Mathematical Models of Energy Storage Technologies Used with Coal FIRST Power Generators on IDAES
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20 FOSSIL-FUELED POWER PLANTS↗
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Results for “mathematical modelling”
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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Mathematical Modeling and Analysis for Emerging Infectious Diseases.
Abstract not provided.
Acquesta, Erin↗
Mathematical Modeling of Binary Mixtures
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Materials science↗
How robust are estimates of key parameters in standard viral dynamic models?
Mathematical models of viral infection have been developed, fitted to data, and provide insight into disease pathogenesis for multiple agents that cause chronic infection, including HIV, hepatitis C, and B virus. However, for agents that cause acute infections or during the acute stage of agents that cause chronic infections, viral load data are often collected after symptoms develop, usually around or after the peak viral load. Consequently, we frequently lack data in the initial phase of viral growth, i.e., when pre-symptomatic transmission events occur. Missing data may make estimating the time of infection, the infectious period, and parameters in viral dynamic models, such as the cell infection rate, difficult. However, having extra information, such as the average time to peak viral load, may improve the robustness of the estimation. Here, we evaluated the robustness of estimates of key model parameters when viral load data prior to the viral load peak is missing, when we know the values of some parameters and/or the time from infection to peak viral load. Although estimates of the time of infection are sensitive to the quality and amount of available data, particularly pre-peak, other parameters important in understanding disease pathogenesis, such as the loss rate of infected cells, are less sensitive. Viral infectivity and the viral production rate are key parameters affecting the robustness of data fits. Fixing their values to literature values can help estimate the remaining model parameters when pre-peak data is missing or limited. We find a lack of data in the pre-peak growth phase underestimates the time to peak viral load by several days, leading to a shorter predicted growth phase. On the other hand, knowing the time of infection (e.g., from epidemiological data) and fixing it results in good estimates of dynamical parameters even in the absence of early data. While we provide ways to approximate model parameters in the absence of early viral load data, our results also suggest that these data, when available, are needed to estimate model parameters more precisely.
59 BASIC BIOLOGICAL SCIENCES↗
System Identification of a DC-DC Buck Converter Based on Two-Channel Relay Method
This work presents a system identification approach based on a two-channel relay applied to a DC-DC buck converter operating in closed-loop with a PI controller to regulate its output voltage. The implemented two-relay method allows system identification while the system is running online. Moreover, the algorithm works in a closed-loop configuration while introducing a minimal perturbation in the converter's operation. The presented algorithm was used to identify the frequency response of the converter with no-prior knowledge about the system structure. Furthermore, the identified transfer function parameters has a good agreement with the mathematical model of the converter. Simulation results of the comparison between the switching model, mathematical model and the identified model are provided to validate the theoretical analysis.
32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
Integrated Process Optimization for Biochemical Conversion
This research is motivated by the challenges faced during biomass processing in bioenergy plants. It has been observed that variations in biomass characteristics, such as moisture, ash, and carbohydrate contents cause variations in feeding of the system which led to underutilization of equipment and the reactor. The objective of this research is to ensure a continuous flow of biomass to the reactor in plants that use the biochemical conversion process to generate liquid fuels. The overall goal is to lower the cost of producing biofuels, which could lead to improving US’s energy independency and growing US’s rural economy. The research team developed analytical models, such as discrete element method (DEM) models and mathematical models. The DEM models are unit-level models that explicitly capture biomass characteristics and quantify the impacts of biomass characteristics on bulk material properties and the performance of specific equipment. The mathematical models are system-level models that capture the impacts of system infeed rate, equipment processing rate, storage location and capacity, and biomass characteristics on system throughput. The functional relations predicting the bulk material properties from DEM models are incorporated to the mathematical models. The models developed were validated and evaluated using data collected at Idaho National Laboratory’s biomass processing facility. Via these models, we identified process control strategies that ensure a continuous flow of biomass to the reactor, while meeting the requirements of biochemical conversion process. Our analysis indicates that sequencing of biomass bales based on moisture level, and carbohydrate contents could have a positive impact on reducing processing time and inventory level and increasing throughput rate. Short bale sequences that repeat frequently, seem to have the greatest impact on improving system’s performance. Based on our experiments, the total annual system operating costs reduced by 20-30%, and the maximum inventory level reduced by 3 to 4 times. The operating costs include the annual equipment amortization cost and processing cost. The implementation of the models developed requires the use of standardized bale format, Radio Frequency Identification technology, sensing and real time monitoring of material attributes, automated material handling equipment, and automated process control. The scope of the model proposed can be extended to include the whole supply chain. The supply chain models help identify how many bales of different biomass feedstock to purchase given biomass availability in the region, biomass price and quality, and the biomass processing capabilities of the biorefinery. Thus, the outcomes of supply chain models can be used to inform the design of long-term contracts among farmers and the biorefinery.
