Monte Carlo Framework Research Articles

Latent Markov time-interaction processes

We present parametric and semiparametric latent Markov time-interaction processes, that are point processes where the occurrence of an event can increase or reduce the probability of future events. We first present time-interaction processes with parametric and nonparametric baselines, then we let model parameters be modulated by a discrete state continuous time latent Markov process. Posterior inference is based on a novel and efficient data augmentation approach in the Markov Chain Monte Carlo framework. We illustrate with a simulation study; and an original application to terrorist attacks in Europe in the period 2001-2017, where we find two distinct latent clusters for the hazard of occurrence of terrorist events, negative association with GDP growth, and self-exciting phenomena.

Active Learning of Boltzmann Samplers and Potential Energies with Quantum Mechanical Accuracy.

Extracting consistent statistics between relevant free energy minima of a molecular system is essential for physics, chemistry, and biology. Molecular dynamics (MD) simulations can aid in this task but are computationally expensive, especially for systems that require quantum accuracy. To overcome this challenge, we developed an approach combining enhanced sampling with deep generative models and active learning of a machine learning potential (MLP). We introduce an adaptive Markov chain Monte Carlo framework that enables the training of one normalizing flow (NF) and one MLP per state, achieving rapid convergence toward the Boltzmann distribution. Leveraging the trained NF and MLP models, we compute thermodynamic observables such as free energy differences and optical spectra. We apply this method to study the isomerization of an ultrasmall silver nanocluster belonging to a set of systems with diverse applications in the fields of medicine and catalysis.

Evolution of Influenza A(H3N2) Viruses in Bhutan for Two Consecutive Years, 2022 and 2023.

Influenza A viruses pose a significant public health threat globally and are characterized by rapid evolution of the hemagglutinin (HA) gene causing seasonal epidemics. The aim of this study was to investigate the evolutionary dynamics of A(H3N2) circulating in Bhutan during 2022 and 2023. We analysed 166 whole-genome sequences of influenza A(H3N2) from Bhutan, obtained from the GISAID database. We employed a Bayesian Markov Chain Monte Carlo (MCMC) framework, with a curated global dataset of HA sequences from regions with significant migration links to Bhutan. Phylogenetic, temporal, and phylogeographic analyses were conducted to elucidate the evolutionary dynamics and spatial dissemination of the viruses. Our phylogenetic analysis identified the circulation of influenza A(H3N2) Clade 3C.2a1b.2a.2 in Bhutan during 2022 and 2023, with viruses further classified into three subclades: 2a.3 (39/166), 2a.3a.1 (58/166) and 2a.3b (69/166). The TMRCA estimates suggest that these viral lineages originated approximately 1.93 years prior to their detection. Phylogeographic analysis indicates introductions from the United States in 2022 and Australia in 2023. The mean evolutionary rate across all gene segments was calculated to be 4.42 × 10-3 substitutions per site per year (95% HPD: 3.19 × 10-3 to 5.84 × 10-3), with evidence of purifying selection and limited genetic diversity. Furthermore, reassortment events were rare, with an estimated rate of 0.045 events per lineage per year. Our findings show that primary forces shaping the local evolution of the influenza A(H3N2) in Bhutan are largely stochastic, with only sporadic instances of adaptive change, and thus underscore the importance of continuous surveillance to mitigate the impact of evolving strains.

RayStation/GATE Monte Carlo simulation framework for verification of proton therapy based on the 12N imaging

Objective.12N, having a half-life of 11 ms, is a highly effective positron emitter that can potentially provide near real-time feedback in proton therapy. There is currently no framework for comparing and validating positron emission imaging of12N. This work describes the development and validation of a Monte Carlo (MC) framework to calculate the images of12N, as well as long-lived isotopes, originating from activation by protons.Approach. The available dual-panel Biograph mCT PET scanner was modeled in GATE and validated by comparing the simulated sensitivity map with the measured one. The distributions of12N and long-lived isotopes were calculated by RayStation and used as the input of GATE simulations. The RayStation/GATE combination was verified using proton beam irradiations of homogeneous phantoms. A 120 MeV pulsed pencil beam with 108protons per pulse was used. Two-dimensional images were created from the GATE output and compared with the images based on the measurements and the 1D longitudinal projection of the full 2D image was used to calculate the12N activity range.Main results. The simulated sensitivity in the center of the FoV (5.44%) agrees well with the measured one (5.41%). The simulated and measured 2D sensitivity maps agree in good detail. The relative difference between the measured and simulated positron activity range for both12N and long-lived isotopes is less than 1%. The broadening of the12N images relative to those of the longer-lived isotopes can be understood in terms of the large positron range of12N.Significance. We developed and validated a MC framework based on RayStation/GATE to support the in-beam PET method for quality assurance of proton therapy. The inclusion of the very short-lived isotope12N makes the framework useful for developing near real-time verification. This represents a significant step towards translating12N real-time in vivo verification to the clinic.

