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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Stochastic noise can be helpful for variational quantum algorithms

Saddle points constitute a crucial challenge for first-order gradient descent algorithms. In notions of classical machine learning, they are avoided, for example, by means of stochastic gradient descent methods. In this work, we provide evidence that the saddle-points problem can be naturally avoided in variational quantum algorithms by exploiting the presence of stochasticity. We prove convergence guarantees and present practical examples in numerical simulations and on quantum hardware. We argue that the natural stochasticity of variational algorithms can be beneficial for avoiding strict saddle points, i.e., those saddle points with at least one negative Hessian eigenvalue. This insight that some levels of shot noise could help is expected to add a new perspective to notions of near-term variational quantum algorithms. Published by the American Physical Society 2025

Liu, Junyu↗
DOE OSTI2020

Classifying and analyzing small-angle scattering data using weighted k nearest neighbors machine learning techniques

A consistent challenge for both new and expert practitioners of small-angle scattering (SAS) lies in determining how to analyze the data, given the limited information content of said data and the large number of models that can be employed. Machine learning (ML) methods are powerful tools for classifying data that have found diverse applications in many fields of science. Here, ML methods are applied to the problem of classifying SAS data for the most appropriate model to use for data analysis. The approach employed is built around the method of weighted k nearest neighbors (wKNN), and utilizes a subset of the models implemented in the SasView package (https://www.sasview.org/) for generating a well defined set of training and testing data. The prediction rate of the wKNN method implemented here using a subset of SasView models is reasonably good for many of the models, but has difficulty with others, notably those based on spherical structures. A novel expansion of the wKNN method was also developed, which uses Gaussian processes to produce local surrogate models for the classification, and this significantly improves the classification accuracy. Further, by integrating a stochastic gradient descent method during post-processing, it is possible to leverage the local surrogate model both to classify the SAS data with high accuracy and to predict the structural parameters that best describe the data. The linking of data classification and model fitting has the potential to facilitate the translation of measured data into results for both novice and expert practitioners of SAS.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Parameter identification methods for low-order gray box building energy models: A critical review

The body of knowledge on gray box building energy modeling (GBBEM) has been developed over the past few decades and has undergone some important changes recently. Starting with simple methods and simple buildings, the science of GBBEM has grown to encompass complex and more computationally intensive techniques and complex commercial buildings. Numerous works including a recent review have considered model structure and inputs in a nearly systematic way, but no extant work systematically reviews the approaches for GBBEM parameter search initialization and final identification, despite this being arguably the most difficult and impactful part of the modeling process. To this end, we critically review 55 extant works describing advantages, limitations, and domain of applicability of several classes of parameter initialization and optimization techniques specifically for GBBEM. We categorize the classes of methods and analyze the evidence of their applicability for different applications within the field of GBBEM. We find an emerging consensus that initialization of parameter searches for anything other than the simplest building elements is often challenging and sometimes requires a stochastic approach to begin the parameter identification process. After this initial process, faster methods have been used in some cases but often the nature of the problem requires stochastic methods for this portion of the process as well. For less complex systems, more deterministic and efficient methods have been shown to be effective. Finally, we draw conclusions as to the domain of applicability of different classes of initialization and optimization techniques for GBBEEM and offer suggestions for research directions that are likely to prove fruitful.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2016

A deterministic alternative to the full configuration interaction quantum Monte Carlo method

Development of exponentially scaling methods has seen great progress in tackling larger systems than previously thought possible. One such approach, full configuration interaction quantum Monte Carlo, is a useful algorithm that allows exact diagonalization through stochastically sampling determinants. The method derives its utility from the information in the matrix elements of the Hamiltonian, along with a stochastic projected wave function, to find the important parts of Hilbert space. Yet, the stochastic representation of the wave function is not required to search Hilbert space efficiently, and here we describe a highly efficient deterministic method that can achieve chemical accuracy for a wide range of systems, including the difficult Cr 2 molecule. We demonstrate for systems like Cr 2 that such calculations can be performed in just a few cpu hours which makes it one of the most efficient and accurate methods that can attain chemical accuracy for strongly correlated systems. Furthermore, our method also allows efficient calculation of excited state energies, which we illustrate with benchmark results for the excited states of C 2 .