09 BIOMASS FUELS↗
Overcoming the Challenges to Enhancing Experimental Plant Biology With Computational Modeling
The study of complex biological systems necessitates computational modeling approaches that are currently underutilized in plant biology. Many plant biologists have trouble identifying or adopting modeling methods to their research, particularly mechanistic mathematical modeling. Here we address challenges that limit the use of computational modeling methods, particularly mechanistic mathematical modeling. We divide computational modeling techniques into either pattern models (e.g., bioinformatics, machine learning, or morphology) or mechanistic mathematical models (e.g., biochemical reactions, biophysics, or population models), which both contribute to plant biology research at different scales to answer different research questions. We present arguments and recommendations for the increased adoption of modeling by plant biologists interested in incorporating more modeling into their research programs. As some researchers find math and quantitative methods to be an obstacle to modeling, we provide suggestions for easy-to-use tools for non-specialists and for collaboration with specialists. This may especially be the case for mechanistic mathematical modeling, and we spend some extra time discussing this. Through a more thorough appreciation and awareness of the power of different kinds of modeling in plant biology, we hope to facilitate interdisciplinary, transformative research.
58 GEOSCIENCES↗
Practical Understanding of Cancer Model Identifiability in Clinical Applications
Mathematical models are a core component in the foundation of cancer theory and have been developed as clinical tools in precision medicine. Modeling studies for clinical applications often assume an individual’s characteristics can be represented as parameters in a model and are used to explain, predict, and optimize treatment outcomes. However, this approach relies on the identifiability of the underlying mathematical models. In this study, we build on the framework of an observing-system simulation experiment to study the identifiability of several models of cancer growth, focusing on the prognostic parameters of each model. Our results demonstrate that the frequency of data collection, the types of data, such as cancer proxy, and the accuracy of measurements all play crucial roles in determining the identifiability of the model. We also found that highly accurate data can allow for reasonably accurate estimates of some parameters, which may be the key to achieving model identifiability in practice. As more complex models required more data for identification, our results support the idea of using models with a clear mechanism that tracks disease progression in clinical settings. For such a model, the subset of model parameters associated with disease progression naturally minimizes the required data for model identifiability.
59 BASIC BIOLOGICAL SCIENCES↗
Identifying Bayesian optimal experiments for uncertain biochemical pathway models
Abstract Pharmacodynamic (PD) models are mathematical models of cellular reaction networks that include drug mechanisms of action. These models are useful for studying predictive therapeutic outcomes of novel drug therapies in silico. However, PD models are known to possess significant uncertainty with respect to constituent parameter data, leading to uncertainty in the model predictions. Furthermore, experimental data to calibrate these models is often limited or unavailable for novel pathways. In this study, we present a Bayesian optimal experimental design approach for improving PD model prediction accuracy. We then apply our method using simulated experimental data to account for uncertainty in hypothetical laboratory measurements. This leads to a probabilistic prediction of drug performance and a quantitative measure of which prospective laboratory experiment will optimally reduce prediction uncertainty in the PD model. The methods proposed here provide a way forward for uncertainty quantification and guided experimental design for models of novel biological pathways.