Steady-state properties of multi-orbital systems using quantum Monte Carlo.

A precise dynamical characterization of quantum impurity models with multiple interacting orbitals is challenging. In quantum Monte Carlo methods, this is embodied by signproblems. A dynamical signproblem makes it exponentially difficult to simulate long times. A multi-orbital signproblem generally results in a prohibitive computational cost for systems with multiple impurity degrees of freedom even in static equilibrium calculations. Here, we present a numerically exact inchworm method that simultaneously alleviates both signproblems, enabling simulation of multi-orbital systems directly in the equilibrium or nonequilibrium steady-state. The method combines ideas from the recently developed steady-state inchworm Monte Carlo framework [Erpenbeck et al., Phys. Rev. Lett. 130, 186301 (2023)] with other ideas from the equilibrium multi-orbital inchworm algorithm [Eidelstein et al., Phys. Rev. Lett. 124, 206405 (2020)]. We verify our method by comparison with analytical limits and numerical results from previous methods.

Adaptive formulation for probabilistic storm surge predictions through sharing of numerical simulation results across storm advisories

As a tropical storm/cyclone approaches landfall, real-time probabilistic predictions for the anticipated surge provide valuable information for emergency preparedness/response decisions. These probabilistic predictions are made through an uncertainty quantification process that involves: (i) generating a sufficiently large ensemble of storm scenarios based on the nominal storm advisory and the anticipated forecast errors; (ii) performing high-fidelity numerical simulations to obtain surge predictions for each storm scenario; and (iii) estimating surge statistics of interest by assembling the simulation results. This process is repeated whenever the nominal storm advisory is updated. The number of storm scenarios utilized in the analysis directly impacts the statistical accuracy of the probabilistic predictions; a larger ensemble improves accuracy but requires greater computational resources to provide predictions with the desired expediency to guide real-time decisions. This paper revisits two recently proposed Monte-Carlo (MC) frameworks that aim to improve accuracy without increasing the computational burden: adaptive importance sampling (AIS) and adaptive multi-fidelity Monte Carlo (AMFMC). The foundational concept behind them is similar: share numerical simulation results across the probabilistic predictions performed for different storm advisories to accelerate the MC estimation. This is achieved differently for each approach, through adaptive development of an importance sampling proposal density (for AIS) or a surrogate model (for AMFMC). Here, a direct comparison between these frameworks is established, focusing on the mechanisms for the information sharing and the challenges encountered in tuning the algorithm adaptive characteristics to provide probabilistic estimates across a large number of quantities of interest (QoIs), corresponding to the surge predictions for different locations within the coastal region of interest. As this large number results in conflicting choices for the adaptive characteristics, a compromise solution needs to be promoted. The efficacy of the two frameworks is examined in detail in this setting, comparing the accuracy of idealized implementations (adaptive decisions independently made for each QoI) to the accuracy of practical implementations (single, compromise decision within the MC implementation). The study also showcases the importance of information sharing across storm advisories in real-time probabilistic storm surge predictions and provides guidelines for an efficient adaptive MC formulation in such settings.

Mechanism-specific chemical energy accommodation with finite-rate surface chemistry in non-equilibrium flow

During atmospheric reentry, the vehicle surface is exposed to highly non-equilibrium flow. The vehicle surface can experience heterogeneous recombination of reactive atoms, which contributes to its aerothermodynamic heating. This process is followed by chemical energy accommodation (CEA), where the released energy is either transferred to the surface or the internal energy modes of the recombined molecule. Heterogeneous recombination can be categorized into Eley–Rideal (ER) and Langmuir–Hinshelwood mechanisms, which differ in their methods of molecule formation and degrees of CEA. The complete CEA assumption may not consider the dependency of CEA on the mechanisms of heterogeneous recombination. This study aims to consider the mechanism-specific CEA for a more accurate prediction of surface heat flux. The authors implement mechanism-specific CEA within the direct simulation Monte Carlo framework using the finite-rate surface chemistry model, resolving elementary surface reactions and assigning a CEA coefficient, β, to each mechanism. The model is verified through comparisons with analytical solutions of surface coverage and validated against benchmark references. A parametric investigation of rarefied hypersonic flow over a two-dimensional cylinder is conducted under different freestream Mach and Knudsen numbers. Results show a reduction in total heat flux of up to 14.44% using mechanism-specific CEA compared to the complete CEA assumption. The reduction is attributed to the relative contribution of the ER mechanism, which can be a function of atomic partial pressure at the boundary layer.

