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Final report on research activities carried out by the PI (Michele Benzi) with his PhD student Massimilano Lupo Pasini and other collaborators under the grant.
This article introduces a validation study of the stochastic particle-resolved aerosol model PartMC with experimental data from an aerosol chamber experiment. For the experiment, a scanning mobility particle sizer and a single-particle soot photometer were used to monitor the aerosol mixing state evolution of two initially externally-mixed aerosol populations of ammonium sulfate and black carbon particles undergoing agglomeration. We applied an efficient optimization algorithm (ProSRS) to determine several unconstrained simulation parameters and were able to successfully reproduce number concentrations and size distributions of mixed particles that formed by agglomeration. The PartMC modeling method in conjunction with the optimization procedure provides a tool for detailed comparisons of chamber experiments and modeling, where aerosol mixing state is the focus of investigation.
The Mathematics and Computation Division of the American Nuclear (ANS) and the Idaho Section of the ANS hosted the 2013 International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering (M and C 2013). This proceedings contains over 250 full papers with topics ranging from reactor physics; radiation transport; materials science; nuclear fuels; core performance and optimization; reactor systems and safety; fluid dynamics; medical applications; analytical and numerical methods; algorithms for advanced architectures; and validation verification, and uncertainty quantification.
A main science goal for the Large Synoptic Survey Telescope (LSST) is to measure the cosmic shear signal from weak lensing to extreme accuracy. One difficulty, however, is that with the short exposure time ({approx_equal}15 seconds) proposed, the spatial variation of the Point Spread Function (PSF) shapes may be dominated by the atmosphere, in addition to optics errors. While optics errors mainly cause the PSF to vary on angular scales similar or larger than a single CCD sensor, the atmosphere generates stochastic structures on a wide range of angular scales. It thus becomes a challenge to infer the multi-scale, complex atmospheric PSF patterns by interpolating the sparsely sampled stars in the field. In this paper we present a new method, psfent, for interpolating the PSF shape parameters, based on reconstructing underlying shape parameter maps with a multi-scale maximum entropy algorithm. We demonstrate, using images from the LSST Photon Simulator, the performance of our approach relative to a 5th-order polynomial fit (representing the current standard) and a simple boxcar smoothing technique. Quantitatively, psfent predicts more accurate PSF models in all scenarios and the residual PSF errors are spatially less correlated. This improvement in PSF interpolation leads to a factor of 3.5 lower systematic errors in the shear power spectrum on scales smaller than {approx} 13, compared to polynomial fitting. We estimate that with psfent and for stellar densities greater than {approx_equal}1/arcmin{sup 2}, the spurious shear correlation from PSF interpolation, after combining a complete 10-year dataset from LSST, is lower than the corresponding statistical uncertainties on the cosmic shear power spectrum, even under a conservative scenario.
This paper first studies the estimated distributed PV hosting capacities of seventeen utility distribution feeders using the Monte Carlo simulation based stochastic analysis, and then analyzes the sensitivity of PV hosting capacity to both feeder and photovoltaic system characteristics. Furthermore, an active distribution network management approach is proposed to maximize PV hosting capacity by optimally switching capacitors, adjusting voltage regulator taps, managing controllable branch switches and controlling smart PV inverters. The approach is formulated as a mixed-integer nonlinear optimization problem and a genetic algorithm is developed to obtain the solution. Multiple simulation cases are studied and the effectiveness of the proposed approach on increasing PV hosting capacity is demonstrated.
Here, this work presents an efficient approach for accelerating multilevel Markov Chain Monte Carlo (MCMC) sampling for large-scale problems using low-fidelity machine learning models. While conventional techniques for large-scale Bayesian inference often substitute computationally expensive high-fidelity models with machine learning models, thereby introducing approximation errors, our approach offers a computationally efficient alternative by augmenting high-fidelity models with low-fidelity ones within a hierarchical framework. The multilevel approach utilizes the low-fidelity machine learning model (MLM) for inexpensive evaluation of proposed samples thereby improving the acceptance of samples by the high-fidelity model. The hierarchy in our multilevel algorithm is derived from geometric multigrid hierarchy. We utilize an MLM to accelerate the coarse level sampling. Training machine learning model for the coarsest level significantly reduces the computational cost associated with generating training data and training the model. We present an MCMC algorithm to accelerate the coarsest level sampling using MLM and account for the approximation error introduced. We provide theoretical proofs of detailed balance and demonstrate that our multilevel approach constitutes a consistent MCMC algorithm. Additionally, we derive the expression for cost reduction due to machine learning model to facilitate cost analysis of the hierarchical sampling algorithm. Our technique is demonstrated on a standard benchmark inference problem in groundwater flow, where we estimate the probability density of a quantity of interest using a four-level MCMC algorithm. Our proposed algorithm accelerates multilevel sampling by a factor of two while achieving similar accuracy compared to sampling using the standard multilevel algorithm.