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS2001

Planning and Scheduling for Fleets of Earth Observing Satellites

We address the problem of scheduling observations for a collection of earth observing satellites. This scheduling task is a difficult optimization problem, potentially involving many satellites, hundreds of requests, constraints on when and how to service each request, and resources such as instruments, recording devices, transmitters, and ground stations. High-fidelity models are required to ensure the validity of schedules; at the same time, the size and complexity of the problem makes it unlikely that systematic optimization search methods will be able to solve them in a reasonable time. This paper presents a constraint-based approach to solving the Earth Observing Satellites (EOS) scheduling problem, and proposes a stochastic heuristic search method for solving it.

Frank, Jeremy↗
DOE OSTI2025

Neural chaos: A spectral stochastic neural operator

Building surrogate models for operators with uncertainty quantification capabilities is essential for many engineering applications where randomness–such as variability in material properties, boundary conditions, and initial conditions–is unavoidable. Polynomial Chaos Expansion (PCE) is widely recognized as a go-to method for constructing stochastic surrogates in both intrusive and non-intrusive ways, and it has recently been used in the context of operator learning. However, its application becomes challenging for complex or high-dimensional processes, as achieving accuracy requires higher-order polynomials, which can increase computational demand and/or the risk of overfitting. Furthermore, PCE requires specialized treatments to manage random variables that are not independent, and these treatments may be problem-dependent or may fail with increasing complexity. Here, in this work, we adopt the same formalism as the spectral expansion used in PCE; however, we replace the classical polynomial basis functions with neural network (NN) basis functions to leverage their expressivity. To achieve this, we propose an algorithm that identifies NN-parameterized basis functions in a purely data-driven manner, without any prior assumptions about the joint distribution of the random variables involved, whether independent or dependent, or about their marginal distributions. The proposed algorithm identifies each NN-parameterized basis function sequentially, ensuring they are orthogonal with respect to the data distribution. The basis functions are constructed directly on the joint stochastic variables without requiring a tensor product structure or assuming independence of the random variables. This approach may offer greater flexibility for complex stochastic models, while simplifying implementation compared to the tensor product structures typically used in PCE to handle random vectors. This is particularly advantageous given the current state of open-source packages, where building and training neural networks can be done with just a few lines of code and extensive community support. We demonstrate the effectiveness of the proposed scheme through several numerical examples of varying complexity and provide comparisons with classical PCE.

Polynomial chaos expansion↗
DOE OSTI2017

Deterministic direct aperture optimization using multiphase piecewise constant segmentation