A framework for in-field and out-of-field patient specific secondary cancer risk estimates from treatment plans using the TOPAS Monte Carlo system

Objective. To allow the estimation of secondary cancer risks from radiation therapy treatment plans in a comprehensive and user-friendly Monte Carlo (MC) framework. Method. Patient planning computed tomography scans were extended superior-inferior using the International Commission on Radiological Protection’s Publication 145 computational mesh phantoms and skeletal matching. Dose distributions were calculated with the TOPAS MC system using novel mesh capabilities and the digital imaging and communications in medicine radiotherapy extension interface. Finally, in-field and out-of-field cancer risk was calculated using both sarcoma and carcinoma risk models with two alternative parameter sets. Result. The TOPAS MC framework was extended to facilitate epidemiological studies on radiation-induced cancer risk. The framework is efficient and allows automated analysis of large datasets. Out-of-field organ dose was small compared to in-field dose, but the risk estimates indicate a non-negligible contribution to the total radiation induced cancer risk. Significance. This work equips the TOPAS MC system with anatomical extension, mesh geometry, and cancer risk model capabilities that make state-of-the-art out-of-field dose calculation and risk estimation accessible to a large pool of users. Furthermore, these capabilities will facilitate further refinement of risk models and sensitivity analysis of patient specific treatment options.

Advancements in field development planning through mathematical analysis for reserves estimation, casing design, accidental events and carbon dioxide storage

The objective of this work is to introduce novel methodologies in specific parts of Field Development Plans (FDPs) by leveraging contemporary technological advancements, industry best practices, and accumulated knowledge. The proposed methodologies comprise volumetric analysis by conducting stochastic simulations within a Monte Carlo framework to evaluate the associated uncertainties and a piston-like CO2 storage scheme (based on the material balance approach) aiming to enhance natural gas production and at the same time store CO2, mitigating climate change. Optimization of drilling operations based on appropriate material selection from commercial casing tables and assignment of a failure probability of casing configuration are also included. Another proposed methodology involves spatial risk analysis simulating accidental events based on the points of interest (POIs) and the distance from the event. Finally, a stochastic analysis of project economics is conducted showing uncertainties of cashflows throughout the economic life of the project and assessing the outcomes using various probabilistic performance metrics. The integration of these methodologies offers a robust framework for enhancing the effectiveness of FDPs and their applications, aligning with the evolving demands and complexities of the oil and gas sector. Such methodologies, rooted in mathematical tools aiming to quantify uncertainty in various ways, can increase production, potentially reducing costs through carbon tax incentives and benefit the environment. The applicability of the proposed methodology is demonstrated at the Frigg field, a natural gas reservoir situated in the Norwegian sector of the North Sea. Given its historical development in the 1970s and 1980s, the Frigg field serves as a rich repository of data and information for comparative analysis and fine-tuning of the proposed methodologies. The present study bridges the gap between theoretical advancements and practical applications, promoting innovation and efficiency within the oil and gas field development processes.

Practical Appearance Model for Foundation Cosmetics

AbstractCosmetic products have found their place in various aspects of human life, yet their digital appearance reproduction has received little attention. We present an appearance model for cosmetics, in particular for foundation layers, that reproduces a range of existing appearances of foundation cosmetics: from a glossy to a matte to an almost velvety look. Our model is a multilayered BSDF that reproduces the stacking of multiple layers of cosmetics. Inspired by the microscopic particulates used in cosmetics, we model each individual layer as a stochastic participating medium with two types of scatterers that mimic the most prominent visual features of cosmetics: spherical diffusers, resulting in a uniform distribution of radiance; and platelets, responsible for the glossy look of certain cosmetics. We implement our model on top of the position‐free Monte Carlo framework, that allows us to include multiple scattering. We validate our model against measured reflectance data, and demonstrate the versatility and expressiveness of our model by thoroughly exploring the range of appearances that it can produce.