The growing necessity for environmentally benign hybrid propulsion systems has led to the development of advanced power management control algorithms to maximize fuel economy and minimize pollutant emissions. This paper surveys the control algorithms for hybrid electric vehicles (HEVs) and plug-in HEVs (PHEVs) that have been reported in the literature to date. The exposition ranges from parallel, series, and power split HEVs and PHEVs and includes a classification of the algorithms in terms of their implementation and the chronological order of their appearance. Remaining challenges and potential future research directions are also discussed.
Generating automated cyber resilience policies for real-world settings is a challenging research problem that must account for uncertainties in system state over time and dynamics between attackers and defenders. In addition to understanding attacker and defender motives and tools, and identifying “relevant” system and attack data, it is also critical to develop rigorous mathematical formulations representing the defender’s decision-support problem under uncertainty. Game-theoretic approaches involving cyber resource allocation optimization with Markov decision processes (MDP) have been previously proposed in the literature. Moreover, advancements in reinforcement learning approaches have motivated the development of partially observable stochastic games (POSGs) in various multi-agent problem domains with partial information. Recent advances in cyber-system state space modeling have also generated interest in potential applicability of POSGs for cybersecurity. However, as is the case in strategic card games such as poker, research challenges using game-theoretic approaches for practical cyber defense applications include: 1) solving for equilibrium and designing efficient algorithms for large-scale, general problems; 2) establishing mathematical guarantees that equilibrium exists; 3) handling possible existence of multiple equilibria; and 4) exploitation of opponent weaknesses. Inspired by advances in solving strategic card games while acknowledging practical challenges associated with the use of game-theoretic approaches in cyber settings, this paper proposes an agent-centric approach for cybersecurity decision-support with partial system state observability.
Artificial intelligence (AI) is rapidly changing the world, from completely controlling routine or mundane tasks like text and image generation, to powering advanced algorithms that control critical systems. The recent advances in generative AI quickly overwhelmed multiple industries from education to finance as first adopters rushed (and continue to rush) to take advantage of the technology. The expanding AI ecosystem presents novel risks and ethical challenges that must be handled to ensure that technology is leveraged fairly and ethically. There are intertwined risks and ethical challenges stemming from the stochastic nature of AI (i.e., intrinsic risks), as well as from specific applications (i.e., extrinsic risks). Appropriately regulating AI requires a systems-approach to develop an integrated solution to these dependent challenges. Thus far, however, questions of risk, ethics and regulation appear to occupy separate spaces. This paper reviews the risks and ethical implications of AI and proposes a system-level approach to integrating ethics and regulation for the nascent industry.
An algorithm is developed for simulation of the motion and reactions of single molecules at a microscopic level. The molecules diffuse in a solvent and react with each other or a polymer and molecules can dissociate. Such simulations are of interest e.g. in molecular biology. The algorithm is similar to the Green's function reaction dynamics (GFRD) algorithm by van Zon and ten Wolde where longer time steps can be taken by computing the probability density functions (PDFs) and then sample from the distribution functions. Our computation of the PDFs is much less complicated than GFRD and more flexible. The solution of the partial differential equation for the PDF is split into two steps to simplify the calculations. The sampling is without splitting error in two of the coordinate directions for a pair of molecules and a molecule-polymer interaction and is approximate in the third direction. The PDF is obtained either from an analytical solution or a numerical discretization. The errors due to the operator splitting, the partitioning of the system, and the numerical approximations are analyzed. The method is applied to three different systems involving up to four reactions. Comparisons with other mesoscopic and macroscopic models show excellent agreement.
