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DOE OSTI2019

Decentralized wind uncertainty management: Alternating direction method of multipliers based distributionally-robust chance constrained optimal power flow

How to manage wind power uncertainty in system operation is an urgent and important issue, especially under substantially increasing penetration levels of wind generation in electric power systems. With increasing numbers of wind power plants (WPPs) integrated into power systems, their variability and uncertain power outputs become a challenge to maintaining system reliability. Traditional stochastic optimization-based models face the curse of dimensionality when the number of WPPs increases. This paper proposes a novel decentralized wind power uncertainty management model. In this model, conventional generators optimize their power capacity output and their participation to mitigate wind power uncertainty locally with only limited information exchange with the system operators. First, a distributionally-robust chance-constrained optimal power flow (DRCC-OPF) model is deployed to schedule the generation and reserve considering the wind power forecast uncertainty. Then, the alternating direction method of multipliers (ADMM) is used to reformulate the DRCC-OPF model into the distributed optimization model for each conventional generator and WPP. The tests on a small PJM 5-bus system and the IEEE 118-bus system demonstrate that the proposed decentralized model can increase the operation reliability without sacrificing system operating cost, especially when the wind power penetration levels are high. Using the proposed model, the optimal solutions can be obtained within one minute, for all studied cases, which verifies the computation efficiency of the proposed decentralized model. Furthermore, considering a large number of WPPs integrated into the system, the proposed decentralized method obtains a lower operating cost within one minute which demonstrates its efficiency to deal with high dimension of uncertainties.

17 WIND ENERGY↗

NASA NTRS2021

Optimal Experimental Design With Fast Neural Network Surrogate Models

Designing optimal experiments minimizes the uncertainty of results and maximizes the efficient use of resources. Herein, machine learning surrogate models and the approximate coordinate exchange (ACE) algorithm are used to determine optimum experimental designs over large or arbitrarily restrictive design spaces. Optimal experimental design is particularly salient in materials science where experiments are expensive and material properties must often be inferred indirectly. The proposed framework is demonstrated by finding optimal experiments with which the hidden constituent properties of composite materials can be most efficiently inferred from observable experimental outcomes. The optimum experimental design is given by an information-theoretic criteria, which maximizes the conditional mutual information between the hidden properties and the expected experimental outcomes. To perform tractable optimization a neural network is trained as a surrogate model to mimic a physics based simulation, which can calculate the expected experimental outcome based on a candidate experimental design and sampled constituent properties. The ACE algorithm is used to optimize over large design spaces with many tests and controlled parameters where an exhaustive search would be intractable even with the surrogate model. Using this approach, optimal experimental designs that are consistent with those produced by heuristic knowledge and established best practices are found; then optimal designs in larger design spaces where heuristic knowledge is unavailable are examined.

machine learning↗

NASA NTRS1989

Generalized mathematical models in design optimization

The theory of optimality conditions of extremal problems can be extended to problems continuously deformed by an input vector. The connection between the sensitivity, well-posedness, stability and approximation of optimization problems is steadily emerging. The authors believe that the important realization here is that the underlying basis of all such work is still the study of point-to-set maps and of small perturbations, yet what has been identified previously as being just related to solution procedures is now being extended to study modeling itself in its own right. Many important studies related to the theoretical issues of parametric programming and large deformation in nonlinear programming have been reported in the last few years, and the challenge now seems to be in devising effective computational tools for solving these generalized design optimization models.

Papalambros, Panos Y.↗

DOE OSTI2024

Enhancing the cooling performance of thermocouples: a power-constrained topology optimization procedure