Controlling a Vlasov–Poisson Plasma by a Particle-in-Cell Method Based on a Monte Carlo Framework

Controlling a Vlasov–Poisson Plasma by a Particle-in-Cell Method Based on a Monte Carlo Framework

Individual-level models of disease transmission incorporating piecewise spatial risk functions

Modelling epidemics is crucial for understanding the emergence, transmission, impact and control of diseases. Spatial individual-level models (ILMs) that account for population heterogeneity are a useful tool, accounting for factors such as location, vaccination status and genetic information.Parametric forms for spatial risk functions, or kernels, are often used, but rely on strong assumptions about underlying transmission mechanisms. Here, we propose a class of non-parametric spatial disease transmission model, fitted within a Bayesian Markov chain Monte Carlo (MCMC) framework, allowing for more flexible assumptions when estimating the effect on spatial distance and infection risk.We focus upon two specific forms of non-parametric spatial infection kernel: piecewise constant and piecewise linear. Although these are relatively simple forms, we find them to produce results in line with, or superior to, parametric spatial ILMs. The performance of these models is examined using simulated data, including under circumstances of model misspecification, and then applied to data from the UK 2001 foot-and-mouth disease.

Impact assessment of self-medication on COVID-19 prevalence in Gauteng, South Africa, using an age-structured disease transmission modelling framework

ObjectiveTo assess the impact of self-medication on the transmission dynamics of COVID-19 across different age groups, examine the interplay of vaccination and self-medication in disease spread, and identify the age group most prone to self-medication.MethodsWe developed an age-structured compartmentalized epidemiological model to track the early dynamics of COVID-19. Age-structured data from the Government of Gauteng, encompassing the reported cumulative number of cases and daily confirmed cases, were used to calibrate the model through a Markov Chain Monte Carlo (MCMC) framework. Subsequently, uncertainty and sensitivity analyses were conducted on the model parameters.ResultsWe found that self-medication is predominant among the age group 15-64 (74.52%), followed by the age group 0-14 (34.02%), and then the age group 65+ (11.41%). The mean values of the basic reproduction number, the size of the first epidemic peak (the highest magnitude of the disease), and the time of the first epidemic peak (when the first highest magnitude occurs) are 4.16499, 241,715 cases, and 190.376 days, respectively. Moreover, we observed that self-medication among individuals aged 15-64 results in the highest spreading rate of COVID-19 at the onset of the outbreak and has the greatest impact on the first epidemic peak and its timing.ConclusionStudies aiming to understand the dynamics of diseases in areas prone to self-medication should account for this practice. There is a need for a campaign against COVID-19-related self-medication, specifically targeting the active population (ages 15-64).

Lateral holding behaviour of torpedo piles in spatially variable soil: Development of a probabilistic design approach

Offshore torpedo piles are increasingly being utilised in deepwater oil and gas development as part of a taut-leg mooring system. As these piles commonly experience inclined loading in service, accurately determining their lateral holding capacity is crucial. Despite the fact that natural soil characteristics exhibit significant spatial variability, existing studies are mostly deterministic in nature. This paper presents probabilistic analyses of the lateral holding capacity of torpedo piles, explicitly considering the spatial variability of soil shear strength. Large deformation finite element calculations are combined with three-dimensional random field generation in a Monte Carlo framework. The results show that while spatial variability does not apparently alter the failure mechanism of laterally loaded torpedo piles, it significantly influences their holding capacity. The routine deterministic calculation, neglecting spatial variability, would probably yield unconservative estimates. To address this challenge, a probabilistic Broms method is developed, which enables engineers to produce lateral holding capacity estimates with varying confidence levels, using local strength data rather than central tendency. Furthermore, endeavours are also made to calibrate the safety factor, extensively employed in deterministic design practices, from a probabilistic perspective, providing practicing engineers with a viable alternative in scenarios where a local strength profile is unavailable.

In silico design of DNA sequences for in vivo nucleosome positioning.

The computational design of synthetic DNA sequences with designer in vivo properties is gaining traction in the field of synthetic genomics. We propose here a computational method which combines a kinetic Monte Carlo framework with a deep mutational screening based on deep learning predictions. We apply our method to build regular nucleosome arrays with tailored nucleosomal repeat lengths (NRL) in yeast. Our design was validated in vivo by successfully engineering and integrating thousands of kilobases long tandem arrays of computationally optimized sequences which could accommodate NRLs much larger than the yeast natural NRL (namely 197 and 237bp, compared to the natural NRL of ∼165bp). RNA-seq results show that transcription of the arrays can occur but is not driven by the NRL. The computational method proposed here delineates the key sequence rules for nucleosome positioning in yeast and should be easily applicable to other sequence properties and other genomes.

