Spiking Neural Algorithms for Markov Process Random Walk.
Abstract not provided.
Severa, William Mark↗
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Data and scripts associated with “Non-random processes impacting organic matter chemistry are maximized in mid-order streams”
NOTE: The manuscript associated with this data package is currently in review. The data may be revised based on reviewer feedback. Upon manuscript acceptance, this data package will be updated with the final dataset and additional metadata. This data package is associated with the publication “Non-random processes impacting organic matter chemistry are maximized in mid-order streams” submitted to Limnology and Oceanography (L&O) by Danczak et al. (in review). This package contains data and scripts used to investigate dissolved organic matter (DOM) molecular chemistry and diversification processes across 47 surface-water sampling sites in the Yakima River Basin, Washington, USA, during an August 2021 sampling campaign. The package contains analyses of ultrahigh-resolution Fourier transform ion cyclotron resonance mass spectrometry (FTICR-MS), geochemical measurements, geospatial attributes, molecular diversity, and meta-metabolome ecological null models needed to reproduce the main manuscript results. The underlying field data were pulled from exising data packages at https://doi.org/10.15485/1892052 (Fulton et al., 2022) and https://doi.org/10.15485/1898914 (Grieger et al., 2022). For details on how to navigate data packages generated by this project, see https://data.ess-dive.lbl.gov/portals/PNNLRiverCorridorSFA/About. We thank the following organizations for providing access to field locations for sample collection: the United States Forest Service, Washington Department of Fish and Wildlife, Washington Department of Natural Resources, the Confederated Tribes and Bands of the Yakama Nation, and the Cowiche Canyon Conservatory. Research was conducted under Washington State Parks and Recreation Commission Scientific Research Permit #210901. We are grateful to the Yakama Nation Tribal Council and Yakama Nation Fisheries for their collaboration in facilitating sample collection and ensuring data usage aligns with their values and worldview. This data package contains an R-Markdown file for analyses and five folders: (1) Data, (2) Geospatial Data, (3) Supplemental_Files, (5) Figures_pdf, (4) and src. The Data folder contains tabular inputs and derived files used in the manuscript analysis. The Geospatial Data folder contains climate and water-balance, hydrologic, land-cover, population/regional water-use, stream, topographic, and stream-order attribute CSV files. The src folder contains scripts used to process data, run analyses, and generate figures. The Figures_pdf folder contains manuscript figure outputs. The Supplemental_Files folder contains supplemental analysis products. All files are .csv, .pdf, .html, .png, .R, .Rmd, .svg, or .tre. This data package is associated with the rcfsa-RC2-SPS_Null_Modeling repository found at https://github.com/river-corridors-sfa/rcfsa-RC2-SPS_Null_Modeling.
54 ENVIRONMENTAL SCIENCES↗
Processing Random and Systematic Experimental Uncertainties in Replicate Tests of Stochastic Phenomena for Real-Space Model Validation.
Abstract not provided.
Romero, Vicente J.↗
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↗
UQpy: A general purpose Python package and development environment for uncertainty quantification
In this paper, we present the UQpy software toolbox, an open-source Python package for general uncertainty quantification (UQ) in mathematical and physical systems. The software serves as both a user-ready toolbox that includes many of the latest methods for UQ in computational modeling and a convenient development environment for Python programmers advancing the field of UQ. The paper presents an introduction to the software's architecture and existing capabilities, divided in the code in a set of modules centered around different UQ tasks such as sampling methods, generation of random processes and random fields, probabilistic inverse modeling, reliability analysis, surrogate modeling, and active learning. The paper also highlights the importance of the RunModel module, which is used to drive simulations in the uncertainty analyses performed in UQpy. This module conveniently allows the user to define computational models directly in Python, or to run simulations from a third-party software in serial or in parallel. To illustrate the various capabilities, two examples are tracked throughout the paper and analyzed repeatedly for various UQ tasks. The first is a Python model solving a nonlinear structural dynamics problem, used to illustrate UQpy's capabilities in sampling and forward propagation of high dimensional random vectors (stochastic processes), and probabilistic inference. The second model is a third-party Abaqus finite element model solving the thermomechanical response of a beam structure. This example is used to illustrate UQpy's capabilities in variance reduction sampling techniques, reliability analysis, surrogate modeling and active learning techniques.