Purpose Direct aperture optimization (DAO) attempts to incorporate machine constraints in the inverse optimization to eliminate the post‐processing steps in fluence map optimization (FMO) that degrade plan quality. Current commercial DAO methods utilize a stochastic or greedy approach to search a small aperture solution space. In this study, we propose a novel deterministic direct aperture optimization that integrates the segmentation of fluence map in the optimization problem using the multiphase piecewise constant Mumford‐Shah formulation. Methods The Mumford‐Shah based direct aperture optimization problem was formulated to include an L2‐norm dose fidelity term to penalize differences between the projected dose and the prescribed dose, an anisotropic total variation term to promote piecewise continuity in the fluence maps, and the multiphase piecewise constant Mumford‐Shah function to partition the fluence into pairwise discrete segments. A proximal‐class, first‐order primal‐dual solver was implemented to solve the large scale optimization problem, and an alternating module strategy was implemented to update fluence and delivery segments. Three patients of varying complexity—one glioblastoma multiforme (GBM) patient, one lung (LNG) patient, and one bilateral head and neck (H&N) patient with 3 PTVs—were selected to test the new DAO method. For each patient, 20 non‐coplanar beams were first selected using column generation, followed by the Mumford‐Shah based DAO (DAO MS ). For comparison, a popular and successful approach to DAO known as simulated annealing—a stochastic approach—was replicated. The simulated annealing DAO (DAO SA ) plans were then created using the same beam angles and maximum number of segments per beam. PTV coverage, PTV homogeneity , and OAR sparing were assessed for each plan. In addition, high dose spillage, defined as the 50% isodose volume divided by the tumor volume, as well as conformity, defined as the van't Riet conformation number, were evaluated. Results DAO MS achieved essentially the same OAR doses compared with the DAO SA plans for the GBM case. The average difference of OAR D max and D mean between the two plans were within 0.05% of the plan prescription dose. The lung case showed slightly improved critical structure sparing using the DAO MS approach, where the average OAR D max and D mean were reduced by 3.67% and 1.08%, respectively, of the prescription dose. The DAO MS plan substantially improved OAR dose sparing for the H&N patient, where the average OAR D max and D mean were reduced by over 10% of the prescription dose. The DAO MS and DAO SA plans were comparable for the GBM and LNG PTV coverage, while the DAO MS plan substantially improved the H&N PTV coverage, increasing D99 by 6.98% of the prescription dose. For the GBM and LNG patients, the DAO MS and DAO SA plans had comparable high dose spillage but slightly worse conformity with the DAO MS approach. For the H&N plan, DAO MS was considerably superior in high dose spillage and conformity to the DAO SA . The deterministic approach is able to solve the DAO problem substantially faster than the simulated annealing approach, with a 9.5‐ to 40‐fold decrease in total solve time, depending on the patient case. Conclusions A novel deterministic direct aperture optimization formulation was developed and evaluated. It combines fluence map optimization and the multiphase piecewise constant Mumford‐Shah segmentation into a unified framework, and the resulting optimization problem can be solved efficiently. Compared to the widely and commercially used simulated annealing DAO approach, it showed comparable dosimetry behavior for simple plans, and substantially improved OAR sparing, PTV coverage, PTV homogeneity, high dose spillage, and conformity for the more complex head and neck plan.

Nguyen, Dan↗
DOE OSTI2017

A robust bi-orthogonal/dynamically-orthogonal method using the covariance pseudo-inverse with application to stochastic flow problems

We develop a new robust methodology for the stochastic Navier–Stokes equations based on the dynamically-orthogonal (DO) and bi-orthogonal (BO) methods . Both approaches are variants of a generalized Karhunen–Loève (KL) expansion in which both the stochastic coefficients and the spatial basis evolve according to system dynamics, hence, capturing the low-dimensional structure of the solution. The DO and BO formulations are mathematically equivalent , but they exhibit computationally complimentary properties. Specifically, the BO formulation may fail due to crossing of the eigenvalues of the covariance matrix, while both BO and DO become unstable when there is a high condition number of the covariance matrix or zero eigenvalues. To this end, we combine the two methods into a robust hybrid framework and in addition we employ a pseudo-inverse technique to invert the covariance matrix. The robustness of the proposed method stems from addressing the following issues in the DO/BO formulation: (i) eigenvalue crossing: we resolve the issue of eigenvalue crossing in the BO formulation by switching to the DO near eigenvalue crossing using the equivalence theorem and switching back to BO when the distance between eigenvalues is larger than a threshold value; (ii) ill-conditioned covariance matrix: we utilize a pseudo-inverse strategy to invert the covariance matrix; (iii) adaptivity: we utilize an adaptive strategy to add/remove modes to resolve the covariance matrix up to a threshold value. In particular, we introduce a soft-threshold criterion to allow the system to adapt to the newly added/removed mode and therefore avoid repetitive and unnecessary mode addition/removal. When the total variance approaches zero, we show that the DO/BO formulation becomes equivalent to the evolution equation of the Optimally Time-Dependent modes . We demonstrate the capability of the proposed methodology with several numerical examples, namely (i) stochastic Burgers equation: we analyze the performance of the method in the presence of eigenvalue crossing and zero eigenvalues; (ii) stochastic Kovasznay flow: we examine the method in the presence of a singular covariance matrix; and (iii) we examine the adaptivity of the method for an incompressible flow over a cylinder where for large stochastic forcing thirteen DO/BO modes are active.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