Abstract Heat pumping through thermoelectric devices has many advantages over traditional cooling. However, their current efficiency is a limiting factor in their implementation. In this paper, we approach the non-convex topology optimization of thermoelectrical elements for cooling applications through the method of moving asymptotes (MMA) to improve their cooling capabilities per watt usage. The optimization problem is defined for a given power budget, aiming for the minimum temperature with a known heat pumping need. The introduction of power as a constraint justifies the introduction of the voltage gradient across the thermocouple as a design variable to maintain the thermoelectrical device in its optimum power-to-heat extraction ratio. To better understand the convergence of this non-convex problem, we present a two-variable analytical thermoelectric optimization model. This example provides information on how to select the penalty parameters used to scale the three material coefficients involved in the problem to obtain lower objective values and better convergence using MMA. The analytical model shows the non-convexity of the problem and provides the recommendation to use penalization coefficients of the form $$p_k=p_{\sigma }>p_{\alpha }=1$$ p k = p σ > p α = 1 for the thermal conductivity, electrical conductivity, and Seebeck coefficients. We tested these penalization coefficients through optimizations of a model based on the 1MC10-031 commercial thermoelectric-cooler (TEC) using the finite element method (FEM). These penalization coefficients provided local minima without the need for volume constraints. With this procedure, we found designs that provided temperatures close to 10 degrees lower using 60% less semiconductor material volume compared to the initial design.

Gutiérrez, G. Reales↗

DOE OSTI2014

TH-C-BRD-10: An Evaluation of Three Robust Optimization Approaches in IMPT Treatment Planning

Purpose: Various robust optimization approaches have been proposed to ensure the robustness of intensity modulated proton therapy (IMPT) in the face of uncertainty. In this study, we aim to investigate the performance of three classes of robust optimization approaches regarding plan optimality and robustness. Methods: Three robust optimization models were implemented in our in-house IMPT treatment planning system: 1) L2 optimization based on worst-case dose; 2) L2 optimization based on minmax objective; and 3) L1 optimization with constraints on all uncertain doses. The first model was solved by a L-BFGS algorithm; the second was solved by a gradient projection algorithm; and the third was solved by an interior point method. One nominal scenario and eight maximum uncertainty scenarios (proton range over and under 3.5%, and setup error of 5 mm for x, y, z directions) were considered in optimization. Dosimetric measurements of optimized plans from the three approaches were compared for four prostate cancer patients retrospectively selected at our institution. Results: For the nominal scenario, all three optimization approaches yielded the same coverage to the clinical treatment volume (CTV) and the L2 worst-case approach demonstrated better rectum and bladder sparing than others. For the uncertainty scenarios, the L1 approach resulted in the most robust CTV coverage against uncertainties, while the plans from L2 worst-case were less robust than others. In addition, we observed that the number of scanning spots with positive MUs from the L2 approaches was approximately twice as many as that from the L1 approach. This indicates that L1 optimization may lead to more efficient IMPT delivery. Conclusion: Our study indicated that the L1 approach best conserved the target coverage in the face of uncertainty but its resulting OAR sparing was slightly inferior to other two approaches.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2026

Sensitivity Analysis of Drivers Water Shortage in the Los Angeles Region During Drought

The code and detailed step-by-step instructions for generating the model output data, processing results, and analysis and plotting are provided at https://github.com/IMMM-SFA/Ferencz_et_al_2026_ER_Water. The PyArtes model is a python adaptation of the Artes model. PyArtes uses many of the same input data and optimization model architecture as Artes. Documentation for the PyArtes model is provided in the Supplement to the paper. The primary data product are simulated monthly water shortages for indoor and outdoor demand under a large ensemble of drought scenarios (>13,000). The droughts are hypothetical and are not based on historical time series data of supply sources - though historical data did help inform ranges explored for supply parameters. Demands are informed by recent 2017-2021 water supply data. Demands used for the model can be accessed at https://github.com/IMMM-SFA/Ferencz_et_al_2026_ER_Water. Simulations resolve demand for over 90 water providers in the study region. The results report 36 months of water shortage data for each indoor and outdoor demand node. The study also developed a multilayer perceptron (MLP) neural network trained on a subset of the simulated shortage ensemble to emulate worst annual water shortage for a given set of parameter multipliers -- provided the parameter values fall within the ranges sampled in the ensemble. Emulated water shortages for synthetic ensembles are in the MLP-generated shortages folder. The MLP model was used to generate larger ensembles to support Sobol analysis that would have been extremely computationally expensive to simulate. Datasets provided in this repository*: Simulated shortages. These results are used for the analysis for Figures 5, 8, and 9 in the paper, and also to train the MLP emulator. .zip file containing outputs for the 13,312 scenario ensemble. Separate .csv files for indoor and outdoor shortage for each scenario. Rows = demand ids (~100), Columns = months (36) Units = acre-feet/month of shortage (shortage = monthly demand - supply). 1 acft = 1233.48 m^3 .csv files of aggregated shortages derived from the 13,312 ensemble Rows = scenarios (13,312), Columns = demand ids (~100) Units = acre-feet/year (either worst annual shortage or total shortage over the 3-year drought) .csv file of the parameter multipliers scenarios for the ensemble .csv file of the parameter ranges and baseline values the multipliers were applied to MLP-generated shortages. These results are used for Figures 4, 6, and 7 in the paper. mwd higher folder: scenario ensembles, emulated worst year total shortages (acft), and Sobol results Emulated shortages. Rows = scenarios, columns = demand ids, units acft Sobol results. Rows = demand ids, columns Sobol (S1, ST, or 95% confidence interval) value for each parameter mwd lower folder: scenario ensembles, emulated worst year total shortages (acft), and Sobol results same organization as mwd higher MLP performance: performance metrics (R^2, RMSE, BIAS, MAPE) for the testing subset (20% or 2,662 scenarios) and simulated vs emulated worst year shortage (acre-feet/year) for every demand node, MWD wholesale regions, and the entire study region (LAC). Supporting data for figures. Figure plotting scripts in the associated GitHub repo. These files support analysis and visualization. Geospatial Data used for plotting simulated water shortages and Sobol results. Dictionary of full names for demand nodes in the model and estimates of water supply by source type informed by Artes input files and California Urban Water Management Planning data: https://water.ca.gov/Programs/Water-Use-And-Efficiency/Urban-Water-Use-Efficiency/Urban-Water-Management-Plans *Readme files provided for each folder.