The explosive growth in data collection and the need to process it efficiently, as well as the desire to automate increasingly complex tasks in transportation, medical care, manufacturing, security and many other fields have motivated a growing interest in neuromorphic computing. Unlike the binary, transistorbased ON/OFF logic gates and separate logic and memory functionalities employed in digital computing, neuromorphic computing is inspired by animal brains that use interconnected synapses and neurons to perform processing, storage and transmission of information at the same location, while only consuming ~20 W or less of power. Motivated by the brain’s efficiency, adaptability, self-learning and resiliency qualities, neuromorphic computing can be broadly defined as an approach to processing and storing information using hardware and algorithms inspired by models of biological neural systems. Present research in neuromorphic computing encompasses approaches that vary significantly in their degree of neuro-inspiration, from systems that only incorporate features such as asynchronous, event-driven operation or use crossbar arrays of non-volatile memory (NVM) elements to accelerate deep neural networks (DNNs), to designs that embrace the extreme parallelism, sparsity, reconfigurability, adaptability, complexity and stochasticity observed in nervous systems. The term ‘neuromorphic’ computing is often credited to Carver Mead, who in the 1980s investigated Si-based analog electronics to replicate functions of the animal retina. Earlier important advances in this field include the work of Frank Rosenblatt, who proposed the concept of the perceptron, Bernard Widrow, who used this concept to build one of the first analog neural networks, the Adaline and many other researchers (see ref. 6 for an historical perspective on neuromorphic computing). With the recent increase in the use of artificial intelligence and large language models, and rising concerns over the associated energy costs, interest in neuromorphic hardware has expanded rapidly. According to some estimates, driven largely by the drastic growth in the training use of artificial intelligence (AI) models using the current computing architectures, the energy cost of computing is projected to reach the energy supply worldwide by 2045. Furthermore, while this is not a realistic outcome, it means that, if more efficient computing technologies are not developed -- soon -- the world will soon become one where demand for energy and market constraints limit the continued increase of societal access to AI and cloud services from data centers. Data centers used for training and use of these models consume hundreds of terawatt hours of electricity, already past 4% of the US electricity demand.
Nowadays, by integrating the cloud radio access network (C-RAN) with the mobile edge cloud computing (MEC) technology, mobile service provider (MSP) can efficiently handle the increasing mobile traffic and enhance the capabilities of mobile devices. But the power consumption has become skyrocketing for MSP and it gravely affects the profit of MSP. Previous work often studied the power consumption in C-RAN and MEC separately while less work had considered the integration of C-RAN with MEC. In this paper, we present an unifying framework for the power-performance tradeoff of MSP by jointly scheduling network resources in C-RAN and computation resources in MEC to maximize the profit of MSP. To achieve this objective, we formulate the resource scheduling issue as a stochastic problem and design a new optimization framework by using an extended Lyapunov technique. Specially, because the standard Lyapunov technique critically assumes that job requests have fixed lengths and can be finished within each decision making interval, it is not suitable for the dynamic situation where the mobile job requests have variable lengths. To solve this problem, we extend the standard Lyapunov technique and design the VariedLen algorithm to make online decisions in consecutive time for job requests with variable lengths. Furthermore, our proposed algorithm can reach time average profit that is close to the optimum with a diminishing gap (1/V) for the MSP while still maintaining strong system stability and low congestion. With extensive simulations based on a real world trace, we demonstrate the efficacy and optimality of our proposed algorithm.
This paper proposes a decentralized energy management system (EMS) for the coordinated operation of networked Microgirds (MGs) in a distribution system. In the grid-connected mode, the distribution network operator (DNO) and each MG are considered as distinct entities with individual objectives to minimize their own operation costs. It is assumed that both dispatchable and renewable energy source (RES)-based distributed generators (DGs) exist in the distribution network and the networked MGs. In order to coordinate the operation of all entities, we apply a decentralized bi-level algorithm to solve the problem with the first level to conduct negotiations among all entities and the second level to update the non-converging penalties. In the islanded mode, the objective of each MG is to maintain a reliable power supply to its customers. In order to take into account the uncertainties of DG outputs and load consumption, we formulate the problems as two-stage stochastic programs. The first stage is to determine base generation setpoints based on the forecasts and the second stage is to adjust the generation outputs based on the realized scenarios. Case studies of a distribution system with networked MGs demonstrate the effectiveness of the proposed methodology in both grid-connected and islanded modes.
In the design of ocean wave energy converters, proper control design is essential to the maximization of the power generation performance for the device. However, in realistic applications, this control design must be undertaken in the presence of model uncertainty. This paper considers the use of robust control theory to optimize the nominal performance for a wave energy converter in stochastic waves, subject to the constraint that the controller be stability-robust to unstructured uncertainties. We formulate the problem as a multi-objective optimal control problem, in which the primary objective is the maximization of power generation for the nominal system, and the competing objective is the norm of the uncertainty input/output channel. This optimal control problem is nonconvex, and we therefore propose an iterative algorithm that can be used to arrive at a local optimal solution. This iterative approach employs the concept of Iterative Convex Overbounding, in the context of the classical Method of Centers. Here, the methodology is demonstrated on a model of a single, buoy- type wave energy converter.