SU-E-J-161: Inverse Problems for Optical Parameters in Laser Induced Thermal Therapy

Purpose: Magnetic resonance-guided laser-induced thermal therapy (MRgLITT) is investigated as a neurosurgical intervention for oncological applications throughout the body by active post market studies. Real-time MR temperature imaging is used to monitor ablative thermal delivery in the clinic. Additionally, brain MRgLITT could improve through effective planning for laser fiber's placement. Mathematical bioheat models have been extensively investigated but require reliable patient specific physical parameter data, e.g. optical parameters. This abstract applies an inverse problem algorithm to characterize optical parameter data obtained from previous MRgLITT interventions. Methods: The implemented inverse problem has three primary components: a parameter-space search algorithm, a physics model, and training data. First, the parameter-space search algorithm uses a gradient-based quasi-Newton method to optimize the effective optical attenuation coefficient, μ-eff. A parameter reduction reduces the amount of optical parameter-space the algorithm must search. Second, the physics model is a simplified bioheat model for homogeneous tissue where closed-form Green's functions represent the exact solution. Third, the training data was temperature imaging data from 23 MRgLITT oncological brain ablations (980 nm wavelength) from seven different patients. Results: To three significant figures, the descriptive statistics for μ-eff were 1470 m{sup −1} mean, 1360 m{sup −1} median, 369 m{sup −1} standard deviation, 933 m{sup −1} minimum and 2260 m{sup −1} maximum. The standard deviation normalized by the mean was 25.0%. The inverse problem took <30 minutes to optimize all 23 datasets. Conclusion: As expected, the inferred average is biased by underlying physics model. However, the standard deviation normalized by the mean is smaller than literature values and indicates an increased precision in the characterization of the optical parameters needed to plan MRgLITT procedures. This investigation demonstrates the potential for the optimization and validation of more sophisticated bioheat models that incorporate the uncertainty of the data into the predictions, e.g. stochastic finite element methods.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
NASA NTRS1989

Parallel and vector computation for stochastic optimal control applications

A general method for parallel and vector numerical solutions of stochastic dynamic programming problems is described for optimal control of general nonlinear, continuous time, multibody dynamical systems, perturbed by Poisson as well as Gaussian random white noise. Possible applications include lumped flight dynamics models for uncertain environments, such as large scale and background random atmospheric fluctuations. The numerical formulation is highly suitable for a vector multiprocessor or vectorizing supercomputer, and results exhibit high processor efficiency and numerical stability. Advanced computing techniques, data structures, and hardware help alleviate Bellman's curse of dimensionality in dynamic programming computations.

