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At least 883 records · Page 49
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Improving Predictions Under Uncertainty of Material Plasma Device Operations

Understanding the properties of materials when exposed to various plasma temperatures and fluxes is essential to the building and operating of fusion reactors. The Material Plasma Exposure eXperiment (MPEX) is an instrument currently being developed by the Department of Energy (DOE) for this purpose. MPEX is expected to come online in stages over the next five years. Proto-MPEX, the predecessor to MPEX, operated from 2014 to 2021, and was designed to understand the generation of plasma temperatures and fluxes at orders of magnitude below what will be obtained by MPEX. This work uses the recently developed stochastic neural network (SNN), a machine learning technique capable of operating under uncertainty to provide a surrogate model for the Proto-MPEX device. We demonstrate that SNN outperforms Bayesian neural network (BNN), a standard in the field of machine learning with uncertainty. The development of a robust surrogate of the Proto-MPEX will aid in the commissioning and operation of the MPEX device.

Archibald, Rick↗
DOE OSTI2024

A Novel Noise-Aware Classical Optimizer for Variational Quantum Algorithms

A key component of variational quantum algorithms (VQAs) is the choice of classical optimizer employed to update the parameterization of an ansatz. It is well recognized that quantum algorithms will, for the foreseeable future, necessarily be run on noisy devices with limited fidelities. Thus, the evaluation of an objective function (e.g., the guiding function in the quantum approximate optimization algorithm (QAOA) or the expectation of the electronic Hamiltonian in variational quantum eigensolver (VQE)) required by a classical optimizer is subject not only to stochastic error from estimating an expected value but also to error resulting from intermittent hardware noise. Model-based derivative-free optimization methods have emerged as popular choices of a classical optimizer in the noisy VQA setting, based on empirical studies. However, these optimization methods were not explicitly designed with the consideration of noise. In this work we adapt recent developments from the “noise-aware numerical optimization” literature to these commonly used derivative-free model-based methods. We introduce the key defining characteristics of these novel noise-aware derivative-free model-based methods that separate them from standard model-based methods. In conclusion, we study an implementation of such noise-aware derivative-free model-based methods and compare its performance on demonstrative VQA simulations to classical solvers packaged in scikit-quant.

classical optimizers↗
DOE OSTI2021

Acquire and Test IDAES Framework Components

The cooperation under the Grid Modernization Initiative and the Applied Energy Tri-Laboratory umbrellas requires mutual understanding of capabilities and a common effort to identify gaps existing in the available computational modeling and analysis tools. In this work, we report acquisition and testing of the National Energy Technology Laboratory’s Institute for the Design of Advanced Energy Systems (IDAES) framework, particularly including both electric power systems production cost model simulator Prescient as well as system optimization IDAES itself. Further, we consider the methods in which developments in Prescient and IDAES for grid-energy simulation and optimization may be included in the Framework for Optimization of ResourCes and Economics (FORCE) ecosystem that has been under collaborative development by Idaho National Laboratory, Argonne National Laboratory, and Oak Ridge National Laboratory. We propose two integration methods to introduce Prescient and IDAES into existing FORCE automated workflows. One integration involves using Prescient as a market reduced-order model and IDAES models similar to how existing Modelica models are used. The other integration involves wrapping the Prescient-IDAES dispatch optimization process with the stochastic capacity optimization workflow in FORCE.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2020

Enabling Catalog Simulations of Transient and Variable Sources Based on LSST Cadence Strategies

The American Astronomical Society. All rights reserved.. The Large Synoptic Survey Telescope (LSST) project will conduct a 10 year multi-band survey starting in 2022. Observing strategies for this survey are being actively investigated, and the science capabilities can be best forecasted on the basis of simulated strategies from the LSST Operations Simulator (OpSim). This paper describes the way in which OpSim simulates a stochastic realization of the sequence of LSST pointings over the survey duration, and is based on a model of the observatory (including telescope) and historical data of observational conditions. OpSim outputs contain a record of each simulated pointing of the survey along with a complete characterization of the pointing in terms of observing conditions, and some useful quantities derived from the characteristics of the pointing. Thus, each record can be efficiently used to derive the properties of observations of all astrophysical sources found in that pointing. However, in order to obtain the time series of observations (light curves) of a set of sources, it is often more convenient to compute all observations of an astrophysical source, and iterate over sources. In this document, we describe the open source python package OpSimSummary, which allows for a convenient reordering. The objectives of this package are to provide users with an Application Programming Interface for accessing all such observations and summarizing this information in the form of intermediate data products usable by third party software such as SNANA, thereby also bridging the gap between official LSST products and preexisting simulation codes.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Mixed stochastic-deterministic time-dependent density functional theory: application to stopping power of warm dense carbon