An approach for multiscale two-phase flow simulation in the direct simulation Monte Carlo framework

To simulate multiscale gas flow with solid particles, Burt's model, based on the Direct Simulation Monte Carlo (DSMC) framework, is widely used to predict gas–solid interactions under the assumption of a negligibly small solid particle diameter compared to the local gas mean free path. However, Burt's model could become inaccurate when the solid particle is large relative to the local gas mean free path. This study introduces the Gas–Solid Synchronous (GSS) model, which predicts gas–solid interactions in continuum gas regions without assuming the local gas flow regime around a solid particle. Similar to Burt's model, the GSS model includes gas-to-solid and solid-to-gas interaction models to consider bidirectional interaction between two phases. The GSS gas-to-solid model is established by selecting accurate semi-empirical force and heat transfer models in comparison with DSMC simulation results. The GSS solid-to-gas model is developed based on the principles of momentum and energy conservation and validated against Burt's solid-to-gas model. The results show that Burt's model could overestimate the interphase force and heat transfer rates when its assumption on solid particle diameter does not hold, but it can reproduce non-equilibrium characteristics of two-phase flows where gas velocity distribution functions do not follow the Maxwell–Boltzmann distribution. By contrast, the GSS model can accurately predict gas–solid interaction in continuum gas flows, while it cannot capture the non-equilibrium nature of two-phase flows. The characteristics and limitations of the two models indicate that using a valid model for each gas–solid interaction could be crucial for accurate simulation of multiscale two-phase flows.

Efficient calculation of unbiased atomic forces in ab initio variational Monte Carlo

quantum Monte Carlo (QMC) is a state-of-the-art numerical approach for evaluating accurate expectation values of many-body wave functions. However, one of the major drawbacks that still hinders widespread QMC applications is the lack of an affordable scheme to compute unbiased atomic forces. In this study, we propose an efficient method to obtain unbiased atomic forces and pressures in the variational Monte Carlo (VMC) framework with the Jastrow-correlated Slater determinant ansatz or the Jastrow antisymmetrized geminal power ansatz, exploiting the gauge-invariant and locality properties of their geminal representation. We demonstrate the effectiveness of our method for H2 and Cl2 molecules and for the cubic boron nitride crystal. Our framework has a better algorithmic scaling with the system size than the traditional finite-difference method and, in practical applications, is as efficient as single-point VMC calculations. Thus, it paves the way to study dynamical properties of materials, such as phonons, and is beneficial for pursuing more reliable machine-learning interatomic potentials based on unbiased VMC forces. Published by the American Physical Society 2024

Geostatistical assessment of groundwater arsenic contamination in the Padana Plain

Arsenic (As) in groundwater from natural and anthropogenic sources is one of the most common pollutants worldwide affecting people and ecosystems. A large dataset from >3600 wells is employed to spatially simulate the depth-averaged As concentration in phreatic and confined aquifers of the Padana Plain (Northern Italy). Results of in-depth geostatistical analysis via PCA and simulations within a Monte Carlo framework allow the understanding of the variability of As concentrations within the aquifers. The most probable As contaminated zones are located along the piedmont areas in the confined aquifers and in the lowland territories in the phreatic aquifers. The distribution of the As contaminated zones has been coupled with hydrogeological, geological, and geochemical information to unravel the sources and mechanisms of As release in groundwater. The reductive dissolution of Fe oxyhydroxides and organic matter mineralization under anoxic conditions resulted to be the major drivers of As release in groundwater. This phenomenon is less evident in phreatic aquifers, due to mixed oxic and reducing conditions. This large-scale study provides a probabilistic perspective on As contamination, e.g. quantifying the spatial probability of exceeding national regulatory limits, and to outline As major sources and drivers.

1636: Real-time in vivo verification of proton therapy using new Monte Carlo framework for head phantom

1636: Real-time in vivo verification of proton therapy using new Monte Carlo framework for head phantom

Accelerated quantum circuit Monte Carlo simulation for heavy quark thermalization

Thermalization of heavy quarks in the quark-gluon plasma is one of the most promising phenomena for understanding the strong interaction. The energy loss and momentum broadening at low momentum can be well described by a stochastic process with drag and diffusion terms. Recent advances in quantum computing, in particular, quantum amplitude estimation (QAE), promise to provide a quadratic speedup in simulating stochastic processes. We introduce and formalize an accelerated quantum circuit Monte Carlo (aQCMC) framework to simulate heavy quark thermalization. With simplified drag and diffusion coefficients connected by Einstein’s relation, we simulate the thermalization of a heavy quark in isotropic and anisotropic mediums using an ideal quantum simulator and compare that to thermal expectations. With Grover-like QAE, we calculate physical observables with quadratically fewer resources, which is a boost over the classical MC simulation that usually requires a large sampling number at the same estimation accuracy. Published by the American Physical Society 2024