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This poster presents an overview of high-frequency forecasting of solar radiation using a hybrid numerical weather prediction and stochastic downscaling model.
In modern science, computer models are often used to understand complex phenomena and a thriving statistical community has grown around analyzing them. This review aims to bring a spotlight to the growing prevalence of stochastic computer models-providing a catalogue of statistical methods for practitioners, an introductory view for statisticians (whether familiar with deterministic computer models or not), and an emphasis on open questions of relevance to practitioners and statisticians. Gaussian process surrogate models take center stage in this review, and these, along with several extensions needed for stochastic settings, are explained. The basic issues of designing a stochastic computer experiment and calibrating a stochastic computer model are prominent in the discussion. Instructive examples, with data and code, are used to describe the implementation of, and results from, various methods.
A Bayesian computational framework for parsimonious inference in stochastic nonlinear dynamical systems is presented. This framework enables the concurrent estimation of system states, time-varying parameters, time-invariant parameters, and the optimal sparsity structure of the model parameters. Because differential equation-based models are often simplified mechanistic or phenomenological representations, robust inference from noisy measurement data requires explicit treatment of model error and uncertainty. Model error and time-varying parameters can be represented as random processes, enabling inference while making minimal assumptions about the underlying sources of discrepancy and variability. Adopting stochastic differential equation representations affords the model significant flexibility, but can also render it susceptible to overfitting during statistical inversion, where the inferred model may track noise rather than the underlying signal. To alleviate the effects of overfitting and to enable the discovery of the optimal sparse representation of the time-invariant parameters, a Bayesian sparse learning algorithm is embedded within the framework. This sparse learning framework adopts an approximate hierarchical Bayesian setting defined by a series of semi-analytical expressions. The model structure inference framework is validated using a stochastic compartmental model for tracking and forecasting active cases of an infectious disease. Compartmental models describe population-level infectious disease dynamics through interactions among population fractions grouped by disease state. Mathematically, such models consist of a system of coupled ordinary differential equations. This example adopts an expressive compartmental model that includes multiple possible interactions between disease states, motivated by early uncertainty surrounding COVID-19 reinfection dynamics and their implications for long-term epidemic forecasting. The sparse learning exercise permits the inference of a priori unknown epidemiological dynamics from simulated public health data, discovering the nested compartmental model that optimizes the trade-off between average data-fit and model complexity. It is shown that inducing sparsity among the model parameters eliminates redundant interactions between compartments, equivalently revealing the optimal coupling structure between differential equations.
In an ongoing effort to improve 3D seismic-wave propagation modeling for frequencies up to 10 Hz, we used cross correlations between vertical-component waveforms from an underground chemical explosion to estimate the statistical properties of small-scale velocity heterogeneities. The waveforms were recorded by a dense 2D seismic array deployed during the Source Physics Experiments for event number 5 (SPE-5) in a series of six underground chemical explosions, conducted at the Nevada National Security Site. The array consisted of 996 geophones with a 50–100 m grid spacing, deployed at the SPE site at the north end of the Yucca Flat basin. The SPE were conducted to investigate the generation and propagation of seismic and acoustic waves from underground explosions. Comparisons of decay rates of waveform cross correlations as function of interstation distance, computed for observed and synthetic seismograms from the SPE-5 chemical explosion, were used to constrain statistical properties of correlated stochastic velocity perturbations representing small-scale heterogeneities added to a geology-based velocity model of the Yucca Flat basin. Using comparisons between recorded and simulated waveform cross correlations, we were able to recover sets of statistical properties of small-scale velocity perturbations in the velocity model that produce the best-fit between the recorded and simulated ground motion. The stochastic velocity fluctuations in the velocity model that produced the smallest misfits have a horizontal correlation distance of between 400 and 800 m, a vertical correlation distance between 100 and 200 m, and a standard deviation of 10% from the nominal model velocity in the alluvium basin layers. They also have a horizontal correlation distance of 1000 m, a vertical correlation distance of 250 m, and a standard deviation of 6% in the underlying and consolidated sedimentary layers, up to a depth of 4 km. Comparisons between observed and simulated wavefields were used to assess the proposed small-scale heterogeneity enhancements to the Yucca Flat basin model. We found that adding a depth-resolved stochastic variability to the geology-based velocity model improves the overall performance of ground-motion simulations of an SPE-5 explosion in the modeled frequency range up to 10 Hz. The results may be applicable to other similar basins.