drought↗

DOE OSTI2016

A modeling framework for optimal energy management of a residential building

Residential buildings are currently equipped with energy production facilities, e.g., solar rooftops and batteries, which in conjunction with smart meters, can function as smart energy hubs coordinating the loads and the resources in an optimal manner. This paper presents a mathematical model for the optimal energy management of a residential building and proposes a centralized energy management system (CEMS) framework for off-grid operation. The model of each component of the hub is integrated within the CEMS. The optimal decisions are determined in real-time by considering these models with realistic parameter settings and customer preferences. Model predictive control (MPC) is used to adapt the optimal decisions on a receding horizon to account for the deviations in the system inputs. Simulation results are presented to demonstrate the feasibility and effectiveness of the proposed CEMS framework. Results show that the proposed CEMS can reduce the energy cost and energy consumption of the customers by approximately 17% and 8%, respectively, over a day. In conclusion, using the proposed CEMS, the total charging cycles of the ESS were reduced by more than 50% in a day.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2015

Computational and human observer image quality evaluation of low dose, knowledge-based CT iterative reconstruction

Purpose: Aims in this study are to (1) develop a computational model observer which reliably tracks the detectability of human observers in low dose computed tomography (CT) images reconstructed with knowledge-based iterative reconstruction (IMR™, Philips Healthcare) and filtered back projection (FBP) across a range of independent variables, (2) use the model to evaluate detectability trends across reconstructions and make predictions of human observer detectability, and (3) perform human observer studies based on model predictions to demonstrate applications of the model in CT imaging. Methods: Detectability (d′) was evaluated in phantom studies across a range of conditions. Images were generated using a numerical CT simulator. Trained observers performed 4-alternative forced choice (4-AFC) experiments across dose (1.3, 2.7, 4.0 mGy), pin size (4, 6, 8 mm), contrast (0.3%, 0.5%, 1.0%), and reconstruction (FBP, IMR), at fixed display window. A five-channel Laguerre–Gauss channelized Hotelling observer (CHO) was developed with internal noise added to the decision variable and/or to channel outputs, creating six different internal noise models. Semianalytic internal noise computation was tested against Monte Carlo and used to accelerate internal noise parameter optimization. Model parameters were estimated from all experiments at once using maximum likelihood on the probability correct, P{sub C}. Akaike information criterion (AIC) was used to compare models of different orders. The best model was selected according to AIC and used to predict detectability in blended FBP-IMR images, analyze trends in IMR detectability improvements, and predict dose savings with IMR. Predicted dose savings were compared against 4-AFC study results using physical CT phantom images. Results: Detection in IMR was greater than FBP in all tested conditions. The CHO with internal noise proportional to channel output standard deviations, Model-k4, showed the best trade-off between fit and model complexity according to AIC{sub c}. With parameters fixed, the model reasonably predicted detectability of human observers in blended FBP-IMR images. Semianalytic internal noise computation gave results equivalent to Monte Carlo, greatly speeding parameter estimation. Using Model-k4, the authors found an average detectability improvement of 2.7 ± 0.4 times that of FBP. IMR showed greater improvements in detectability with larger signals and relatively consistent improvements across signal contrast and x-ray dose. In the phantom tested, Model-k4 predicted an 82% dose reduction compared to FBP, verified with physical CT scans at 80% reduced dose. Conclusions: IMR improves detectability over FBP and may enable significant dose reductions. A channelized Hotelling observer with internal noise proportional to channel output standard deviation agreed well with human observers across a wide range of variables, even across reconstructions with drastically different image characteristics. Utility of the model observer was demonstrated by predicting the effect of image processing (blending), analyzing detectability improvements with IMR across dose, size, and contrast, and in guiding real CT scan dose reduction experiments. Such a model observer can be applied in optimizing parameters in advanced iterative reconstruction algorithms as well as guiding dose reduction protocols in physical CT experiments.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2017