Warm dense matter (WDM) describes an intermediate phase, between condensed matter and classical plasmas, found in natural and man-made systems. In a laboratory setting, WDM is often created dynamically. It is typically laser or pulse-power generated and can be difficult to characterize experimentally. Measuring the energy loss of high energy ions, caused by a WDM target, is both a promising diagnostic and of fundamental importance to inertial confinement fusion research. However, electron coupling, degeneracy, and quantum effects limit the accuracy of easily calculable kinetic models for stopping power, while high temperatures make the traditional tools of condensed matter, e.g. time-dependent density functional theory (TD-DFT), often intractable. In this study, we have developed a mixed stochastic-deterministic approach to TD-DFT which provides more efficient computation while maintaining the required precision for model discrimination. Recently, this approach showed significant improvement compared to models when compared to experimental energy loss measurements in WDM carbon. Here, we describe this approach and demonstrate its application to warm dense carbon stopping across a range of projectile velocities. We compare direct stopping-power calculation to approaches based on combining homogeneous electron gas response with bound electrons, with parameters extracted from our TD-DFT calculations.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

A Novel use of Direct Simulation Monte-Carlo to Model Dynamics of COVID-19 Pandemic Spread

In this report, we evaluate a novel method for modeling the spread of COVID-19 pandemic. In this new approach we leverage methods and algorithms developed for fully-kinetic plasma physics simulations using Particle-In-Cell (PIC) Direct Simulation Monte-Carlo (DSMC) models. This approach then leverages Sandia-unique simulation capabilities, and High-Performance Computer (HPC) resources and expertise in particle-particle interactions using stochastic processes. Our hypothesis is that this approach would provide a more efficient platform with assumptions based on physical data that would then enable the user to assess the impact of mitigation strategies and forecast different phases of infection. This work addresses key scientific questions related to the assumptions this new approach must make to model the interactions of people using algorithms typically used for modeling particle interactions in physics codes (kinetic plasma, gas dynamics). The model developed uses rational/physical inputs while also providing critical insight; the results could serve as inputs to, or alternatives for, existing models. The model work presented was developed over a four-week time frame, thus far showing promising results and many ways in which this model/approach could be improved. This work is aimed at providing a proof-of-concept for this new pandemic modeling approach, which could have an immediate impact on the COVID-19 pandemic modeling, while laying a basis to model future pandemic scenarios in a manner that is timely and efficient. Additionally, this new approach provides new visualization tools to help epidemiologists comprehend and articulate the spread of this and other pandemics as well as a more general tool to determine key parameters needed in order to better predict pandemic modeling in the future. In the report we describe our model for pandemic modeling, apply this model to COVID-19 data for New York City (NYC), assess model sensitivities to different inputs and parameters and , finally, propagate the model forward under different conditions to assess the effects of mitigation and associated timing. Finally, our approach will help understand the role of asymptomatic cases, and could be extended to elucidate the role of recovered individuals in the second round of the infection, which is currently being ignored.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2020

Stochastic Analysis for Long Term Capital Structures, Systems, and Components Refurbishment and Replacement

