of predicting ensemble averages of primary quantities at different neighboring thermodynamic conditions to the original simulated MCMCs. Moreover, this extrapolation technique is extended to predict second derivative properties (e.g. heat capacity and fluid compressibility). The method works by reweighting and reconstructing generated MCMCs in canonical ensemble for Lennard-Jones particles. In this paper, system's potential energy, pressure, isochoric heat capacity and isothermal compressibility along isochors, isotherms and paths of changing temperature and density from the original simulated points were extrapolated. Finally, an optimized set of Lennard-Jones parameters (ε, σ) for single site models were proposed for methane, nitrogen and carbon monoxide.
Metal hydrides are important across diverse applications, such as hydrogen storage, batteries, gas sensors, nuclear reactions, and high-temperature superconductivity. Previous computational studies of metal hydrides under extreme pressures, e.g., 𝑂(10 2 ) GPa, usually treat them as stoichiometric compounds without considering interstitial lattice disorder. As pressures become more moderate in the 𝑂(10 0 ) GPa and below range, hydrogen disorder at interstitial lattice sites becomes prominent, e.g., in the N-doped Lu hydride that was recently claimed superconducting near 1 GPa. Further adding compositional complexity from alloying and/or multielement interstitial occupation makes elucidating pressure- and temperature-dependent observables intractable by first-principles calculations alone. We therefore propose a lattice graph neural-network surrogate modeling approach to predict configuration- and pressure-dependent equation-of-state properties. Their efficiency permits Monte Carlo simulations to calculate Gibbs energies and pressure-dependent phase diagrams, thereby revealing insights into the synthesis conditions required for achieving desired phase equilibria. We demonstrate this concept for the compositionally complex cubic Lu(H,N,Va) 3 system where three constituents (hydrogen, nitrogen and vacancy) have disordered multielement interstitial occupancies and insights into pressure-dependent phase equilibria are critically needed, e.g., N-doping levels can significantly lower dehydrogenation temperatures and provide a new strategy to optimize hydrogen-storage alloys. This work can improve the thermodynamic understanding of the Lu-H-N system and help rational synthesis of N-doped Lu hydrides, but more generally demonstrates an efficient approach to model pressure-dependent thermodynamics of multicomponent solid solutions.
Purpose: Monte Carlo simulations play a vital role in the understanding of the fundamental limitations, design, and optimization of existing and emerging medical imaging systems. Efforts in this area have resulted in the development of a wide variety of open-source software packages. One such package, hybridMANTIS, uses a novel hybrid concept to model indirect scintillator detectors by balancing the computational load using dual CPU and graphics processing unit (GPU) processors, obtaining computational efficiency with reasonable accuracy. In this work, the authors describe two open-source visualization interfaces, webMANTIS and visualMANTIS to facilitate the setup of computational experiments via hybridMANTIS. Methods: The visualization tools visualMANTIS and webMANTIS enable the user to control simulation properties through a user interface. In the case of webMANTIS, control via a web browser allows access through mobile devices such as smartphones or tablets. webMANTIS acts as a server back-end and communicates with an NVIDIA GPU computing cluster that can support multiuser environments where users can execute different experiments in parallel. Results: The output consists of point response and pulse-height spectrum, and optical transport statistics generated by hybridMANTIS. The users can download the output images and statistics through a zip file for future reference. In addition, webMANTIS provides a visualization window that displays a few selected optical photon path as they get transported through the detector columns and allows the user to trace the history of the optical photons. Conclusions: The visualization tools visualMANTIS and webMANTIS provide features such as on the fly generation of pulse-height spectra and response functions for microcolumnar x-ray imagers while allowing users to save simulation parameters and results from prior experiments. The graphical interfaces simplify the simulation setup and allow the user to go directly from specifying input parameters to receiving visual feedback for the model predictions.
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Over the past several years, the graphics processing unit (GPU) technology has rapidly gained ground in scientific computing due to its outstanding performance and programmability. GPU implementation of Monte Carlo radiation transport for dose calculations has been reported by many investigators. The majority of these studies adopted single-precision floating point format because of the higher peak floating point operations per second (FLOPS) the GPUs can deliver than double-precision. It has been known that calculation using single-precision is more prone to numerical round-off errors, especially when a single tally data is accumulated 'atomically' and repeatedly by thousands of GPU threads. To mitigate this problem, the least intrusive solution in theory is to replace the single-precision atomic-add tally function with a double-precision version. However, the complexity lies in the fact that some GPUs (Nvidia GPUs prior to the Pascal generation; all current AMD GPUs) do not readily offer such double-precision function at hardware level, and that software emulation is too slow to use if not optimized properly. This paper discusses several atomic-add tally methods with reduced numerical errors used throughout ARCHER development. The original software-based compare-and-swap method (CAS) was shown to be inefficient due to high intra-warp thread contention, whereas the improved software-based warp-aggregated method (WAG) and Kahan summation method (KAS) eliminated the thread contention and performed very well on Kepler and Maxwell GPUs, being more than 13 times faster than CAS in our tests. The hardware-based (HB) double-precision atomic-add feature available on Pascal and Volta GPUs exceeded software emulation and offered the best performance universally, so did WIB, a combination of WAG and HB methods. It was also shown that in a single-precision dose engine, KAS managed to maintain high reliability when the single-precision atomic-add tally underestimated the dose by 25%. (authors)
Non-adiabatic dynamics, where systems non-radiatively transition between electronic states, plays a crucial role in many photo-physical processes, such as fluorescence, phosphorescence, and photoisomerization. Methods for the simulation of non-adiabatic dynamics are typically either numerically impractical, highly complex, or based on approximations which can result in failure for even simple systems. Recently, the Semiclassical Monte Carlo (SCMC) approach was developed in an attempt to combine the accuracy of rigorous semiclassical methods with the efficiency and simplicity of widely used surface hopping methods. However, while SCMC was found to be more efficient than other semiclassical methods, it is not yet as efficient as is needed to be used for large molecular systems. Here, we have developed two new methods: the accelerated-SCMC and the accelerated-SCMC with re-Gaussianization, which reduce the cost of the SCMC algorithm up to two orders of magnitude for certain systems. In most cases shown here, the new procedures are nearly as efficient as the commonly used surface hopping schemes, with little to no loss of accuracy. This implies that these modified SCMC algorithms will be of practical numerical solutions for simulating non-adiabatic dynamics in realistic molecular systems.