97 MATHEMATICS AND COMPUTING↗
Mathematical Programming Models for Shale Oil & Gas Development: A Review and Perspective
Here, in this paper, we provide a comprehensive review of mathematical programming models for shale oil & gas development, and we offer a perspective on outstanding research opportunities. We distinguish contributions in five major topic areas, namely: (1) development planning, (2) water management, (3) production optimization, (4) supplies, gathering & processing, and (5) life cycle analysis & sustainability. We highlight how various types of mathematical programming models (i.e., linear programs, nonlinear programs, mixed-integer linear programs, mixed-integer nonlinear programs) have been proposed primarily by the Process Systems Engineering community to address the respective decision-making problems, and we highlight instances of successful deployment in industry. Finally, based on a critical assessment of the existing body of work, we identify opportunities for future research across the major topic areas.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Implementation and evaluation of multi-dual mode counter-current chromatography in the CUP Modeler software
Counter-current chromatography (CCC) is a separation technique that utilizes immiscible solvent pairs as stationary and mobile phases, which imparts numerous benefits compared to solid-liquid chromatography including the ability to treat either the more-dense or less-dense solvent layer as the mobile phase. Multi-dual mode (MDM) is a CCC elution mode capable of improving the separation of closely eluting compounds by alternating upper- and lower-layer solvent flows in opposing directions within the same separation. While some effort has been made to model MDM, implementation of these models in experimental design has yet to be widely adopted. Accordingly, we further developed our previously published cell utilized partitioning (CUP) model to include MDM predictions with CCC and packaged the full suite of CUP modeling capabilities into a user-friendly, open-source tool called the CUP Modeler. The mathematical model for MDM CCC was derived and validated with experimental separation of ethyl guaiacol (EG) and ethyl phenol (EP), two compounds that co-elute in our previously demonstrated reductive catalytic fractionation (RCF) lignin monomer isolation method. The developed MDM model provided insights into the effect of multiple operating parameters - including stationary phase retention, flow rate, column efficiency, feed concentration ratio, selectivity factor, and solute distribution ratios - on the separation yields, productivity, and purities. Our model agreed with prevailing understanding of MDM but also revealed new insights including that the ideal distribution ratios for co-eluting solutes to be separated by MDM is between 1.1 and 1.5, with the lower value ideally close to 1.25. Overall, this work provides fundamental insights for MDM process design and enables broader adoption of general liquid-liquid chromatography with a new, open-source user-friendly interface.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Sequentially calibrating a Bayesian microsimulation model to incorporate new information and assumptions
Background: Microsimulation models are mathematical models that simulate event histories for individual members of a population. They are useful for policy decisions because they simulate a large number of individuals from an idealized population, with features that change over time, and the resulting event histories can be summarized to describe key population-level outcomes. Model calibration is the process of incorporating evidence into the model. Calibrated models can be used to make predictions about population trends in disease outcomes and effectiveness of interventions, but calibration can be challenging and computationally expensive. Methods: This paper develops a technique for sequentially updating models to take full advantage of earlier calibration results, to ultimately speed up the calibration process. A Bayesian approach to calibration is used because it combines different sources of evidence and enables uncertainty quantification which is appealing for decision-making. We develop this method in order to re-calibrate a microsimulation model for the natural history of colorectal cancer to include new targets that better inform the time from initiation of preclinical cancer to presentation with clinical cancer (sojourn time), because model exploration and validation revealed that more information was needed on sojourn time, and that the predicted percentage of patients with cancers detected via colonoscopy screening was too low. Results: The sequential approach to calibration was more efficient than recalibrating the model from scratch. Incorporating new information on the percentage of patients with cancers detected upon screening changed the estimated sojourn time parameters significantly, increasing the estimated mean sojourn time for cancers in the colon and rectum, providing results with more validity. Conclusions: A sequential approach to recalibration can be used to efficiently recalibrate a microsimulation model when new information becomes available that requires the original targets to be supplemented with additional targets.