As commercial Nuclear Power Plants (NPPs) pursue extended plant operation in the form of Second License Renewal (SLR), opportunities exist for these plants to provide capital investments to ensure long-term safe and economic performance. At the current time, several utilities have announced an intention to pursue extended operation for one or more of their NPPs via SLR . The goal of this research is to develop a risk-informed approach to evaluate and prioritize plant capital investments made in preparation for, and during the period of, extended plant operations to support decisions for NPP operations. Since the capital investments are influenced by various factors, such as markets, safety and regulatory, the decision-making process of NPP operations should take into account relevant factors for balancing risks, costs and profits. The traditional method of capital budgeting is based on the priority list of candidate projects using economic measures such as benefit-investment ratio, net present value (NPV) and internal rate of return. In the literatures, the problem of capital budgeting or the variant can be represented by an appropriate knapsack problem. The knapsack approach to capital budgeting takes as input as investment, along with the cost and profit of each project. The objective of capital budgeting is to find the combination of the binary decisions for every investment such that the overall profit is as large as possible. The output is a collection of projects to be carried out, and we refer this selected collection of projects as a project portfolio. One limitation of traditional optimization models for capital budgeting is that they do not account for risk/uncertainty in profit and cost streams associated with individual projects, they do not account for risk in resource availability in future years [1,2,3]. Projects can incur cost over-runs, especially when projects are large, performed infrequently, and when there is risk regarding technical viability, external contractors, and/or suppliers of requisite parts and materials. Occasionally, projects are performed ahead of schedule and with cost savings. Planned budgets for capital improvements can be cut and key personnel may be lost. Or, there may be surprise windfalls in budgets for maintenance activities due to decreased costs for “unplanned” maintenance. In these cases, how should we resolve capital budgeting when we have risk forecasts for costs, profits and budgets? One approach we proposed in this summary is to re-solve the optimization models based on assumed statistical distributions of given parameters. If these distributions were not available, a two-stage stochastic optimization approach can be used to provide priority lists to decision-makers to support better risk-informed decisions [4, 5]. In this summary, we will only focus on the first approach.

42 ENGINEERING↗
DOE OSTI2022

Exponential Escape Rate of Filamentary Incubation in Mott Spiking Neurons

Mott materials such as vanadium oxides, when subject to a strong applied voltage, present an inhomogeneous insulator-to-metal transition with formation of metallic filaments within the insulating bulk. This property is enabling the development of compact and power-efficient neuromorphic devices known as Mott neurons. However, the nature of the transition has not been fully understood yet, as it may be attributed to different effects, including Joule self-heating and hot-carrier injection. Moreover, the experimental determination of the threshold voltage needed to induce the transition has proven to be challenging, as the transition becomes increasingly unpredictable when the threshold is approached. The physical understanding of these issues would not only deepen our understanding of Mott insulators, but would also be an important step toward the realization of neuromorphic devices based on such materials. In this work we use numerical simulations based on the Mott resistor network model to study the nature of the filament incubation and formation process. Here, we show that both electronic and thermal effects, in the form of current density focusing and Joule self-heating, respectively, contribute to the filamentary incubation and growth. Remarkably, we find that the percolation of the metallic filaments near the threshold is intrinsically stochastic, qualitatively similar to the familiar Arrhenius activated behavior and to the stochastic firing of biological neurons. More precisely, we characterize the filament percolation as a Poisson point process, which has the same probability distribution as mathematical models of neuronal firing with an exponential escape rate. Finally, we support the numerical simulation results by performing experiments in VO 2 that are in agreement with the exponential escape rate behavior. Thus, we establish a functionality of Mott insulators that opens a path toward implementing neuromorphic hardware with quantum materials.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

A modular methodology for time-domain stochastic seismic wave propagation

Presented here is a modular methodology for time-domain stochastic seismic wave propagation analysis. Presented methodology is designed to analyse uncertain seismic motions as an input, propagating through uncertain material. Traditional approach for uncertain wave propagation relies on models that include deep bedrock, local soil site, and their random process and random field information. Such models can become quite large and computationally intractable. The modular approach proposed herein features two step approach that allows separate consideration of the deep bedrock and local site along with corresponding random field information. In this work, the first step considers an auxiliary stochastic motions problem in the bedrock. Stochastic local site response can then be simulated in a reduced domain within certain depth from the surface. Application of uncertain seismic motions at depth, for local uncertain site response is done using stochastic effective forces developed through the Domain Reduction Method. By using Hermite polynomial chaos expansion to represent the non-Gaussian random field of material parameters and non-stationary random process of seismic motion, the proposed modular methodology is formulated using intrusive stochastic Galerkin approach, as seen in the Stochastic Elastic–Plastic Finite Element Method (SEPFEM). Developed modular methodology is illustrated using a 1-D stochastic seismic wave propagation analysis with three cases, and simulation results are also verified with results from conventional approach.