KL extinction measurements are common in literature concerning soot producing sprays because of their nonintrusiveness. Unfortunately, these measurements often rely on bold assumptions of uniform and monodisperse spherical particles. In this work, a Spray A case is simulated using a highly detailed 3D stochastic soot model and the measured and simulated soot volume fraction are compared. Although the simulated volume fraction magnitude is approximately correct, features are much sharper than in the measured data. Optical models based on particle shape are applied to the simulated soot particles to nd the local optical thickness. The modeled optical thickness aligns with the measured volume fraction much more closely than the simulated volume fraction indicating KL extinction measurements are not simply related to soot volume fraction.
Traditional stochastic modeling of reactive systems limits the domain of applicability of the associated path thermodynamics to systems involving a single elementary reaction at the origin of each observed change in composition. An alternative stochastic modeling has recently been proposed to overcome this limitation. These two ways of modeling reactive systems are in principle incompatible. Here, the question thus arises about choosing the appropriate type of modeling to be used in practical situations. In the absence of sufficiently accurate experimental results, one way to address this issue is through the microscopic simulation of reactive fluids, usually based on hard-sphere dynamics in the Boltzmann limit. In this paper, we show that results obtained through such simulations unambiguously confirm the predictions of traditional stochastic modeling, invalidating a recently proposed alternative.
Variations of physical and chemical characteristics of biomass reduce equipment utilization and increase operational costs of biomass processing. Biomass processing facilities use sensors to monitor the changes in biomass characteristics. Integrating sensory data into the operational decisions in biomass processing will increase its flexibility to the changing biomass conditions. In this paper, we propose a multi-stage stochastic programming model that minimizes the expected operational costs by identifying the initial inventory level and creating an operational decision policy for equipment speed settings. These policies take the sensory information data and the current biomass inventory level as inputs to dynamically adjust inventory levels and equipment settings according to the changes in the biomass' characteristics. We ensure that a prescribed target reactor utilization is consistently achieved by penalizing the violation of the target reactor feeding rate. A case study is developed using real-world data collected at Idaho National Laboratory's biomass processing facility. We show the value of multi-stage stochastic programming from an extensive computational experiment. Our sensitivity analysis indicates that updating the infeed rate of the system, the processing speed of equipment, and bale sequencing based on the moisture level of biomass improves the processing rate of the reactor and reduces operating costs.
Wildfires represent a critical environmental hazard with multifaceted implications for ecosystems, communities, and public health [1]. The escalating frequency and intensity of wildfires globally have intensified the urgency for robust segmentation methodologies to facilitate effective mitigation, response, and recovery strategies [2]. Accurate wildfire segmentation is pivotal for delineating fire boundaries, assessing progression patterns, and prioritizing resource allocation during emergency scenarios. Furthermore, precise segmentation enables stakeholders, including policymakers, environmental scientists, and emergency responders, to formulate evidence-based strategies, thereby minimizing socio-economic disruptions and ecological degradation. Consequently, advancing wildfire segmentation techniques through innovative technological interventions remains a paramount research imperative. Although foundational in wildfire segmentation, traditional deterministic models exhibit inherent limitations that compromise their efficacy in dynamic and uncertain environments. These models often operate on rigid algorithms prioritizing deterministic classifications, thereby overlooking the inherent complexities and uncertainties associated with wildfire behavior and satellite data variability. Such deterministic frameworks tend to produce oversimplified representations that fail to capture the intricate nuances of evolving fire dynamics, spatial heterogeneity, and environmental interactions [1]. Consequently, the deterministic approach’s propensity for uncertainty collapsing [1, 3] hampers the accuracy, reliability, and applicability of segmentation outcomes in real-world scenarios. Contrastingly, stochastic models offer a more nuanced and adaptable framework for wildfire segmentation. By integrating probabilistic elements into the modeling paradigm, stochastic approaches, particularly probabilistic approaches such as variational auto encoders (VAEs) [4], facilitate comprehensive uncertainty assessment, enabling researchers to quantify and incorporate uncertainties into segmentation outcomes effectively. This probabilistic nature empowers stochastic models to encapsulate variability, account for data inconsistencies, and adapt to evolving environmental conditions, enhancing segmentation accuracy, reliability, and robustness. Embracing stochastic methodologies thus catalyzes advancements in wildfire science by fostering a more holistic, adaptive, and resilient segmentation framework. Despite VAEs demonstrating significant promise in various applications, they come with inherent limitations that have garnered attention within the machine learning community. One of the primary drawbacks lies in their reliance on static priors, which essentially assume a fixed distribution for latent variables, thereby limiting the model’s flexibility to capture complex data structures effectively [5]. This static nature leads to suboptimal representations, especially when dealing with complex and high-dimensional data. Additionally, VAEs often struggle with generating sharp and realistic samples, a phenomenon commonly referred to as mode collapse [5, 7, 6]. Furthermore, the optimization process in VAEs, which involves balancing the reconstruction loss and the regularization term, can sometimes be challenging to fine-tune [7]. In recent efforts to address these shortcomings, alternative approaches like Vector Quantized Variational Auto encoders(VQ-VAEs) [7], address the challenges by incorporating discrete latent variables and leveraging techniques that enhance the quality and diversity of generated samples while maintaining efficient training dynamics. VQ-VAEs propose a dynamic prior distribution generation mechanism that diverges from the static priors commonly associated with traditional VAEs. This dynamic approach allows for more adaptive and context-aware latent variable representations, thereby potentially capturing complex data structures more effectively. Unlike autoregressive prior models such as PixelCNN, which, despite their ability to model dependencies across data dimensions, suffer from significant computational inefficiencies and lack flexibility in handling diverse datasets. In our work, we propose to use a generative quantum-compatible approach to help alleviate the shortcomings of autoregressive prior model in VQ-VAEs. Restricted Boltzmann Machines (RBMs) are a viable alternative prior model that can learn prior distributions in a faster and more flexible manner. In this research endeavor, we meticulously curate a state-of-the-art dataset leveraging satellite MODIS data in conjunction with VIIRS fire masks, derived from Fire Radiative Power (FRP), thereby encapsulating diverse wildfire scenarios and environmental contexts. We developed a conditional VQ-VAE architecture with the RBM prior model that is trained in a supervised manner for segmenting wildfire masks. This innovative approach synergistically harnesses deep learning capabilities, enabling the generation of segmentation maps characterized by heightened precision, granularity, and contextual relevance. Furthermore, replacing the autoregressive prior learning method proposed by the original VQ-VAE with a prior density approximation via quantum-compatible RBM facilitates expedited inference processes, augments flexibility in prior sampling, optimizes computational efficiency and establishes a groundbreaking benchmark in wildfire segmentation methodologies.
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Abstract We thank the authors for this interesting paper that highlights important ideas and concepts for the future of climate model ensembles and their storage, as well as future uses of stochastic emulators. Stochastic emulators are particularly relevant because of the statistical nature of climate model ensembles, as discussed in previous work of the authors (Castruccio et al. in J Clim 32:8511–8522, 2019; Hu and Castruccio in J Clim 34:8409–8418, 2021). We thank the authors for sharing of some of their data with us in order to illustrate this discussion. In the following, in Sect. 1 we discuss alternative techniques currently used and studied, namely lossy compression and ideas emerging from the climate modeling community, that could feed the discussion on ensemble and storage. In that section, we also present numerical results of compression performed on the data shared by the authors. In Sect. 2, we discuss the current statistical model proposed by the authors and its context. We discuss other potential uses of stochastic emulators in climate and Earth modeling.
We report home energy management systems (HEMS) have been shown to reduce energy bills and to provide grid services including peak demand reduction and demand flexibility. However, uncertainty in residential energy systems is a significant issue and can reduce the benefits of a HEMS to the homeowner or grid operator. Sources of uncertainty include weather forecasts, predictions of energy-related occupant activities (e.g., hot water draws), and parameter estimation for the building envelope and energy-consuming equipment. This paper tackles the problem of uncertainty by developing a framework that simulates HEMS in uncertain conditions and evaluates the performance of multiple control strategies. A linear, reduced-order residential building model for model predictive control applications is derived and compared to a full-order model. Stochastic model predictive control is shown to perform better than deterministic and heuristic methods when considering realistic forecasts with uncertainty. The framework can evaluate the performance of HEMS in real-world applications, which can help de-risk HEMS deployment.
In this paper we focus on the parameter estimation of dynamic load models with stochastic terms-in particular, load models where protection settings are uncertain, such as in aggregated air conditioning units. We show how the uncertainty in the aggregated protection characteristics can be formulated as a stochastic differential equation with process noise. We cast the parameter inversion within a Bayesian parameter estimation framework, and we present methods to include process noise. We demonstrate the benefits of considering stochasticity in the parameter estimation and the risks of ignoring it.
Fiber reinforced composites are desirable in applications where low weight and high strength are needed, but are susceptible to variability and flaws during manufacturing, making failure predictions difficult. These flaws may occur at the microscale where mechanical properties vary locally due to regions of fiber clusters and matrix pockets. In this study, a multiscale approach was taken to model 3-point bend, 4-point bend, and tensile experiments of a unidirectional composite from only having microstructure scans of these samples and constituent properties from literature. These scans were sampled with different sized windows, and statistically equivalent microstructures were generated, then simulated for stiffness, strength, and fracture toughness using a reduced order micromechanical model and NASA’s Multiscale Analysis Tool (NASMAT). Mesoscale models were created with equivalent element sizes to microstructures and properties sampled from microscale simulation results. Results showed how microscale size affects certain mechanical properties. Also shown is how well mesoscale models agree to experiments when using stochastic element properties and varying element size.
Uncertainty quantification (UQ) plays a major role in verification and validation for computational engineering models and simulations, and establishes trust in the predictive capability of computational models. In the materials science and engineering context, where the process-structure-property-performance linkage is well known to be the only road mapping from manufacturing to engineering performance, numerous integrated computational materials engineering (ICME) models have been developed across a wide spectrum of length-scales and time-scales to relieve the burden of resource-intensive experiments. Within the structure-property linkage, crystal plasticity finite element method (CPFEM) models have been widely used since they are one of a few ICME toolboxes that allows numerical predictions, providing the bridge from microstructure to materials properties and performances. Several constitutive models have been proposed in the last few decades to capture the mechanics and plasticity behavior of materials. While some UQ studies have been performed, the robustness and uncertainty of these constitutive models have not been rigorously established. In this work, we apply a stochastic collocation (SC) method, which is mathematically rigorous and has been widely used in the field of UQ, to quantify the uncertainty of three most commonly used constitutive models in CPFEM, namely phenomenological models (with and without twinning), and dislocation-density-based constitutive models, for three different types of crystal structures, namely face-centered cubic (fcc) copper (Cu), body-centered cubic (bcc) tungsten (W), and hexagonal close packing (hcp) magnesium (Mg). Our numerical results not only quantify the uncertainty of these constitutive models in stress-strain curve, but also analyze the global sensitivity of the underlying constitutive parameters with respect to the initial yield behavior, which may be helpful for robust constitutive model calibration works in the future.
The stochastic theory of neutron transport is extended to describe the cumulative distribution of fission numbers and deposited fission energy in a multiplying assembly. Solutions for the probability distributions are obtained using analytical approximations and Monte Carlo simulation in lumped geometry and in symmetric homogeneous and heterogeneous spheres. The results show the development of a power-law tail in the steady state fission number and deposited energy distributions when the medium is critical, independent of the fission neutron multiplicity distribution and domain heterogeneity. In contrast, the asymptotic decay is faster than exponential in subcritical media due to rapid chain extinction and in supercritical media due to the increasing probability of chain divergence. Here, a formal asymptotic analysis of the problem in lumped geometry with an arbitrary fission neutron multiplicity confirms the existence of power-law tails at critical.
A new approach to validation of the Poisson stochastic radiative transfer method is proposed. In contrast to other validations of stochastic models, the main parameter of the Poisson model responsible for cloud geometrical structure - cloud aspect ratio - is determined entirely by matching measurements and calculations of the direct solar radiation. If the measurements of the direct solar radiation is unavailable, it was shown that there is a range of the aspect ratios that allows the stochastic model to accurately approximate the average measurements of surface downward and cloud top upward fluxes. Realizations of the fractionally integrated cascade model are taken as a prototype of real measurements.
This paper provides a coherent and efficient computational framework for stochastic multiscale analysis of material systems in the presence of parametric uncertainties and modeling errors. Uncertainty in those model parameters that are not deduced as upscaled quantities is attributed to an uncertainty “germ”. While such parameters can appear at any scale, they are predominant at the finest analysis scale. Additional uncertainties stemming from statistical estimation, attributed to lack of data and model error, are associated with each submodel contributing to the multiscale system. Here, a robust and efficient framework based on a generalized extended polynomial chaos expansion (gEPCE) is proposed to simultaneously propagate all these uncertainties in order to provide a probabilistic representation of specific quantities of interest (QoI). We characterize the full probability distribution of the QoI and the uncertainty in the failure probability pertaining to its tails. By combining gEPCE with kernel density estimation (KDE) and directional derivatives, we construct sensitivity measures that connect these statistical metrics of QoI to the various sources of uncertainty to assess their individual and combined impacts. An illustrative problem featuring three-point bending of a composite beam is investigated to demonstrate the presented approach.
The authors have developed a methodology for cost-effective fatigue design of structures subject to random fatigue loading. A stochastic model for fatigue crack propagation under random loading has been discussed. Fracture mechanics is then used to estimate the parameters of the model and the residual strength of structures with cracks. The stochastic model and residual strength variations have been used to develop procedures for estimating the probability of failure and its changes with inspection frequency. This information on reliability is then used to construct an objective function in terms of either a total weight function or cost function. A procedure for selecting the design variables, subject to constraints, by optimizing the objective function has been illustrated by examples. In particular, optimum design of stiffened panel has been discussed.