We present a multiple-set overlapping-domain decomposed strategy for parallelizing the Monte Carlo Synthetic Acceleration method. Monte Carlo Synthetic Acceleration methods use the Neumann-Ulam class of Monte Carlo solvers for linear systems to accelerate a fixed-point iteration sequence. Effective parallel algorithms for these methods require the parallelization of the underlying Neumann-Ulam solvers. To do this in a domain decomposed environment, we borrow strategies traditionally implemented in Monte Carlo particle transport to parallelize the problem. The parallel Neumann-Ulam and multiple-set overlapping-domain decomposition algorithms are presented along with parallel scaling data for the resulting implementation using the Titan Cray XK7 machine at Oak Ridge National Laboratory.
Here, this report presents an accelerated kinetic Monte Carlo (KMC) method to compute the diffusivity of hydrogen in hcp metals and alloys, considering both thermally activated hopping and quantum tunneling. The acceleration is achieved by replacing regular KMC jumps in trapping energy basins formed by neighboring tetrahedral interstitial sites, with analytical solutions for basin exiting time and probability. Parameterized by density functional theory (DFT) calculations, the accelerated KMC method is shown to be capable of efficiently calculating hydrogen diffusivity in α-Zr and Zircaloy, without altering the kinetics of long-range diffusion. Above room temperature, hydrogen diffusion in α-Zr and Zircaloy is dominated by thermal hopping, with negligible contribution from quantum tunneling. The diffusivity predicted by this DFT + KMC approach agrees well with that from previous independent experiments and theories, without using any data fitting. The diffusivity along < c > is found to be slightly higher than that along < a >, with the anisotropy saturated at about 1.20 at high temperatures, resolving contradictory results in previous experiments. Demonstrated using hydrogen diffusion in α-Zr, the same method can be extended for on-lattice diffusion in hcp metals, or systems with similar trapping basins.
We present a novel synthetic-acceleration-based Monte Carlo method for solving the equilibrium thermal radiation diffusion equation in three spatial dimensions. The algorithm performance is compared against traditional solution techniques using a Marshak benchmark problem and a more complex multiple material problem. Our results show that our Monte Carlo method is an effective solver for sparse matrix systems. For solutions converged to the same tolerance, it performs competitively with deterministic methods including preconditioned conjugate gradient and GMRES. We also discuss various aspects of preconditioning the method and its general applicability to broader classes of problems.
Purpose: I am presenting a parameterized 3D GPU accelerated electron Monte Carlo second check program. Method: I wrote the 3D grid dose calculation algorithm in CUDA and utilized an NVIDIA GeForce GTX 780 Ti to run all of the calculations. The electron path beyond the distal end of the cone is governed by four parameters: the amplitude of scattering (AMP), the mean and width of a Gaussian energy distribution (E and α), and the percentage of photons. In my code, I adjusted all parameters until the calculated PDD and profile fit the measured 10×10 open beam data within 1%/1mm. I then wrote a user interface for reading the DICOM treatment plan and images in Python. In order to verify the algorithm, I calculated 3D dose distributions on a variety of phantoms and geometries, and compared them with the Eclipse eMC calculations. I also calculated several patient specific dose distributions, including a nose and an ear. Finally, I compared my algorithm’s computation times to Eclipse’s. Results: The calculated MU for all of the investigated geometries agree with the TPS within the TG-114 action level of 5%. The MU for the nose was < 0.5 % different while the MU for the ear at 105 SSD was ∼2 %. Calculation times for a 12MeV 10×10 open beam ranged from 1 second for a 2.5 mm grid resolution with ∼15 million particles to 33 seconds on a 1 mm grid with ∼460 million particles. Eclipse calculation runtimes distributed over 10 FAS workers were 9 seconds to 15 minutes respectively. Conclusion: The GPU accelerated second check allows quick MU verification while accounting for patient specific geometry and heterogeneity.