58 GEOSCIENCES↗
DOE OSTI2024

Stochastic reconstruction of fracture network pattern using spatial point processes

Fracture spatial patterns can strongly affect fluid flow in the subsurface. Proximity and distribution of fractures control reservoir flow behavior over various length scales. In many studies, however, simplified geometrical patterns are generated for fractures which may lead to unrealistic subsurface models. Here we introduce a new method for characterization and modeling of fracture spatial patterns based on outcrop observations. We use Ripley's K-function to characterize the arrangement of fracture barycenters and intersection points over various length scales. In addition, we use semivariograms to quantify spatial correlation in fracture intensity maps. Using this information, we develop a stochastic algorithm that generates two-dimensional fracture network realizations with spatial properties similar to those of a real fracture network measured in the field. Numerical simulation models indicate that the generated fracture realizations exhibit similar flow behaviors as that of the original fracture network. Furthermore, such modeling tools expand and improve our capability in building representative fracture models and in quantification of uncertainty in naturally and hydraulically fractured reservoirs.

58 GEOSCIENCES↗
DOE OSTI2022

Learning generative neural networks with physics knowledge

Deep generative neural networks have enabled modeling complex distributions, but incorporating physics knowledge into the neural networks is still challenging and is at the core of current physics-based machine learning research. To this end, we propose a physics generative neural network (PhysGNN), a new class of generative neural networks for learning unknown distributions in a physical system described by partial differential equations (PDE). PhysGNN couples PDE systems with generative neural networks. It is a fully differentiable model that allows back-propagation of gradients through both numerical PDE solvers and generative neural networks, and is trained by minimizing the discrete Wasserstein distance between generated and observed probability distributions of the PDE outputs using the stochastic gradient descent method. Moreover, PhysGNN does not require adversarial training like standard generative neural networks, which offers better stability than adversarial training. We show that PhysGNN can learn complex distributions in stochastic inverse problems, where conventional methods such as maximum likelihood estimation and momentum matching methods may be inapplicable when little knowledge is known about the form of unknown distributions or the physical model is too complex. Furthermore, our method allows physics-based generative neural network training for learning complex distributions in the context of differential equations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

COMPUTATIONAL MODELING OF IGNITION AND PREMIXED FLAME PROPAGATION INITIATED BY A PRE-CHAMBER TURBULENT JET

Addressing the pressing need for reduced carbon emissions, Turbulent Jet Ignition (TJI) emerges as a promising technology for ultra-lean combustion, offering enhanced thermal efficiencies and minimized cyclic variability in spark-ignited engines. To facilitate rapid testing and integration of this technology, a robust computational modeling framework is crucial. This study delves into the predictive capabilities of computational models for main-chamber ignition and premixed flame propagation using a single-cycle TJI rig measured by Biswas et al. (Applied Thermal Engineering, vol 106, 2016). Employing an open-source compressible flow simulation solver with Large Eddy Simulation (LES) for turbulence modeling, the investigation integrates the conventional Laminar Finite Rate Chemistry (LFRC) model alongside the transported Probability Density Method (PDF) for turbulence-chemistry interaction. A fully-consistent Eulerian Monte-Carlo Fields (EMCF) method is utilized to approximate the transported PDF, while Interaction by Exchange with Mean is employed to close micro-mixing terms in stochastic differential equations. A reduced chemical reaction mechanism with 21 species and 84 reactions (DRM-19) is used for solving chemical kinetics, and a double Gaussian energy deposition model is used to approximate the spark ignition in the pre-chamber. An unstructured O-grid mesh with 0.3 million cells in the prechamber and 1 million cells in the main chamber is employed. Results are divided into two phases: pre-chamber initialization and full TJI simulations. Validation of the predicted pre-chamber flame propagation and the lean ignition in the main-chamber is carried out by using available experimental data. Under quiescent conditions, both the LFRC and transported PDF methods largely underestimate the flame speed and subsequent pressure growth in the pre-chamber. A linear momentum forcing technique is applied to investigate the impact of initial turbulence in the pre-chamber, demonstrating a notable influence on flame propagation. Fine-tuning of the forcing coefficient reproduces the sudden pressure growth observed in the experiment. The experimentally validated pre-chamber simulation serves as the initial condition for the full TJI simulations. It is found that the LFRC model fails to predict lean-ignition in the main-chamber, resulting in a misfiring event. Incorporation of turbulence-chemistry interaction using the transported PDF method substantially improves the prediction of the ignition event in the main-chamber, achieving fair qualitative agreement and quantitative validation of combustion parameters within ±10% of the reported experimental data. The rich simulation results consisting of a full set of statistical description of the thermo-chemical states enable us to gain deep insights into the ignition mechanisms in the main chamber, which is limited when done experimentally. A novel dual ignition phenomenon is revealed in the TJI rig for the first time. Initially, a primary ignition kernel is formed at a downstream location which eventually detaches from the main jet. As the jet momentum decreases, a secondary ignition event follows, this time at a more upstream location which eventually combines with the primary ignition kernel to form a single connected flame front. Investigation of these ignition sequences in chemical composition space reveal distinct differences between the two. The primary ignition event in the main-chamber is followed by a large concentration of active radicals from the pre-chamber jet, accelerating the chain-branching steps, characterizing what has been referred to as flame ignition. In contrast, the secondary ignition occurs in the absence of active radicals in the pre-chamber jet, hence characterized as jet ignition. Further analysis of the effect of pre-chamber jet characteristics on lean ignition in the main-chamber is conducted by setting up cases with different initial pressure ratios (por) between the two chambers, a non-dimensional parameter, ranging from 1.2 to 3.2. As the initial pressure ratio increases, jet momentum increases, with dual ignition observed in cases above por= 2.2. Case with por= 3.2 lead to misfiring. The effect of ignition sequence on global combustion characteristics of TJI is analyzed. Dual ignition events lead to non-monotonicity in combustion characteristics such as global reaction progress variable, flame penetration, and global heat release rate. In dual ignition events, although the rate of fuel consumption and global heat release rate is initially lower, the secondary ignition leads to a sudden increase in flame surface area, resulting in a sudden jump and promoting the overall performance of the TJI system.