97 MATHEMATICS AND COMPUTING↗
Stochastic Modeling in a Multimaterial Continuum Mixture Shock Physics Code
Stochastic modelling approaches are presented to capture random effects at multiple time and length scales. Random processes that occur at the microscale produce nondeterministic effects at the macroscale. Here we present three stochastic modeling approaches that describe random processes at microscopic length scales and map these processes to the macroscopic length scale. The first stochastic modeling approach is based upon a particle based numerical technique to solve a Stochastic Differential Equation (SDE) using an arbitrary diffusion process to capture random processes at the microstructural level. The second approach prescribes a Probability Density Function (PDF) for the drift and diffusion of the random variable derived using the forward and backward Kolmogorov equations. This method requires mean and drift evolution PDF transport equations. The third approach is the coupling of multiple random variables which are dependent on each other. The relationship of the PDFs and a coupling function, known as a copula, produces a Joint Probability Density Function (JPDF). These stochastic modeling approaches are implemented into a Multiple Component (MC) shock physics computational code and used to model statistical fracture and reactive flow applications.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Contact Processes with Random Recovery Rates and Edge Weights on Complete Graphs
In this paper we are concerned with the contact process with random recovery rates and edge weights on the complete graph with n vertices. We show that the model has a critical value which is inversely proportional to the product of the mean of the edge weight and the mean of the inverse of the recovery rate. In the subcritical case, the process dies out before an amount of time with order O(log n) with high probability as n→+∞. In the supercritical case, the process survives for an amount of time with order exp {O(n)} with high probability as n→+∞.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Experimental quantum Bernoulli factories via Bell-basis measurements
Randomness processing in the Bernoulli factory framework provides a concrete setting in which quantum resources can outperform classical ones. We experimentally demonstrate quantum randomness processing based on Bell-basis measurements of two identical input quoins prepared on IBM superconducting hardware. Using only the measurement outcomes (and no external classical randomness source), we realize the classically inconstructible Bernoulli doubling primitive f(p)=2p, and, as intermediate outputs from the same Bell-measurement statistics, an exact fair coin f(p)=1/2 and the classically inconstructible function f(p)=4p(1−p). We benchmark the measured output biases against ideal predictions and discuss the impact of device noise. Our results establish a simple resource-efficient experimental primitive for quantum-to-classical randomness processing and support the viability of quantum Bernoulli factories for quantum-enhanced stochastic simulation and sampling tasks.
Roy, Tanay [Fermilab] (ORCID:000000019442862X)↗
Time domain probabilistic seismic risk analysis using ground motion prediction equations of Fourier amplitude spectra
Modeling of Fourier amplitude spectra (FAS) of seismic motions has gained much attention in engineering seismology. In the past few years, several ground motion prediction equations (GMPEs) and inter-frequency correlation structure of FAS have been established. Due to many preferable characteristics of FAS, probabilistic seismic hazard/risk analysis is rapidly changing from ergodic, spectrum acceleration Sa(T 0 )-based approach to non-ergodic, site-specific, FAS-based approach. This paper presents time domain intrusive framework for probabilistic seismic risk analysis using GMPE of FAS. Herein, methodology for time domain stochastic ground motion modeling based on GMPEs of FAS is presented in some detail. The simulated uncertain motions are modeled as a random process and represented by polynomial chaos Karhunen-Loève expansion. The random process excitations are further propagated into the uncertain structural system using Galerkin stochastic finite element method (SFEM). Probabilistic evolution of structural response is solved, and such solution is used to develop seismic risk for any damage state. The presented framework is illustrated through seismic risk analysis of a four-story building subjected to possible earthquakes from two strike slip faults. The influences of the epistemic uncertainties in source stress drop Δσ and site attenuation κ0 on seismic risk are investigated. The need for non-ergodic seismic risk analysis with source-specific and site specific characterizations is emphasized.
58 GEOSCIENCES↗
Non-stationary Almost Sure Invariance Principle for Hyperbolic Systems with Singularities
We investigate a wide class of two-dimensional hyperbolic systems with singularities, and prove the almost sure invariance principle (ASIP) for the random process generated by sequences of dynamically Hölder observables. The observables could be unbounded, and the process may be non-stationary and need not have linearly growing variances. Our results apply to Anosov diffeomorphisms, Sinai dispersing billiards and their perturbations. The random processes under consideration are related to the fluctuation of Lyapunov exponents, the shrinking target problem, etc.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Solving inverse problems in stochastic models using deep neural networks and adversarial training
Inverse problems associated with stochastic models constitute a significant portion of scientific and engineering applications. In such cases the unknown quantities are distributions. The applicability of traditional methods is limited because of their demanding assumptions or prohibitive computational consumption; for example, maximum likelihood methods require closed-form density functions, and Markov Chain Monte Carlo needs a large number of simulations. We propose a new method that estimates the unknown distribution by matching the statistical properties between observed and simulated random processes. We leverage the expressive power of neural networks to approximate the unknown distribution and use a discriminative neural network for computing the statistical discrepancies between the observed and simulated random processes. Here we demonstrated numerically that the proposed methods can estimate both the model parameters and learn complicated unknown distributions.
42 ENGINEERING↗
Predicting initial trans-membrane pressure across cycles in the ultrafiltration process using random forest
With growing freshwater scarcity, direct potable reuse (DPR) systems that reclaim wastewater for drinking are becoming increasingly important for sustainable water supply. Reliable operation requires minimizing downtime in ultrafiltration (UF) units, where membrane fouling leads to elevated trans-membrane pressure (TMP). This study develops data-driven regression models based on random forest (RF) and autoregressive (AR) approaches to forecast the initial TMP at the start of each UF filtration cycle in a pilot-scale DPR system. The RF model consistently outperforms baseline methods, including historical mean, last observation carried forward, and AR models, across multiple forecast horizons, achieving the lowest root mean square error. To evaluate how different classes of process variables contribute to TMP dynamics over time, we examine the feature importance of independent input variables across multiple forecast horizons. This analysis provides insight into the temporal relevance of operational and sensor-derived features, guiding control and monitoring strategies. Additionally, the impact of hyperparameter tuning on TMP prediction performance is assessed for both direct and recursive RF modelling approaches. The proposed RF framework establishes a robust foundation for predictive monitoring and real-time optimization of UF operations, supporting sustainable and reliable water reuse.
direct potable reuse↗
Exponential Bound for the Heating Rate of Periodically Driven Spin Systems
For the nuclear spin system of a solid in the presence of an inhomogeneous magnetic field, we have found a rigorous bound for the heating rate of the system under the action of a high-frequency magnetic field, which is applied, for example, to create effective Hamiltonians. We consider the autocorrelation function (ACF) of a spin rotating in a local field whose fluctuations are specified by a Gaussian random process. The correlation function of a random field is taken as the sum of a static inhomogeneous contribution and a time-dependent contribution expressed self-consistently via the spin ACF. The ACF singularities on the imaginary time axis whose coordinates determine the exponents of exponential asymptotics in the high-frequency domain are investigated. The dependences of the coordinates on field inhomogeneity for various approximations have been derived. The wing of the ACF spectrum in the cumulant approximation is shown to serve as a rigorous upper bound for the wing of the ACF spectrum and, consequently, for the heating rate of the system when subjected to variable magnetic fields. We have established that randomly distributed inhomogeneous magnetic fields increase the wings of the ACF spectra and, thus, speed up the system’s heating.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Anscombe-type theorem and moderate deviations for trajectories of a compound renewal process
An Anscombe-type theorem for the large deviations principle for trajectories of a random process is proved. As a consequence, the moderate deviations principle for the compound renewal processes is obtained.
97 MATHEMATICS AND COMPUTING↗
Sensitivity Analysis in the Presence of Intrinsic Stochasticity for Discrete Fracture Network Simulations
Abstract Large‐scale discrete fracture network (DFN) simulators are standard fare for studies involving the sub‐surface transport of particles since direct observation of real world underground fracture networks is generally infeasible. While these simulators have successfully been used in several engineering applications, estimates of output quantities of interest (QoI) — such as breakthrough time of particles reaching the edge of the system — suffer from two distinct types of uncertainty. A run of a DFN simulator requires several parameters to be set that dictate the placement and size of fractures, the density of fractures, and the overall permeability of the system; uncertainty on the proper parameters will lead to uncertainty in the QoI, called epistemic uncertainty. Furthermore, since these input settings to DFN simulators control the stochastic processes which place fractures and govern flow, understanding how this randomness affects the QoI requires several runs of the simulator at distinct random seeds. The uncertainty in the QoI attributed to different realizations (i.e., different seeds) of the same random process (i.e., identical input parameters) leads to a second type of uncertainty, called aleatoric uncertainty. In this paper, we perform a Sensitivity Analysis, which directly attributes the uncertainty observed in the QoI to the epistemic uncertainty from each input parameter and to the aleatoric uncertainty. Beyond the specific takeaways on which input variables influence uncertainty in the QoI the most, a major contribution of this paper is the introduction of a statistically rigorous workflow for characterizing the uncertainty in DFN flow simulations that exhibit heteroskedasticity.
58 GEOSCIENCES↗
Vectorization techniques for probability distribution functions using VecCore
Probability distribution functions (PDFs) are very used in modeling random processes and physics simulations. Improving the performance of algorithms that generate many random numbers under complex PDFs is often a very challenging task when methods as direct functions are not available. In this work we present general strategies on how to vectorize some PDFs using VecCore library. We show the results for the Exponential, Gaussian, discrete Poisson and Gamma probability distributions.
Chaparro Amaro, Oscar R.↗
Random field optimization
Herein we present a new modeling paradigm for optimization that we call random field optimization. Random fields are a powerful modeling abstraction that aims to capture the behavior of random variables that live on infinite-dimensional spaces (e.g., space and time) such as stochastic processes (e.g., time series, Gaussian processes, and Markov processes), random matrices, and random spatial fields. This paradigm involves sophisticated mathematical objects (e.g., stochastic differential equations and space-time kernel functions) and has been widely used in neuroscience, geoscience, physics, civil engineering, and computer graphics. Despite of this, however, random fields have seen limited use in optimization; specifically, existing optimization paradigms that involve uncertainty (e.g., stochastic programming and robust optimization) mostly focus on the use of finite random variables. This trend is rapidly changing with the advent of statistical optimization (e.g., Bayesian optimization) and multi-scale optimization (e.g., integration of molecular sciences and process engineering). Our work extends a recently-proposed abstraction for infinite-dimensional optimization problems by capturing more general uncertainty representations. Moreover, we discuss solution paradigms for this new class of problems based on finite transformations and sampling, and identify open questions and challenges.
97 MATHEMATICS AND COMPUTING↗
SANS characterization of time dependent, slow molecular exchange in an SDS micellar system
Here, we have investigated the molecular exchange of sodium dodecyl sulfate (SDS) micelles in aqueous solution by time-resolved small angle neutron scattering (TR-SANS) measurements as a function of the surfactant and salt concentration. Starting with deuterated (d-SDS) and protonated (h-SDS) SDS micelles, surfactant exchange across the micelles leads to a randomized distribution of d-SDS and h-SDS within each micelle. By employing the contrast matching technique, we have studied this randomization process which is a direct measure of the molecular exchange of this system. Our results show that the randomization of the pure h-SDS and d-SDS micelles occurs in two steps: first, an almost instantaneous drop in the scattering intensity is observed where ~80% of the micelles are randomized (contrast matched). After this, micelle randomization progresses slowly spanning over ~100 hours. Importantly, we show that the kinetics in the second step are dominated by the formation of domains rich in either h-SDS, d-SDS and randomized (50 : 50 h-SDS : d-SDS). The slow exchange step is modeled via a phenomenological approach by drawing analogy to the Langmuir adsorption theory. Finally, the effects of the surfactant and salt concentrations on the instantaneous, and the time dependent randomization of SDS micelles are discussed.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