The existing fleet of U.S. nuclear power plants is in the process of extending its lifetime and increasing the power generated from these plants via power uprates. In order to evaluate the impact of these factors on the safety of the plant, the Risk-Informed Safety Margin Characterization (RISMC) project aims to provide insight to decision makers through a series of simulations of the plant dynamics for different initial conditions (e.g., probabilistic analysis and uncertainty quantification). This paper demonstrates how Idaho National Laboratory (INL) researchers use the RISMC Toolkit to investigate complex nuclear plant phenomena using RAVEN and RELAP-7. The analysis focused on a highly relevant topic currently facing some nuclear power plants – specifically flooding issues. This research and development looked at challenges to a hypothetical pressurized water reactor, including: (1) a potential loss of off-site power followed by the possible loss of all diesel generators (i.e., a station black-out event), (2) earthquake induced station-blackout, and (3) a potential earthquake induced tsunami flood. The analysis is performed by using a set of codes: a thermal-hydraulic code (RELAP-7), a flooding simulation tool (NEUTRINO) and a stochastic analysis tool (RAVEN) – these are currently under development at INL. Using RAVEN, we were able to perform multiple RELAP-7 simulation runs by changing specific parts of the model in order to reflect specific aspects of different scenarios, including both the failure and recovery of critical components. The simulation employed traditional statistical tools (such as Monte-Carlo sampling) and more advanced machine-learning based algorithms to perform uncertainty quantification in order to understand changes in system performance and limitations as a consequence of power uprate. Qualitative and quantitative results obtained gave a detailed picture of the issues associated with potential accident scenarios. These types of insights can provide useful material for decision makers to perform risk-informed margins management.
Here this short note presents a new method for stochastic reduced order (SROM) model based on BONUS reweighting scheme. An illustrative case study of IGCC power plant compares the new method with the neural network based reduced order model. The new method shows promising results.
An advection-diffusion-limited dissolution model of an object being eroded by a two-dimensional potential flow is presented. By taking advantage of the conformal invariance of the model, a numerical method is introduced that tracks the evolution of the object boundary in terms of a time-dependent Laurent series. Simulations of a variety of dissolving objects are shown, which shrink and collapse to a single point in finite time. The simulations reveal a surprising exact relationship, whereby the collapse point is the root of a non-Analytic function given in terms of the flow velocity and the Laurent series coefficients describing the initial shape. This result is subsequently derived using residue calculus. The structure of the non-Analytic function is examined for three different test cases, and a practical approach to determine the collapse point using a generalized Newton-Raphson root-finding algorithm is outlined. These examples also illustrate the possibility that the model breaks down in finite time prior to complete collapse, due to a topological singularity, as the dissolving boundary overlaps itself rather than breaking up into multiple domains (analogous to droplet pinch-off in fluid mechanics). In conclusion, the model raises fundamental mathematical questions about broken symmetries in finite-Time singularities of both continuous and stochastic dynamical systems.
The SAGUARO (Scalable Algorithms for Groundwater Uncertainty Analysis and Robust Optimization) Project focused on the development of scalable numerical algorithms for large-scale Bayesian inversion in complex systems that capitalize on advances in large-scale simulation-based optimization and inversion methods. The project was a collaborative effort among MIT, the University of Texas at Austin, Georgia Institute of Technology, and Sandia National Laboratories. The research was directed in three complementary areas: efficient approximations of the Hessian operator, reductions in complexity of forward simulations via stochastic spectral approximations and model reduction, and employing large-scale optimization concepts to accelerate sampling. The MIT₋Sandia component of the SAGUARO Project addressed the intractability of conventional sampling methods for large-scale statistical inverse problems by devising reduced-order models that are faithful to the full-order model over a wide range of parameter values; sampling then employs the reduced model rather than the full model, resulting in very large computational savings. Results indicate little effect on the computed posterior distribution. On the other hand, in the Texas₋Georgia Tech component of the project, we retain the full-order model, but exploit inverse problem structure (adjoint-based gradients and partial Hessian information of the parameter-to-observation map) to implicitly extract lower dimensional information on the posterior distribution; this greatly speeds up sampling methods, so that fewer sampling points are needed. We can think of these two approaches as "reduce then sample" and "sample then reduce." In fact, these two approaches are complementary, and can be used in conjunction with each other. Moreover, they both exploit deterministic inverse problem structure, in the form of adjoint-based gradient and Hessian information of the underlying parameter-to-observation map, to achieve their speedups.