Hanson, F. B.↗
DOE OSTI2016

Kinetic Monte Carlo Simulation of Hydrogen Diffusion in Tungsten

Nuclear fusion is considered as the most promising sustainable energy source. If achieved, it could provide electricity to the mankind for millions of years. During the reaction, the fusion ash is continuously removed from the magnetic gap, the divertor region, and the divertor facing component is subjected to intense plasma bombardment. It is proposed to use tungsten as the divertor facing material, because it has low physical sputtering yield and superior thermomechanical properties. However, the high mobility of hydrogen in tungsten and the high bombardment flux bring the hydrogen isotopes deep into the tungsten tile. The presence of hydrogen in tungsten tends to weaken the gram boundaries and produce surface blistering. The ejection of tungsten particulates into the plasma core will cool the reaction and cease the fusion reactions. Therefore, it is important to have a detailed understanding of the hydrogen diffusion in tungsten bulk. The KMC method is a stochastic computer simulation to predict the time evolution of a certain system. Typically, at a given time, the system will evolve through a few possible paths with known probabilities. In each step, the KMC method analyzes the entire system and randomly determines the system evolving events based on all transition rates of all possible events and advance the physical time. This process is repeated till the simulation of the entire physical time is completed. In previous work, the authors developed a kinetic Monte Carlo (KMC) algorithm and program to simulate hydrogen diffusion process on tungsten reconstructed surface. In this article, this KMC method is extended to model the hydrogen diffusion in tungsten bulk. The diffusion coefficients are calculated and fitted to the Arrhenius equation. The result matches the experiment measurement very well. KMC diffusion simulation needs the locations of the hydrogen trapping sites, diffusion paths and the corresponding diffusion energy barriers. The hydrogen interstitial sites in tungsten crystal have been thoroughly studied by density function theory (DFT) and molecular dynamics (MD). Johnson and Carter used DFT to determine the preferred location of the hydrogen interstitial sites m tungsten crystal, which are the tetrahedral sites (T-sites) in body-centered-cubic (bcc) lattice surfaces. All T-sites are located on the surfaces of a lattice cell. There are four T-sites per surface and twelve T-sites per lattice cell. The hydrogen atoms diffuse by traveling from one T-site to one of its nearest four T-site neighbors. Thus, each T-site is surrounded by two neighbors on the same surface, and one neighbor on each of the two adjacent surfaces perpendicular to the surface holding the center T-site. The diffusion barrier between two neighboring T-sites was calculated to be 0.38 eV. Knowing the diffusion path, energy barrier, and the crystal structure, the KMC simulation is readily to be performed. Based on other researchers' DFT calculations, the hydrogen stable interstitial site in tungsten bulk is determined as the tetrahedral site on the surface of the bee lattice. Each T-site has 4 neighbors and the energy barrier between two adjacent T-sites are estimated to be 0.38 eV. Based on those facts and the KMC theory, a MATLAB program is developed to model the hydrogen diffusion in tungsten bulk. In the MATLAB program, substrate temperature, hydrogen concentration, physical time to be simulated, and the number of cycles are all customizable. To compare the KMC determined diffusion coefficients with experiment results in the literature, the simulations are performed for temperature 300 K - 2500 K and low hydrogen concentration (0.1%), mimicking the experiment condition. The calculated diffusion coefficients match the reference values measured by the experiment under low hydrogen concentration condition. The results are also fitted to the Arrhenius equation. The pre-exponential factor and the average activation energy in Arrhenius equation are obtained. The good agreement between simulation and experiment proves that the developed KMC algorithm truly reflect the well-established theory of interstitial hydrogens in tungsten. The developed program could easily be used to model the diffusion process and predict the diffusion coefficients under other concentrations and temperatures. This work is part of the ongoing development of hydrogen diffusion in tungsten integrating surface diffusion (previous work), bulk diffusion (this work), and adsorption/desorption on surface (future work)

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2015

Adaptive hybrid simulations for multiscale stochastic reaction networks

The probability distribution describing the state of a Stochastic Reaction Network (SRN) evolves according to the Chemical Master Equation (CME). It is common to estimate its solution using Monte Carlo methods such as the Stochastic Simulation Algorithm (SSA). In many cases, these simulations can take an impractical amount of computational time. Therefore, many methods have been developed that approximate sample paths of the underlying stochastic process and estimate the solution of the CME. A prominent class of these methods include hybrid methods that partition the set of species and the set of reactions into discrete and continuous subsets. Such a partition separates the dynamics into a discrete and a continuous part. Simulating such a stochastic process can be computationally much easier than simulating the exact discrete stochastic process with SSA. Moreover, the quasi-stationary assumption to approximate the dynamics of fast subnetworks can be applied for certain classes of networks. However, as the dynamics of a SRN evolves, these partitions may have to be adapted during the simulation. We develop a hybrid method that approximates the solution of a CME by automatically partitioning the reactions and species sets into discrete and continuous components and applying the quasi-stationary assumption on identifiable fast subnetworks. Our method does not require any user intervention and it adapts to exploit the changing timescale separation between reactions and/or changing magnitudes of copy-numbers of constituent species. We demonstrate the efficiency of the proposed method by considering examples from systems biology and showing that very good approximations to the exact probability distributions can be achieved in significantly less computational time. This is especially the case for systems with oscillatory dynamics, where the system dynamics change considerably throughout the time-period of interest.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Development and Application of a Risk Analysis Toolkit for Plant Resources Optimization

This report summarizes the R&D activities of the Risk Informed Asset Management (RIAM) project during fiscal year 2020 (FY20). This project focuses on the development of methods designed to optimize plant operations (e.g., maintenance/replacement schedule, optimal maintenance posture) provided system/component health/cost data. This project development lives in cooperation with the Plant Health Management (PHM) project which focuses on the development of methods that integrate component health data and propagate such information at the system level to evaluate most relevant sources of risk. This year’s activities for the RIAM project focused on the continuation of schedule optimization algorithms developed in FY19. While in FY19 we focused on both deterministic and stochastic capital budgeting methods, in FY20 we moved forward by implementing two versions of schedule optimization methods. The first one reformulates the capital budgeting problem in a distributionally robust form which allows the user to rely on data directly rather than proposing a distribution from the data itself. The second version reformulates the capital budgeting explicitly using risk measures as variables to maximize/minimize. Lastly, we focused on the development of methods designed to identify the optimal maintenance posture based on the Pareto Frontier analysis. Rather than performing a tradeoff analysis (i.e., identify the absolute best posture), the Pareto Frontier analysis performs a trade space exploration approach (i.e., identify value and costs of several postures and have the analyst perform the task of imposing desired value and cost constraints). This is performed by identifying maintenance postures that maximize value (e.g., system availability) and minimize operational costs, i.e., the Pareto frontier in a value-cost trade space.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Hybrid stochastic simulation of reaction-diffusion systems with slow and fast dynamics

In this paper, we present a novel hybrid method to simulate discrete stochastic reaction-diffusion models arising in biochemical signaling pathways. We study moderately stiff systems, for which we can partition each reaction or diffusion channel into either a slow or fast subset, based on its propensity. Numerical approaches missing this distinction are often limited with respect to computational run time or approximation quality. We design an approximate scheme that remedies these pitfalls by using a new blending strategy of the well-established inhomogeneous stochastic simulation algorithm and the tau-leaping simulation method. The advantages of our hybrid simulation algorithm are demonstrated on three benchmarking systems, with special focus on approximation accuracy and efficiency.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Communication: Fully coherent quantum state hopping

In this paper, we describe a new and fully coherent stochastic surface hopping method for simulating mixed quantum-classical systems. We illustrate the approach on the simple but unforgiving problem of quantum evolution of a two-state quantum system in the limit of unperturbed pure state dynamics and for dissipative evolution in the presence of both stationary and nonstationary random environments. We formulate our approach in the Liouville representation and describe the density matrix elements by ensembles of trajectories. Population dynamics are represented by stochastic surface hops for trajectories representing diagonal density matrix elements. These are combined with an unconventional coherent stochastic hopping algorithm for trajectories representing off-diagonal quantum coherences. The latter generalizes the binary (0,1) “probability” of a trajectory to be associated with a given state to allow integers that can be negative or greater than unity in magnitude. Unlike existing surface hopping methods, the dynamics of the ensembles are fully entangled, correctly capturing the coherent and nonlocal structure of quantum mechanics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