60 APPLIED LIFE SCIENCES↗
Current State, Challenges, and Opportunities in Genome-Scale Resource Allocation Models: A Mathematical Perspective
Stoichiometric genome-scale metabolic models (generally abbreviated GSM, GSMM, or GEM) have had many applications in exploring phenotypes and guiding metabolic engineering interventions. Nevertheless, these models and predictions thereof can become limited as they do not directly account for protein cost, enzyme kinetics, and cell surface or volume proteome limitations. Lack of such mechanistic detail could lead to overly optimistic predictions and engineered strains. Initial efforts to correct these deficiencies were by the application of precursor tools for GSMs, such as flux balance analysis with molecular crowding. In the past decade, several frameworks have been introduced to incorporate proteome-related limitations using a genome-scale stoichiometric model as the reconstruction basis, which herein are called resource allocation models (RAMs). This review provides a broad overview of representative or commonly used existing RAM frameworks. This review discusses increasingly complex models, beginning with stoichiometric models to precursor to RAM frameworks to existing RAM frameworks. RAM frameworks are broadly divided into two categories: coarse-grained and fine-grained, with different strengths and challenges. Discussion includes pinpointing their utility, data needs, highlighting framework strengths and limitations, and appropriateness to various research endeavors, largely through contrasting their mathematical frameworks. Finally, promising future applications of RAMs are discussed.
59 BASIC BIOLOGICAL SCIENCES↗
Individualized empirical baselines for evaluating the energy performance of existing buildings
The evaluation of building energy performance requires a baseline for comparison. Common empirical baselines are usually used for existing buildings since they are fast and convenient. However, the same type of building at the same location will receive the same baseline despite their difference in usage. Individualized baselines by creating building energy models are possible solutions, but it is labor intensive and time-consuming. To fill the gap, this study is to develop individualized empirical baselines for existing buildings in a fast way. First, common empirical baselines are created based on survey data. Then, to get training samples, building energy models for large-scale existing buildings are created and simulated. So finally, based on simulation results, mathematical models to get individualized empirical baselines in a fast way are created. U.S. medium office buildings were used as an example to demonstrate the method. We developed 30 mathematical models for medium office buildings in two vintages (constructed before 1980 and after 1980) and 15 climate zones. The mean absolute percentage errors (MAPE) between the individualized empirical baselines and the modeled baselines for those 30 mathematical models are all lower than 5.5%. An engineer can obtain the individualized empirical baseline for an existing building in a few seconds by using the open-source tool we developed.
32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
Elucidating Cycling Rate-Dependent Electrochemical Strains in Sodium Iron Phosphate Cathodes for Na-ion Batteries
Battery electrodes materials undergo significant mechanical instabilities which affects their longevity and exert rate-limitations during the cycling process. In this study, we investigate the rate-dependent mechanical response of sodium iron phosphate (NaFePO4, NFP) cathodes during Na intercalation via galvanostatic cycling at different rates by employing digital image correlation, electrochemical methods, and mathematical model. The mechanical behaviour of the electrode shows strong dependance on the applied scan rate. At slower rates, electrode shows asymmetrical strain generation between anodic and cathodic cycles, which is attributed to the formation of cathode-electrolyte interface layers. The electrode undergoes smaller strain generation when cycled at slower rates when the same amount of Na ions is removed or inserted into the electrode. A mathematical model was developed to predict strain evolution in the composite electrode as well as the concentration profile of the Na ions in the electrode particles. Rate-dependent and time dependent factors on the strain generation in the electrode are attributed to the capacity-dependent intercalation strains, rate-dependent mismatch strains, and time-dependent irreversible strains. The combination of in situ strain measurements with the analytical model provided new insight into the electrochemically induced mechanical deformations in Na-ion cathode electrodes.