42 ENGINEERING↗
DOE OSTI2023

Surrogate Model Based Optimization for Finding Robust Deep Learning Model Architectures

Deep Learning (DL) models are increasingly used throughout the sciences. However, their performance and usefulness depend greatly on their architecture which is defined by hyperparameters such as the number of nodes, layers, the learning rate, etc. Tuning these hyperparameters is time-consuming because evaluating their performance requires a lengthy training step. Stochastic optimizers used in training lead to performance variability and potentially prediction reliability issues. In this talk, we will describe an automated optimization method based on surrogate models and active learning strategies for tuning DL model architectures. We take into account the prediction variability with the goal to identify architectures that make reliable and robust predictions. We demonstrate our developments on an application arising in particle physics.

deep learning↗
DOE OSTI2021

Transport in Stochastic Media with Random Chord Length Distributions

Thermal radiation transport computations in binary Markovian random mixtures rely almost exclusively on the Levermore-Pomraning (LP) model which is obtained by applying a heuristic closure to the ensemble averaged random medium transport equation. The validity of this model has been extensively tested by comparing numerical results over a broad parameter range (material types and mixing parameters) against benchmark solutions in planar geometry. The conditions under which the LP-model provides useful results and when it breaks down are now well established, but work to date has been largely restricted to homogeneous mixing statistics, i.e., the mean chord lengths of both materials are taken to be spatially constant. In recent work, this limitation was relaxed by allowing the mean chord lengths and, in a consistent fashion, the volume fractions in the LP-model to vary spatially and in a follow-up investigation benchmark solutions were obtained by ensemble averaging results over material realizations sampled from a nonhomogeneous Poisson process (NHPP). Numerical experiments in rod geometry with specifically linear and quadratic spatial dependence of chord lengths showed that the material averaged radiation intensities vary nonmonotonically with depth into the medium, in stark contrast to solutions obtained assuming uniform chord lengths. Moreover, depending on the local optical thickness and strength of scattering, the LP-model results showed locally more nuanced deviations from the benchmark solutions than was the case with constant chord lengths. These limited numerical investigations highlight the nontrivial qualitative and quantitative consequences of nonhomogeneous mixing statistics, in particular that closure approximations may not be uniformly valid or invalid over the problem domain.