Exploring the impact of increased solar deployment levels on residential electricity bills in India

Here, in this study, the impact of increased solar penetration in the electricity generation mix on residential electricity consumer bills is explored. The study comprises of two sections: simulation of wholesale electricity rates and retail rate modeling. In the first stage, wholesale prices were modeled using a bottom-up long term unit commitment optimization model for different energy mix scenarios based on increased solar penetration, ranging from 5 to 40% on energy basis. The simulations indicated a fall in wholesale prices with increased solar penetration, a result of merit order effect. The simulated wholesale prices were then used to model retail rates for residential consumers. Four different types of retail rates were designed: flat rate, real time pricing, time of use and critical peak pricing. The impact of these retail rate mechanisms on electricity bills of residential consumers was analyzed and it was found that the bill savings achieved from time varying rates are greater than for time invariant rates. With increased solar penetration, customers with time-varying rates are likely to benefit the most from electricity bill savings. Although consumers with flat rate gain bill savings with increased solar penetration, the savings are likely to be lower than with time-varying rates.

14 SOLAR ENERGY↗

DOE OSTI2013

ALMA OBSERVATIONS OF SPT-DISCOVERED, STRONGLY LENSED, DUSTY, STAR-FORMING GALAXIES

We present Atacama Large Millimeter/submillimeter Array (ALMA) 860 {mu}m imaging of four high-redshift (z = 2.8-5.7) dusty sources that were detected using the South Pole Telescope (SPT) at 1.4 mm and are not seen in existing radio to far-infrared catalogs. At 1.''5 resolution, the ALMA data reveal multiple images of each submillimeter source, separated by 1''-3'', consistent with strong lensing by intervening galaxies visible in near-IR imaging of these sources. We describe a gravitational lens modeling procedure that operates on the measured visibilities and incorporates self-calibration-like antenna phase corrections as part of the model optimization, which we use to interpret the source structure. Lens models indicate that SPT0346-52, located at z = 5.7, is one of the most luminous and intensely star-forming sources in the universe with a lensing corrected FIR luminosity of 3.7 Multiplication-Sign 10{sup 13} L{sub Sun} and star formation surface density of 4200 M{sub Sun} yr{sup -1} kpc{sup -2}. We find magnification factors of 5 to 22, with lens Einstein radii of 1.''1-2.''0 and Einstein enclosed masses of 1.6-7.2 Multiplication-Sign 10{sup 11} M{sub Sun }. These observations confirm the lensing origin of these objects, allow us to measure their intrinsic sizes and luminosities, and demonstrate the important role that ALMA will play in the interpretation of lensed submillimeter sources.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2016

Bidding strategy for microgrid in day-ahead market based on hybrid stochastic/robust optimization