Ozdogru, Bertan↗
Optimizing Batch Crystallization with Model-based Design of Experiments
Adaptive and self-optimizing intelligent systems such as digital twins are increasingly important in science and engineering. Digital twins utilize mathematical models to provide added precision to decision-making. However, physics-informed models are challenging to build, calibrate, and validate with existing data science methods. Model-based design of experiments (MBDoE) is a popular framework for optimizing data collection to maximize parameter precision in mathematical models and digital twins. In this work, we apply MBDoE, facilitated by the open-source package Pyomo.DoE, to train and validate mathematical models for batch crystallization. We quantitatively examined the estimability of the model parameters for experiments with different cooling rates. This analysis provides a quantitative explanation for the heuristic of using multiple experiments at different cooling rates.
Lynch, Hailey↗
Towards verifiable cancer digital twins: tissue level modeling protocol for precision medicine
Cancer exhibits substantial heterogeneity, manifesting as distinct morphological and molecular variations across tumors, which frequently undermines the efficacy of conventional oncological treatments. Developments in multiomics and sequencing technologies have paved the way for unraveling this heterogeneity. Nevertheless, the complexity of the data gathered from these methods cannot be fully interpreted through multimodal data analysis alone. Mathematical modeling plays a crucial role in delineating the underlying mechanisms to explain sources of heterogeneity using patient-specific data. Intra-tumoral diversity necessitates the development of precision oncology therapies utilizing multiphysics, multiscale mathematical models for cancer. This review discusses recent advancements in computational methodologies for precision oncology, highlighting the potential of cancer digital twins to enhance patient-specific decision-making in clinical settings. We review computational efforts in building patient-informed cellular and tissue-level models for cancer and propose a computational framework that utilizes agent-based modeling as an effective conduit to integrate cancer systems models that encode signaling at the cellular scale with digital twin models that predict tissue-level response in a tumor microenvironment customized to patient information. Furthermore, we discuss machine learning approaches to building surrogates for these complex mathematical models. These surrogates can potentially be used to conduct sensitivity analysis, verification, validation, and uncertainty quantification, which is especially important for tumor studies due to their dynamic nature.
60 APPLIED LIFE SCIENCES↗
TNet: A Model-Constrained Tikhonov Network Approach for Inverse Problems
Deep learning (DL), in particular deep neural networks, by default is purely data-driven and in general does not require physics. This is the strength of DL but also one of its key limitations when applied to science and engineering problems in which underlying physical properties—such as stability, conservation, and positivity—and accuracy are required. DL methods in their original forms are often not capable of respecting the underlying mathematical models or achieving desired accuracy even in big-data regimes. On the other hand, many data-driven science and engineering problems, such as inverse problems, typically have limited experimental or observational data, and DL would overfit the data in this case. Leveraging information encoded in the underlying mathematical models, we argue, not only compensates for missing information in low data regimes but also provides opportunities to equip DL methods with the underlying physics, hence promoting better generalization. This paper develops a model-constrained DL approach and its variant TNet—a Tikhonov neural network—which are capable of learning not only information hidden in the training data but also in the underlying mathematical models to solve inverse problems governed by partial differential equations in low data regimes. We provide the constructions and some theoretical results for the proposed approaches for both linear and nonlinear inverse problems. Since TNet is designed to learn inverse solutions with Tikhonov regularization, it is interpretable: in fact it recovers Tikhonov solutions for linear cases while potentially approximating Tikhonov solutions for nonlinear inverse problems. We also prove that data randomization can enhance not only the smoothness of the networks but also their generalizations. Comprehensive numerical results confirm the theoretical findings and show that with even as little as 1 training data sample for one-dimensional (1D) deconvolution, 5 for an inverse 2D heat conductivity problem, 100 for inverse initial conditions for a time-dependent 2D Burgers’s equation, and 50 for inverse initial conditions for 2D Navier–Stokes equations, TNet solutions can be as accurate as Tikhonov solutions while being several orders of magnitude faster. Furthermore, this is possible owing to the model-constrained term, replications, and randomization.
97 MATHEMATICS AND COMPUTING↗