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DOE OSTI2024

Evidential Deep Learning: Enhancing Predictive Uncertainty Estimation for Earth System Science Applications

Abstract Robust quantification of predictive uncertainty is a critical addition needed for machine learning applied to weather and climate problems to improve the understanding of what is driving prediction sensitivity. Ensembles of machine learning models provide predictive uncertainty estimates in a conceptually simple way but require multiple models for training and prediction, increasing computational cost and latency. Parametric deep learning can estimate uncertainty with one model by predicting the parameters of a probability distribution but does not account for epistemic uncertainty. Evidential deep learning, a technique that extends parametric deep learning to higher-order distributions, can account for both aleatoric and epistemic uncertainties with one model. This study compares the uncertainty derived from evidential neural networks to that obtained from ensembles. Through applications of the classification of winter precipitation type and regression of surface-layer fluxes, we show evidential deep learning models attaining predictive accuracy rivaling standard methods while robustly quantifying both sources of uncertainty. We evaluate the uncertainty in terms of how well the predictions are calibrated and how well the uncertainty correlates with prediction error. Analyses of uncertainty in the context of the inputs reveal sensitivities to underlying meteorological processes, facilitating interpretation of the models. The conceptual simplicity, interpretability, and computational efficiency of evidential neural networks make them highly extensible, offering a promising approach for reliable and practical uncertainty quantification in Earth system science modeling. To encourage broader adoption of evidential deep learning, we have developed a new Python package, Machine Integration and Learning for Earth Systems (MILES) group Generalized Uncertainty for Earth System Science (GUESS) (MILES-GUESS) ( https://github.com/ai2es/miles-guess ), that enables users to train and evaluate both evidential and ensemble deep learning. Significance Statement This study demonstrates a new technique, evidential deep learning, for robust and computationally efficient uncertainty quantification in modeling the Earth system. The method integrates probabilistic principles into deep neural networks, enabling the estimation of both aleatoric uncertainty from noisy data and epistemic uncertainty from model limitations using a single model. Our analyses reveal how decomposing these uncertainties provides valuable insights into reliability, accuracy, and model shortcomings. We show that the approach can rival standard methods in classification and regression tasks within atmospheric science while offering practical advantages such as computational efficiency. With further advances, evidential networks have the potential to enhance risk assessment and decision-making across meteorology by improving uncertainty quantification, a longstanding challenge. This work establishes a strong foundation and motivation for the broader adoption of evidential learning, where properly quantifying uncertainties is critical yet lacking.

Schreck, John S.↗

DOE OSTI2023

Uncertainty-aware molecular dynamics from Bayesian active learning for phase transformations and thermal transport in SiC

Abstract Machine learning interatomic force fields are promising for combining high computational efficiency and accuracy in modeling quantum interactions and simulating atomistic dynamics. Active learning methods have been recently developed to train force fields efficiently and automatically. Among them, Bayesian active learning utilizes principled uncertainty quantification to make data acquisition decisions. In this work, we present a general Bayesian active learning workflow, where the force field is constructed from a sparse Gaussian process regression model based on atomic cluster expansion descriptors. To circumvent the high computational cost of the sparse Gaussian process uncertainty calculation, we formulate a high-performance approximate mapping of the uncertainty and demonstrate a speedup of several orders of magnitude. We demonstrate the autonomous active learning workflow by training a Bayesian force field model for silicon carbide (SiC) polymorphs in only a few days of computer time and show that pressure-induced phase transformations are accurately captured. The resulting model exhibits close agreement with both ab initio calculations and experimental measurements, and outperforms existing empirical models on vibrational and thermal properties. The active learning workflow readily generalizes to a wide range of material systems and accelerates their computational understanding.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Transmission Operator Workflows for Real-Time Reliability Studies: A Review of Control Room Practices and Naturalistic Decision Making