In this paper, we propose an optimal bidding strategy in the day-ahead market of a microgrid consisting of intermittent distributed generation (DG), storage, dispatchable DG and price responsive loads. The microgrid coordinates the energy consumption or production of its components and trades electricity in both the day-ahead and real-time markets to minimize its operating cost as a single entity. The bidding problem is challenging due to a variety of uncertainties, including power output of intermittent DG, load variation, day-ahead and real-time market prices. A hybrid stochastic/robust optimization model is proposed to minimize the expected net cost, i.e., expected total cost of operation minus total benefit of demand. This formulation can be solved by mixed integer linear programming. The uncertain output of intermittent DG and day-ahead market price are modeled via scenarios based on forecast results, while a robust optimization is proposed to limit the unbalanced power in real-time market taking account of the uncertainty of real-time market price. Numerical simulations on a microgrid consisting of a wind turbine, a PV panel, a fuel cell, a micro-turbine, a diesel generator, a battery and a responsive load show the advantage of stochastic optimization in addition to robust optimization.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2025

Refinery Integration Analysis: Pathways, Challenges, and Opportunities

Integrating biomass-derived intermediates into traditional petroleum refineries presents unique challenges and opportunities, requiring innovative analysis approaches that account for biofuel producers and refiners. Consequently, teams within the National Renewable Energy Laboratory (NREL) have developed a comprehensive refinery integration analysis framework that combines experimental data, detailed techno-economic analyses of bio-conversion pathways, and economic projections within refinery linear programming (LP) optimization models. These models enable the identification of promising bio-integration strategies tailored to specific refinery configurations, economic conditions, and production goals. They also capture upstream and downstream impacts, highlighting critical bottlenecks and research opportunities for increasing the share of biogenic feedstocks in traditional refining operations. Refinery models are also packaged into a broader bio-economy optimization framework which enables biofuel supply chain optimization with standalone biofuel production and refinery co-processing/repurposing options. This presentation discusses promising refinery bio-integration strategies along with key challenges and opportunities identified using NREL's refinery and bio-economy optimization frameworks.

09 BIOMASS FUELS↗

NASA NTRS1980

Model error estimation for large space systems

In-flight estimation of large structure model errors may have to be carried out in order to detect inevitable deficiencies in large structure controller/estimator models. These error estimates can most efficiently be obtained by the minimization of a quadratic functional of the model errors and on the subsequent analysis of the resulting optimal model error estimates. An integral operator approach to estimation leads to a geometrical interpretation of the model error estimation process. One of the significant insights gained with this interpretation is that the actual but unknown model errors can be decomposed as the sum of two distinct components that are orthogonal in some sense. One of these components is a so-called minimal error vector that retains many of the significant dynamics of the actual errors. The basic ideas in the model error estimation approach are first set forth with a two-dimensional analogy that has most of the essential features of the general estimation problem. The generalized results are then established and their application to a reference large structure model illustrated.

Rodriguez, G.↗

NASA NTRS2019

Inducing Bistability in Collapsible Tubular Masts Booms with Thin-Ply Composite Shells

Bistable rollable booms are favorable when a low strain energy requirement for the coiled state is imposed and have more controllable deployment when compared to monostable booms. An inextensional analytical model describing the bending deformation mechanics of Collapsible Tubular Mast (CTM) booms was used to determine how design variables induce bistability, or the existence of two strain energy wells in the rolled-up and unrolled states. The effects of varying lamina material, laminate layup, and shell arc geometries between different inner and outer shell segments on the second strain energy well and stiffness properties were determined for boom cross-sections formed by circular segments. The full design space for two-walled composite CTM booms was explored to evaluate the validity of the developed analytical model. Optimized CTM boom designs were experimentally characterized for comparisons against model results. The model under-predicted the stable coiled diameter of the co-cured two-walled booms by up to 8.9% and 23.4% for the individual thin shells wrapped alone.

Andrew J Lee↗

DOE OSTI2024

Integrating Human Factors in Dynamic Rideshare Assignment: Willingness-To-Pay for Delay

Dynamic ride-sharing (DRS) has been projected to be a key solution to lowering system-wide congestion. Despite recent developmental progress, demand studies for DRS suggest low levels of willingness for travelers to use such services. The disconnect between DRS system designs and user preferences limits the application impacts of DRS in the real world. Therefore, this paper aims to design a new DRS trip/vehicle assignment strategy by considering the user preferences of choices under different levels of service. In this study, an agent-based simulation approach is used to model a fleet of shared vehicles that allows DRS. An optimization model is developed to match riders to vehicles while accounting for traveler delay and delay acceptance. