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Results for “Stochastic process”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 361 records · Page 20
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Quantification of microtubule stutters: dynamic instability behaviors that are strongly associated with catastrophe

Microtubules (MTs) are cytoskeletal fibers that undergo dynamic instability (DI), a remarkable process involving phases of growth and shortening separated by stochastic transitions called catastrophe and rescue. Dissecting DI mechanism(s) requires first characterizing and quantifying these dynamics, a subjective process that often ignores complexity in MT behavior. We present a Statistical Tool for Automated Dynamic Instability Analysis (STADIA) that identifies and quantifies not only growth and shortening, but also a category of intermediate behaviors that we term “stutters.” During stutters, the rate of MT length change tends to be smaller in magnitude than during typical growth or shortening phases. Quantifying stutters and other behaviors with STADIA demonstrates that stutters precede most catastrophes in our in vitro experiments and dimer-scale MT simulations, suggesting that stutters are mechanistically involved in catastrophes. Related to this idea, we show that the anticatastrophe factor CLASP2γ works by promoting the return of stuttering MTs to growth. STADIA enables more comprehensive and data-driven analysis of MT dynamics compared with previous methods. The treatment of stutters as distinct and quantifiable DI behaviors provides new opportunities for analyzing mechanisms of MT dynamics and their regulation by binding proteins.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2021

An explicitly solvable energy-conserving algorithm for pitch-angle scattering in magnetized plasmas

In this work, we develop an Explicitly Solvable Energy-Conserving (ESEC) algorithm for the Stochastic Differential Equation (SDE) describing the pitch-angle scattering process in magnetized plasmas. The Cayley transform is used to calculate both the deterministic gyromotion and stochastic scattering, affording the algorithm to be explicitly solvable and exactly energy conserving. An unusual property of the SDE for pitch-angle scattering is that its coefficients diverge at the zero velocity and do not satisfy the global Lipschitz condition. Consequently, when standard numerical methods, such as the Euler-Maruyama (EM), are applied, numerical convergence is difficult to establish. For the proposed ESEC algorithm, its energy-preserving property enables us to overcome this obstacle. We rigorously prove that the ESEC algorithm is order 1/2 strongly convergent. This result is confirmed by detailed numerical studies. For the case of pitch-angle scattering in a magnetized plasma with a constant magnetic field, the numerical solution is benchmarked against the analytical solution, and excellent agreements are found.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
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 OSTI2021

Modular supply chain optimization considering demand uncertainty to manage risk

Supply chain under demand uncertainty has been a challenging problem due to increased competition and market volatility in modern markets. Flexibility in planning decisions makes modular manufacturing a promising way to address this problem. We report the problem of multiperiod process and supply chain network design is considered under demand uncertainty. A mixed integer two-stage stochastic programming problem is formulated with integer variables indicating the process design and continuous variables to represent the material flow in the supply chain. The problem is solved using a rolling horizon approach. Benders decomposition is used to reduce the computational complexity of the optimization problem. To promote risk-averse decisions, a downside risk measure is incorporated in the model. The results demonstrate the several advantages of modular designs in meeting product demands. A pareto-optimal curve for minimizing the objectives of expected cost and downside risk is obtained.

42 ENGINEERING↗
DOE OSTI2023

Social network structure and the spread of complex contagions from a population genetics perspective

Ideas, behaviors, and opinions spread through social networks. If the probability of spreading to a new individual is a non-linear function of the fraction of the individuals’ affected neighbors, such a spreading process becomes a “complex contagion”. This non-linearity does not typically appear with physically spreading infections, but instead can emerge when the concept that is spreading is subject to game theoretical considerations (e.g. for choices of strategy or behavior) or psychological effects such as social reinforcement and other forms of peer influence (e.g. for ideas, preferences, or opinions). Here we study how the stochastic dynamics of such complex contagions are affected by the underlying network structure. Motivated by simulations of complex contagions on real social networks, we present a framework for analyzing the statistics of contagions with arbitrary non-linear adoption probabilities based on the mathematical tools of population genetics. The central idea is to use an effective lower-dimensional diffusion process to approximate the statistics of the contagion. This leads to a tradeoff between the effects of ”selection” (microscopic tendencies for an idea to spread or die out), random drift, and network structure. Our framework illustrates intuitively several key properties of complex contagions: stronger community structure and network sparsity can significantly enhance the spread, while broad degree distributions dampen the effect of selection compared to random drift. Finally, we show that some structural features can exhibit critical values that demarcate regimes where global contagions become possible for networks of arbitrary size. Our results draw parallels between the competition of genes in a population and memes in a world of minds and ideas. Our tools provide insight into the spread of information, behaviors, and ideas via social influence, and highlight the role of macroscopic network structure in determining their fate.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2022

Understanding the Drivers of Atlantic Multidecadal Variability using a Stochastic Model Hierarchy

The relative importance of ocean and atmospheric dynamics in generating Atlantic Multidecadal Variability (AMV) remains an open question. Comparisons between climate models with SLAB and fully-dynamic (FULL) ocean components are often used to explore this question, but cannot reveal how individual ocean processes generate these differences. We build a hierarchy of physically interpretable stochastic models to investigate the contribution of two upper-ocean processes to AMV: the role of seasonal variation and mixed-layer entrainment. This interpretability arises from the stochastic model’s simplified representation of sea surface temperature (SST), considering only the local upper ocean response to white-noise atmospheric forcing and its impact on surface heat exchange. We focus on understanding differences between SLAB and FULL non-eddy resolving pre-industrial control simulations of the Community Earth System Model 1 (CESM), and estimate the stochastic model parameters from each respective simulation. Despite its simplicity, the stochastic model reproduces temporal characteristics of SST variability in the SPG, including reemergence, seasonal-to-interannual persistence and power spectra. Furthermore, unrealistically persistent SST of the CESM-SLAB ocean simulation is reproduced in the equivalent stochastic model configuration where the mixed-layer depth (MLD) is constant. The stochastic model also reveals that vertical entrainment primarily damps SST variability, thus explaining why SLAB exhibits larger SST variance than FULL. Here, the stochastic model driven by temporally stochastic, spatially coherent forcing patterns reproduces the canonical AMV pattern. However, the amplitude of low-frequency variability remains underestimated, suggesting a role for ocean dynamics beyond entrainment.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Storage ring nonlinear dynamics optimization with multi-objective multi-generation Gaussian process optimizer

Nonlinear beam dynamics optimization is essential in a low emittance storage ring design. Multi-objective optimization algorithms are needed in order to simultaneously optimize the dynamic aperture and the momentum aperture. In this study we demonstrate the application of a highly efficient stochastic optimization algorithm, the multi-generation Gaussian process optimizer (MG-GPO), to storage ring nonlinear dynamics optimization by successfully applying the method to the SPEAR3 upgrade lattice. It is shown that the new method, owing to its capability of selecting high rank candidates from a large number of trial solutions, converges significantly faster than the commonly used traditional algorithms, multi-objective genetic algorithms (MOGA) and particle swarm optimization (PSO).

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2020

TurboRVB: A many-body toolkit for ab initio electronic simulations by quantum Monte Carlo

TurboRVB is a computational package for ab initio Quantum Monte Carlo (QMC) simulations of both molecular and bulk electronic systems. The code implements two types of well established QMC algorithms: Variational Monte Carlo (VMC) and diffusion Monte Carlo in its robust and efficient lattice regularized variant. A key feature of the code is the possibility of using strongly correlated many-body wave functions (WFs), capable of describing several materials with very high accuracy, even when standard mean-field approaches [e.g., density functional theory (DFT)] fail. The electronic WF is obtained by applying a Jastrow factor, which takes into account dynamical correlations, to the most general mean-field ground state, written either as an antisymmetrized geminal power with spin-singlet pairing or as a Pfaffian, including both singlet and triplet correlations. This WF can be viewed as an efficient implementation of the so-called resonating valence bond (RVB) Ansatz, first proposed by Pauling and Anderson in quantum chemistry [L. Pauling, The Nature of the Chemical Bond (Cornell University Press, 1960)] and condensed matter physics [P.W. Anderson, Mat. Res. Bull 8, 153 (1973)], respectively. The RVB Ansatz implemented in TurboRVB has a large variational freedom, including the Jastrow correlated Slater determinant as its simplest, but nontrivial case. Moreover, it has the remarkable advantage of remaining with an affordable computational cost, proportional to the one spent for the evaluation of a single Slater determinant. Therefore, its application to large systems is computationally feasible. The WF is expanded in a localized basis set. Several basis set functions are implemented, such as Gaussian, Slater, and mixed types, with no restriction on the choice of their contraction. The code implements the adjoint algorithmic differentiation that enables a very efficient evaluation of energy derivatives, comprising the ionic forces. Thus, one can perform structural optimizations and molecular dynamics in the canonical NVT ensemble at the VMC level. For the electronic part, a full WF optimization (Jastrow and antisymmetric parts together) is made possible, thanks to state-of-the-art stochastic algorithms for energy minimization. In the optimization procedure, the first guess can be obtained at the mean-field level by a built-in DFT driver. The code was efficiently parallelized by using a hybrid MPI-OpenMP protocol, which is also an ideal environment for exploiting the computational power of modern Graphics Processing Unit accelerators.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

On Transfer Learning Of Neural Networks Using Bi-Fidelity Data For Uncertainty Propagation

Due to their high degree of expressiveness, neural networks have recently been used as surrogate models for mapping inputs of an engineering system to outputs of interest. Once trained, neural networks are computationally inexpensive to evaluate and remove the need for repeated evaluations of computationally expensive models in uncertainty quantification applications. However, given the highly parameterized construction of neural networks, especially deep neural networks, accurate training often requires large amounts of simulation data that may not be available in the case of computationally expensive systems. In this paper, to alleviate this issue for uncertainty propagation, we explore the application of transfer learning techniques using training data generated from both high- and low-fidelity models. We explore two strategies for coupling these two datasets during the training procedure, namely, the standard transfer learning and the bi-fidelity-weighted learning. In the former approach, a neural network model mapping the inputs to the outputs of interest is trained based on the low-fidelity data. The high-fidelity data are then used to adapt the parameters of the upper layer(s) of the low-fidelity network, or train a simpler neural network to map the output of the low-fidelity network to that of the high-fidelity model. In the latter approach, the entire low-fidelity network parameters are updated using data generated via a Gaussian process model trained with a small high-fidelity dataset. The parameter updates are performed via a variant of stochastic gradient descent with learning rates given by the Gaussian process model. Using three numerical examples, we illustrate the utility of these bi-fidelity transfer learning methods where we focus on accuracy improvement achieved by transfer learning over standard training approaches.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Nucleation-mediated reshaping of facetted metallic nanocrystals: Breakdown of the classical free energy picture

Shape stability is key to avoiding degradation of performance for metallic nanocrystals synthesized with facetted non-equilibrium shapes to optimize properties for catalysis, plasmonics, and so on. Reshaping of facetted nanocrystals is controlled by the surface diffusion-mediated nucleation and growth of new outer layers of atoms. Here, Kinetic Monte Carlo (KMC) simulation of a realistic stochastic atomistic-level model is applied to precisely track the reshaping of Pd octahedra and nanocubes. Unexpectedly, separate constrained equilibrium Monte Carlo analysis of the free energy profile during reshaping reveals a fundamental failure of the classical nucleation theory (CNT) prediction for the reshaping barrier and rate. Why? Nucleation barriers can be relatively low for these processes, so the system is not locally equilibrated before crossing the barrier, as assumed in CNT. This claim is supported by an analysis of a first-passage problem for reshaping within a master equation framework for the model that reasonably captures the behavior in KMC simulations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Fast and Universal Kohn-Sham Density Functional Theory Algorithm for Warm Dense Matter to Hot Dense Plasma

Understanding many processes, e.g., fusion experiments, planetary interiors, and dwarf stars, depends strongly on microscopic physics modeling of warm dense matter and hot dense plasma. This complex state of matter consists of a transient mixture of degenerate and nearly free electrons, molecules, and ions. This regime challenges both experiment and analytical modeling, necessitating predictive ab initio atomistic computation, typically based on quantum mechanical Kohn-Sham density functional theory (KS-DFT). However, cubic computational scaling with temperature and system size prohibits the use of DFT through much of the warm dense matter regime. A recently developed stochastic approach to KS-DFT can be used at high temperatures, with the exact same accuracy as the deterministic approach, but the stochastic error can converge slowly and it remains expensive for intermediate temperatures (< 50 eV). Here we have developed a universal mixed stochastic-deterministic algorithm for DFT at any temperature. This approach leverages the physics of KS-DFT to seamlessly integrate the best aspects of these different approaches. We demonstrate that this method significantly accelerated self-consistent field calculations for temperatures from 3 to 50 eV, while producing stable molecular dynamics and accurate diffusion coefficients.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2019

Quasi-Stochastic Approximation and Off-Policy Reinforcement Learning: Preprint

The Robbins-Monro stochastic approximation algorithm is a foundation of many algorithmic frameworks for reinforcement learning and often an efficient approach to solving (or approximating the solution to) complex optimal control problems. In many cases, however, practitioners are unable to apply these techniques because of an inherent high variance. This paper aims to provide a general foundation for 'quasi-stochastic approximation,' in which all of the processes under consideration are deterministic, much like quasi-Monte Carlo for variance reduction in simulation. The variance reduction can be substantial, subject to tuning of pertinent parameters in the algorithm. This paper introduces a new coupling argument to establish the optimal rate of convergence provided the gain is sufficiently large. These results are established for linear models and tested also in nonideal settings. A major application of these general results is a new class of reinforcement learning algorithms for deterministic state space models. In this setting, the main contribution is a class of algorithms for approximating the value function for a given policy, using a different policy designed to introduce exploration.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2022

TOF-SIMS analysis of decoherence sources in superconducting qubits

Superconducting qubits have emerged as a potentially foundational platform technology for addressing complex computational problems deemed intractable with classical computing. Despite recent advances enabling multiqubit designs that exhibit coherence lifetimes on the order of hundreds of μs, material quality and interfacial structures continue to curb device performance. Two-level system defects in the thin superconducting film and adjacent dielectric regions introduce stochastic noise and dissipate electromagnetic energy at the cryogenic operating temperatures. In this study, we utilize time-of-flight secondary ion mass spectrometry to understand the role specific fabrication procedures play in introducing such dissipation mechanisms in these complex systems. We interrogated Nb thin films and transmon qubit structures fabricated through slight modifications in the processing and vacuum conditions. We find that when the Nb film is sputtered onto the Si substrate, oxide and silicide regions are generated at various interfaces. We also observe that impurity species, such as niobium hydrides and carbides, are incorporated within the niobium layer during the subsequent lithographic patterning steps. The formation of these resistive compounds likely impacts the superconducting properties of the Nb thin film. Additionally, we observe the presence of halogen species distributed throughout the patterned thin films. We conclude by hypothesizing the source of such impurities in these structures in an effort to intelligently fabricate superconducting qubits and extend coherence times moving forward.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Probability Density Function Control of Frequency Fluctuations in Renewable-Rich Power Systems

The stochastic nature of renewable energy sources (RESs) necessitates treating power system frequency response as a random process with a nonstationary probability density function (PDF). Here, based upon the stochastic distribution control theory originated by the second author, this paper proposes a novel stochastic controller to improve the frequency PDF in power grids when integrating a large amount of RESs, thereby minimizing the effects of uncertainties and enhancing overall system stability. The key idea is to manipulate the controllable power generation resources so that the frequency PDF is make to follow a target PDF by using the stochastic distribution control theory originated by the second author. The proposed method can easily be plugged into existing automatic generation controls for multi-area transmission grids. The proposed method is validated via a modified Kundar's two area system and 240-bus Western Electricity Coordinating Council systems. The simulation results show that the proposed control shapes the frequency PDF narrower and sharper, leading to a notable improvement toward minimizing the effects of randomness and uncertainty during grid operation.

frequency↗
DOE OSTI2021

Stochastically estimated covariance matrices for independent and cumulative fission yields in the ENDF/B-VIII.0 and JEFF-3.3 evaluations

A Monte-Carlo method for the generation of correlation and covariance matrices for independent and cumulative fission yields has been developed. The method uses a constrained Monte-Carlo resampling structure in order to vary evaluated fission yield libraries in a way that meets basic conservation principles. This results in the generation of correlation/covariance matrices with limited model bias and uncertainty; the matrices are primarily reflective of the evaluated fission yield uncertainties and correlations that arise from the evaluation process. This method has been applied to generate correlation and covariance matrices for all of the fissioning systems of the ENDF/B-VIII.0 and JEFF-3.3 evaluations, marking the first time such matrices have been generated for all of these systems. These covariance matrices have been published online for immediate public use. These correlation and covariance matrices can be used to improve uncertainty estimation in calculations of reactor antineutrino emission rates, decay heat problems, and nuclear forensics.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Manifold learning for coarse-graining atomistic simulations: Application to amorphous solids

In this work, we introduce a generalized machine learning framework to probabilistically parameterize upper-scale models in the form of nonlinear PDEs consistent with a continuum theory, based on coarse-grained atomistic simulation data of mechanical deformation and flow processes. The proposed framework utilizes a hypothesized coarse-graining methodology with manifold learning and surrogate-based optimization techniques. Coarse-grained high-dimensional data describing quantities of interest of the multiscale models are projected onto a nonlinear manifold whose geometric and topological structure is exploited for measuring behavioral discrepancies in the form of manifold distances. A surrogate model is constructed using Gaussian process regression to identify a mapping between stochastic parameters and distances. Derivative-free optimization is employed to adaptively identify a unique set of parameters of the upper-scale model capable of rapidly reproducing the system's behavior while maintaining consistency with coarse-grained atomic-level simulations. The proposed method is applied to learn the parameters of the shear transformation zone (STZ) theory of plasticity that describes plastic deformation in amorphous solids as well as coarse-graining parameters needed to translate between atomistic and continuum representations. We show that the methodology is able to successfully link coarse-grained microscale simulations to macroscale observables and achieve a high-level of parity between the models across scales.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Revealing melt flow instabilities in laser powder bed fusion additive manufacturing of aluminum alloy via in-situ high-speed X-ray imaging

Laser metal additive manufacturing technologies enable the fabrication of geometrically and compositionally complex parts unachievable by conventional manufacturing methods. However, the certification and qualification of additively manufactured parts are greatly hindered by the stochastic melt flow instabilities intrinsic to the process, which has not been explicitly revealed by direct observation. Here, we report the mechanisms of the melt flow instabilities in laser powder bed fusion additive manufacturing process revealed by in-situ high-speed high-resolution synchrotron X-ray imaging. Here we identified powder/droplet impact, significant keyhole oscillation, and melting-mode switching as three major mechanisms for causing melt flow instabilities. We demonstrated the detrimental consequences of these instabilities brought to the process, and presented new understanding on the melt flow evolution and keyhole oscillation. This work provides critical insights into process instabilities during laser metal additive manufacturing, which may guide the development of instability mitigation approaches. The results reported here are also important for the development and validation of high-fidelity computational models.

36 MATERIALS SCIENCE↗