42 ENGINEERING↗
DOE OSTI2022

Moving the needle: Employing deep reinforcement learning to push the boundaries of coarse-grained vaccine models

Highly mutable infectious disease pathogens (hm-IDPs) such as HIV and influenza evolve faster than the human immune system can contain them, allowing them to circumvent traditional vaccination approaches and causing over one million deaths annually. Agent-based models can be used to simulate the complex interactions that occur between immune cells and hm-IDP-like proteins (antigens) during affinity maturation—the process by which antibodies evolve. Compared to existing experimental approaches, agent-based models offer a safe, low-cost, and rapid route to study the immune response to vaccines spanning a wide range of design variables. However, the highly stochastic nature of affinity maturation and vast sequence space of hm-IDPs render brute force searches intractable for exploring all pertinent vaccine design variables and the subset of immunization protocols encompassed therein. To address this challenge, we employed deep reinforcement learning to drive a recently developed agent-based model of affinity maturation to focus sampling on immunization protocols with greater potential to improve the chosen metrics of protection, namely the broadly neutralizing antibody (bnAb) titers or fraction of bnAbs produced. Using this approach, we were able to coarse-grain a wide range of vaccine design variables and explore the relevant design space. Our work offers new testable insights into how vaccines should be formulated to maximize protective immune responses to hm-IDPs and how they can be minimally tailored to account for major sources of heterogeneity in human immune responses and various socioeconomic factors. Our results indicate that the first 3 to 5 immunizations, depending on the metric of protection, should be specially tailored to achieve a robust protective immune response, but that beyond this point further immunizations require only subtle changes in formulation to sustain a durable bnAb response.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2022

Stochastic and a posteriori optimization to mitigate coil manufacturing errors in stellarator design

Abstract It was recently shown in Wechsung et al (2022 Proc. Natl Acad. Sci. USA 119 e2202084119) that there exist electromagnetic coils that generate magnetic fields, which are excellent approximations to quasi-symmetric fields and have very good particle confinement properties. Using a Gaussian process-based model for coil perturbations, we investigate the impact of manufacturing errors on the performance of these coils. We show that even fairly small errors result in noticeable performance degradation. While stochastic optimization yields minor improvements, it is not possible to mitigate these errors significantly. As an alternative to stochastic optimization, we then formulate a new optimization problem for computing optimal adjustments of the coil positions and currents without changing the shapes of the coil. These a-posteriori adjustments are able to reduce the impact of coil errors by an order of magnitude, providing a new perspective for dealing with manufacturing tolerances in stellarator design.

Physics↗
DOE OSTI2021

Evaluating Gaussian process metamodels and sequential designs for noisy level set estimation

Abstract We consider the problem of learning the level set for which a noisy black-box function exceeds a given threshold. To efficiently reconstruct the level set, we investigate Gaussian process (GP) metamodels. Our focus is on strongly stochastic simulators, in particular with heavy-tailed simulation noise and low signal-to-noise ratio. To guard against noise misspecification, we assess the performance of three variants: (i) GPs with Student- t observations; (ii) Student- t processes (TPs); and (iii) classification GPs modeling the sign of the response. In conjunction with these metamodels, we analyze several acquisition functions for guiding the sequential experimental designs, extending existing stepwise uncertainty reduction criteria to the stochastic contour-finding context. This also motivates our development of (approximate) updating formulas to efficiently compute such acquisition functions. Our schemes are benchmarked by using a variety of synthetic experiments in 1–6 dimensions. We also consider an application of level set estimation for determining the optimal exercise policy of Bermudan options in finance.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Blinking statistics and molecular counting in direct stochastic reconstruction microscopy (dSTORM)

Abstract Motivation Many recent advancements in single-molecule localization microscopy exploit the stochastic photoswitching of fluorophores to reveal complex cellular structures beyond the classical diffraction limit. However, this same stochasticity makes counting the number of molecules to high precision extremely challenging, preventing key insight into the cellular structures and processes under observation. Results Modelling the photoswitching behaviour of a fluorophore as an unobserved continuous time Markov process transitioning between a single fluorescent and multiple dark states, and fully mitigating for missed blinks and false positives, we present a method for computing the exact probability distribution for the number of observed localizations from a single photoswitching fluorophore. This is then extended to provide the probability distribution for the number of localizations in a direct stochastic optical reconstruction microscopy experiment involving an arbitrary number of molecules. We demonstrate that when training data are available to estimate photoswitching rates, the unknown number of molecules can be accurately recovered from the posterior mode of the number of molecules given the number of localizations. Finally, we demonstrate the method on experimental data by quantifying the number of adapter protein linker for activation of T cells on the cell surface of the T-cell immunological synapse. Availability and implementation Software and data available at https://github.com/lp1611/mol_count_dstorm. Supplementary information Supplementary data are available at Bioinformatics online.

Patel, Lekha↗