This report provides an overview of real-time reliability study tools and their use by power system operators in the control room environment. After introducing some of the nuances of the control room environment and the differences in perspectives between power system engineers and operators, the roles and responsibilities of key entities involved in RTCA workflows are introduced. These are specifically the transmission system operator (TOP) and reliability coordinator (RC), which are required to run tools such as real-time contingency analysis (RTCA) as part of a real-time reliability assessment every 30 minutes, as dictated by a series of standards issued by the North American Electric Reliability Corporation (NERC). The process by which power systems operators operate the grid is discussed in terms of naturalistic decision making (NDM) and the recognition-primed decision-making (RPD) model. This cognitive model describe how experts working in high-risk, high-stress environments make safety-critical decisions under uncertainty and time pressure. For power system operators, the mental simulations involved in the traditional RPD model are supplemented by physics-based simulations using numerical tools, such as RTCA, to improve situational awareness and effectiveness of control actions. Next, a generic workflow is introduced to describe operator decision making for running RTCA tools and responding to system violations on a pre-contingent basis. The types of analysis performed and control actions chosen by power system operators are described in detail. The overall high-level workflow is then expanded in subsequent sections, with special attention given to high-voltage violations, low-voltage violations, and thermal overloads. Each type of violation is described in detail, with explanations of common causes, impacts on equipment and customers, and mitigation strategies. An additional workflow diagram is provided for each type of violation.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2024

CCUS 2024, Interpreting the strain tensor Larry Murdoch Interpreting strain tensor data to characterize and monitor reservoirs for CO2 storage and other applications

Recent advances in instrumentation have made it feasible to measure the transient strain tensor caused by small changes in fluid volume or pressure in the subsurface and this has opened the door to new opportunities for characterization and monitoring during CCUS. We have demonstrated this method by deploying strainmeters at shallow depths (30 to 40m) and then conducting injection well tests in an underlying reservoir at 530m depth. The resulting data indicated that the horizontal strain at shallow strainmeters was tensile and the vertical strain was compressive. The radial strain was less than the horizontal strain, and the strain rates decreased from 100 nanostrain/day to roughly 10 ne/d over a few days (1 nanostrain = 1 part per billion strain). We then used the strain data to estimate reservoir properties, geometry and pressure through inversion of poroelastic forward models using both numerical and novel analytical methods. The average horizontal strain in the caprock resembles the transient pressure in the underlying reservoir and classic type-curve methods from transient well testing can be used for preliminary interpretations of strain data. We have developed fast, closed-form analytical solutions to a pressurized poroelastic inclusion and inhomogeneity in a half-space. Numerical models developed using finite element methods allow more details of the subsurface to be included in the inversion, but they require much longer run times and this makes inversion cumbersome using standard methods. We have developed an inversion approach that uses a proxy model created using machine learning to do most of the forward calculations. This approach markedly reduces the computational requirements and makes it feasible to use Bayesian inversion with large numerical models. Bayesian inversion is important because it provides predictions with uncertainties, which makes the results useful for decision making. We have shown with field tests and simulations that the strain tensor in the caprock is sensitive to pressure in the reservoir, reservoir properties and boundaries, and pressure in the caprock caused by leaks. These results indicate that measuring and interpreting the shallow strain tensor could be a valuable tool for both initial reservoir characterization efforts and long-term monitoring during CCUS. Recent advances in instrumentation have made it feasible to measure the transient strain tensor caused by small changes in fluid volume or pressure in the subsurface and our objective was to evaluate opportunities for strain monitoring during characterization and monitoring for CCUS. Our approach was to deploy strainmeters at shallow depths (30 to 40m) and then conduct injection well tests in an underlying reservoir at 530m depth. The results indicate that the horizontal strain at shallow strainmeters was tensile and the vertical strain was compressive. The radial strain was less than the horizontal strain, and the strain rates decreased from 100 nanostrain/day to roughly 10 ne/d over a few days (1 nanostrain = 1 part per billion strain). We then used the strain data to estimate reservoir properties, geometry and pressure through inversion of poroelastic forward models using both numerical and novel analytical methods. The average horizontal strain in the caprock resembles the transient pressure in the underlying reservoir and classic type-curve methods from transient well testing can be used for preliminary interpretations of strain data. We have developed fast, closed-form analytical solutions to a pressurized poroelastic inclusion and inhomogeneity in a half-space. Numerical models developed using finite element methods allow more details of the subsurface to be included in the inversion, but they require much longer run times and this makes inversion cumbersome using standard methods. We have developed an inversion approach that uses a proxy model created using machine learning to do most of the forward calculations. This approach markedly reduces the computational requirements and makes it feasible to use Bayesian inversion with large numerical models. Bayesian inversion is important because it provides predictions with uncertainties, which makes the results useful for decision making. In conclusion, we have shown with field tests and simulations that the strain tensor in the caprock is sensitive to pressure in the reservoir, reservoir properties and boundaries, and pressure in the caprock caused by leaks. These results indicate that measuring and interpreting the shallow strain tensor could be a valuable tool for both initial reservoir characterization efforts and long-term monitoring during CCUS.

Murdoch, Larry↗

DOE OSTI2025

Advancements in Constitutive Model Calibration: Leveraging the Power of Full‐Field DIC Measurements and In Situ Load Path Selection for Reliable Parameter Inference

Accurate material characterization and model calibration are essential for computationally supported high-consequence engineering decisions. Historically, characterization and calibration methods (1) use simplified test specimen geometries and global data, (2) cannot guarantee that sufficient characterization data are collected for a specific model of interest, (3) use deterministic methods that provide best-fit parameter values with no uncertainty quantification, and (4) are sequential, inflexible, and time-consuming. This work brings together several recent advancements into an improved workflow called interlaced characterization and calibration (ICC) that advances the state-of-the-art in constitutive model calibration. The ICC paradigm (1) employs tools to efficiently use full-field data to calibrate high-fidelity material models, (2) aligns the data needed with the data collected by adopting an optimal experimental design protocol, (3) quantifies parameter uncertainty through Bayesian inference and (4) incorporates these advancements into a quasi real-time feedback loop. The ICC framework is demonstrated here on the calibration of a material model using simulated full-field data for an aluminium cruciform specimen being deformed biaxially. The cruciform is actively driven through the myopically preferred load path using Bayesian optimal experimental design, which selects load steps that yield the maximum expected information gain (EIG). Principal component analysis (PCA) is performed on the model predictions of full-field displacements, and fast surrogate models are built to approximate the input-output relationships of the expensive finite element model. Furthermore, the tools developed and demonstrated here show that high-fidelity constitutive models can be efficiently and reliably calibrated with quantified uncertainty, thus supporting credible decision-making and potentially increasing the agility of solid mechanics modelling by enabling utilization of computational simulations at earlier stages of the design cycle.

Bayesian optimal experimental design↗

DOE OSTI2025

Projections of future climate for U.S. national assessments: past, present, future

Climate assessments consolidate our understanding of possible future climate conditions as represented by climate projections, which are largely based on the output of global climate models. Over the past 30 years, the scientific insights gained from climate projections have been refined through model structural improvements, emerging constraints on climate feedbacks, and increased computational efficiency. Within the same period, the process of assessing and evaluating information from climate projections has become more defined and targeted to inform users. As the size and audience of climate assessments has expanded, the framing, relevancy, and accessibility of projections has become increasingly important. This paper reviews the use of climate projections in national climate assessments (NCA) while highlighting challenges and opportunities that have emerged over time. Reflections and lessons learned address the continuous process to understand the broadening assessment audience and evolving user needs. Insights for future NCA development include (1) identifying benchmarks and standards for evaluating downscaled datasets, (2) expanding efforts to gather research gaps and user needs to inform how climate projections are presented in the assessment (3) providing practitioner guidance on the use, interpretation, and reporting of climate projections and uncertainty to better inform decision-making.

Assessment↗

DOE OSTI2022

The Geothermal Artificial Intelligence for geothermal exploration

Exploration of geothermal resources involves analysis and management of a large number of uncertainties, which makes investment and operations decisions challenging. Remote Sensing (RS), Machine Learning (ML) and Artificial Intelligence (AI) have potential in managing the challenges of geothermal exploration. In this paper, we present a methodology that integrates RS, ML and AI to create an initial assessment of geothermal potential, by resorting to known indicators of geothermal areas namely mineral markers, surface temperature, faults and deformation. We demonstrated the implementation of the method in two sites (Brady and Desert Peak geothermal sites) that are close to each other but have different characteristics (Brady having clear surface manifestations and Desert Peak being a blind site). Here, we processed various satellite images and geospatial data for mineral markers, temperature, faults and deformation and then implemented ML methods to obtain pattern of surface manifestation of geothermal sites. We developed an AI that uses patterns from surface manifestations to predict geothermal potential of each pixel. We tested the Geothermal AI using independent data sets obtaining accuracy of 92-95%; also tested the Geothermal AI trained on one site by executing it for the other site to predict the geothermal / non-geothermal delineation, the Geothermal AI performed quite well in prediction with 72-76% accuracy.

15 GEOTHERMAL ENERGY↗

DOE OSTI2025

Swing Contract-Based Valuation for Distributed Energy Resources in Transactive Energy Systems: A Reinforcement Learning Approach

With the proliferation of distributed energy resources (DERs) and power grids with high fractions of renewable energy, market constructs are evolving to allow DERs to participate in multiple possible markets, at different levels of grid hierarchy. The effective participation of DERs in market environments is aided by swing contract-based pricing mechanisms, whereby DERs have a two-part compensation structure – one for their reservation/commitment and another for performancedriven ex-post payment for their actual mobilization during dispatch. In this paper, we propose a reinforcement learningbased (Q-learning) approach that allows a rational DER agent to select the market it wants to participate in within a composite market environment where individual markets are coordinated by possibly different actors. The proposed Q-learning framework aids DERs in their self-valuation by implicitly maximizing their own payoff through market participation, assuming a swing contract-based compensation structure. We complement our work through simulation-based investigations where factors affecting the DER decision making process, such as parametric uncertainties in market (and grid) environments, are studied.

Naqvi, Syed Ahsan Raza↗

DOE OSTI2025

Navigating Uncertainty: Challenges in Visualizing Ensemble Data and Surrogate Models for Decision Systems

Uncertainty visualization plays a critical role in transforming ensemble simulation data into actionable insights by effectively communicating various dimensions of uncertainty within a system. The emergence of artificial intelligence-driven surrogate models trained on multirun ensemble data offers a transformative opportunity to replace computationally intensive simulations with fast estimates, enabling users to explore data spaces with unprecedented depth and interactivity. However, integrating ensemble data and surrogate models into decision-making workflows and tools introduces novel challenges for uncertainty visualization. These include reconciling and clearly communicating the unique uncertainties associated with ensembles and their surrogate model estimates, and leveraging these approximations to inform actionable decisions. This work explores these challenges in the context of high-dimensional data visualization, bridging discrete datasets with their continuous representations and addressing the complexities of systems that support iterative navigation between input and output spaces. We evaluate the role of uncertainty visualization in fostering intuitive, actionable interactions and identify critical hurdles in advancing this frontier of computational simulation.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Neural correspondence to spectrum of environmental uncertainty in multiple-cue probability judgment system with time delay

Despite state-of-the-art technologies like artificial intelligence, human judgment is critically essential in cooperative systems, such as the multi-agent system (MAS), which collect information among agents based on multiple-cue judgment. Human agents can prevent impaired situational awareness of automated agents by confirming situations under environmental uncertainty. System error caused by uncertainty can result in an unreliable system environment, and this environment affects the human agent, resulting in non-optimal decision-making in MAS. Thus, it is necessary to know how human behavior is changed to capture system reliability under uncertainty. Another issue affecting MAS is time delay, which can delay agent information transfer, resulting in low performance and instability. However, it is difficult to find studies on the influence of time delay on human agents. This study is about understanding the human decision-making process under a specific system reliability environment by uncertainty with time delay. We used concepts of expected and unexpected uncertainty to implement reliability of the system usage environment with three types of time delay conditions: no time delay, regular time delay, and irregular time delay conditions. We used electroencephalogram (EEG) for human cognitive neural mechanisms in multiple-cue judgment systems to understand human decision-making. In the reliability of system usage environment, the unreliable system environment significantly creates less memory load by less utilization of system rules for decision-making. In terms of time delay, delayed information delivery does not significantly affect memory load for decision-making.

cognitive process↗

DOE OSTI2025

GenAI4UQ: A software for forward and inverse uncertainty quantification using conditional generative AI

We introduce GenAI4UQ, a software package for forward and inverse uncertainty quantification in model calibration, parameter estimation, and ensemble forecasting. GenAI4UQ leverages a generative AI-based conditional modeling framework to address limitations of traditional inverse modeling techniques, such as Markov Chain Monte Carlo (MCMC) methods. By replacing computationally intensive iterative processes with a direct, learned mapping, GenAI4UQ enables efficient calibration of input parameters and generation of predictions directly from observations. The software supports rapid ensemble forecasting with robust uncertainty quantification while maintaining computational and storage efficiency. Built-in auto-tuning of hyperparameters simplifies model training, ensuring accessibility for users with varying expertise. Its versatile conditional generative framework is applicable across diverse scientific domains. While GenAI4UQ offers significant advantages in flexibility and efficiency, users should interpret its uncertainty estimates with caution in data-sparse scenarios, as the model may overestimate uncertainty—an effect common to all surrogate-based approaches including MCMC with surrogate models. Despite this, GenAI4UQ transforms inverse modeling by providing a fast, reliable, and user-friendly solution. It empowers researchers and practitioners to quickly estimate parameter distributions and generate model predictions for new observations, facilitating efficient decision-making and advancing the state of uncertainty quantification in computational modeling.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Enabling Scale-Up Through Multi-Fidelity Adaptive Computing

We present ideas from our ongoing work in adaptive computing - an optimization framework that allows us to strategically deploy various fidelity level experiments and simulations to guide decision making. The framework aims to enable uncertainty quantified scale-up of simulations and experiments, which causes increased complexity. A key feature of the framework is the integration of user-specified local model trustworthiness estimates. Adaptive sampling strategies allow us to optimally exploit the multiple fidelity level information and trustworthiness measures to arrive at the best decisions within a highly limited budget of objective function evaluations.

adaptive sampling↗

DOE OSTI2021

Farmer characteristics and decision-making: A model for bioenergy crop adoption

We report the commercial development of biofuels and bioproducts depends on whether renewable biomass feedstock is available while not directly competing with the production of food. Farmers are one of the most important stakeholders in the biofuel supply chain and confront a range of uncertainties while entering the bioenergy market. Their decision-making process is extremely complex and rarely purely rational. Modeling farmer behavior requires considering a wide range of individual-level factors, socio-temporal dynamics, institutional settings, and their interactions. These characteristics make agent-based modeling a suitable framework for evaluating such systems. We developed a model to simulate farmer bioenergy crop adoption behavior across a 50-county study region in Nebraska, Kansas, and Colorado. The analysis considers adoption decisions for two bioenergy feedstocks, crop residues and energy crops. We examine the influence of individual and farm characteristics, market structure, social networks, and media influence on farmer adoption decisions. Our results indicate that different factors can have varied impacts on the speed of adoption for the crop residues and energy crops. Identifying levers that have the most impact on grower adoption can inform the design of interventions both from policy and private sector standpoints with important implications for the future the bioenergy industry.

09 BIOMASS FUELS↗

DOE OSTI2026

Uncertainty guided online ensemble for non-stationary data streams in fusion science

Machine Learning (ML) is poised to play a pivotal role in the development and operation of next-generation fusion devices. Fusion data shows non-stationary behavior with distribution drifts, resulted by both experimental evolution and machine wear-and-tear. ML models assume stationary distribution and fail to maintain performance when encountered with such non-stationary data streams. Online learning techniques have been leveraged in other domains, however it has been largely unexplored for fusion applications. In this paper, we investigate online learning for continuous adaptation to drifting data streams in the prediction of Toroidal Field (TF) coils deflection at the DIII-D fusion facility. We further address the short-term performance degradation inherent to standard online learning, which arises because ground truth is unavailable at prediction time. To mitigate this issue, we propose an uncertainty-guided online ensemble framework. The method leverages the Deep Gaussian Process Approximation (DGPA) for calibrated uncertainty estimation and uses these uncertainty measures to guide a meta-algorithm that aggregates predictions from learners trained over different historical horizons. Our results show that online learning reduces prediction error by 80% compared to a static model. The online ensemble and the proposed uncertainty-guided ensemble further reduce error by approximately 6%, and 10% respectively, relative to standard single-model online learning, while also providing calibrated uncertainty estimates to support operational decision-making.

AI↗

DOE OSTI2024

Uncertainty-Informed Volume Visualization using Implicit Neural Representation

The increasing adoption of Deep Neural Networks (DNNs) has led to their application in many challenging scientific visualization tasks. While advanced DNNs offer impressive generalization capabilities, understanding factors such as model prediction quality, robustness, and uncertainty is crucial. These insights can enable domain scientists to make informed decisions about their data. However, DNNs inherently lack ability to estimate prediction uncertainty, necessitating new research to construct robust uncertainty-aware visualization techniques tailored for various visualization tasks. In this work, we propose uncertainty-aware implicit neural representations to model scalar field data sets effectively and comprehensively study the efficacy and benefits of estimated uncertainty information for volume visualization tasks. We evaluate the effectiveness of two principled deep uncertainty estimation techniques: (1) Deep Ensemble and (2) Monte Carlo Dropout (MC-Dropout). These techniques enable uncertainty-informed volume visualization in scalar field data sets. Our extensive exploration across multiple data sets demonstrates that uncertainty-aware models produce informative volume visualization results. Moreover, integrating prediction uncertainty enhances the trustworthiness of our DNN model, making it suitable for robustly analyzing and visualizing real-world scientific volumetric data sets.

Saklani, Shanu↗

DOE OSTI2023

A game-theoretic approach to nuclear fuel cycle transition analysis under uncertainty

We present a novel methodology for optimizing nuclear fuel cycle transitions that incorporates a game-theoretic approach and captures interactions among multiple decision makers. The methodology is demonstrated using a two-person sequential game with uncertainty, where the two players represent a policy maker and an electric utility company, though the method generalizes to any number and type of individual decision making entities. Coupled with a sophisticated nuclear fuel cycle simulator, rich transition scenarios may be analyzed to identify robust transition strategies. These strategies explicitly treat uncertainties using a stochastic programming approach, devising optimal near-term hedging strategies that simultaneously consider all possible states of the world, maintaining flexibility to allow for intelligent recourse decisions once uncertainties are resolved. In the demonstration game, reactor technology and fuel cycle scheme adopted by the electric utility are shown to depend on both the policy maker’s decisions and the distributions over uncertain technological and economic outcomes.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2024

Stakeholder-driven carbon neutral pathways for Thailand and Bangkok: integrated assessment modeling to inform multilevel climate governance

Thailand has established a target of carbon neutrality by 2050. Reaching this goal will require coordination and collaboration between stakeholders spanning sectors and scales, including energy system decision makers, land managers, and city planners. Robust decarbonization scenarios incorporating current plans and targets, additional measures needed, and trade-offs between strategies can help stakeholders make informed decisions in the face of uncertainty. Through iterative engagement with decision makers at the city and national levels, we develop and analyze carbon neutral scenarios for Thailand that incorporate Bangkok’s role using a global integrated assessment model. We find that Thailand can reach carbon neutrality through power sector decarbonization, energy efficiency improvements, widespread electrification, and advanced technologies including carbon capture and storage and hydrogen. Negative emissions technologies will also be needed to offset Thailand and Bangkok’s hardest-to-abate CO 2 emissions. Bangkok, as a major population and economic center, contributes significantly to Thailand’s energy demand and emissions and can therefore play an important role in climate change mitigation. Accordingly, our results underscore the importance of subnational climate action in meeting Thailand’s carbon neutral goal. Our analysis also indicates that without sustained land-based carbon sequestration, much more mitigation effort will be needed in Thailand’s energy sector, including at the subnational scale, to reach carbon neutrality. These insights can help stakeholders identify priorities, consider tradeoffs, and make decisions that will impact Bangkok and Thailand’s long-term climate change mitigation potential. This analysis demonstrates how stakeholder engagement in integrated assessment modeling can facilitate and inform multilevel climate governance.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2021

Survey on stochastic distribution systems: A full probability density function control theory with potential applications

Complex systems seen either in general engineering practice or economics are subjected to ever increased uncertainties that are mostly represented as random variables or parameters, and the characteristics of random variables are represented by their probability density functions (PDFs). Controlling their PDFs means to shape their stochastic distributions and in general it would provide a full treatment for system analysis and operational control and optimization. This leads to the development of stochastic distribution control (SDC) systems theory in the past decades, where the original aim of the controller design is to realize a shape control of the distributions of certain random variables in their PDFs sense for some engineering processes. Indeed, once the PDFs of these random variables or parameters are used to describe their distribution characters, the control task is to obtain control signals so that the output PDFs of stochastic systems are made to follow their target PDFs. The subject of SDC was initially originated for non-Gaussian stochastic control systems design but has found a wide spectrum of applications in general systems in terms of data-driven modeling, analysis, signal processing (filtering), data mining via multivariable statistics, decision-making (optimization) for systems subjected to uncertainties and even in economics. In this context, SDC constitutes an effective primer tool for complex system analysis, control and operational optimizations. In this review paper, a detailed survey of the developments on the research of SDC systems will be made together with their wide spectrum applications and future perspectives.

42 ENGINEERING↗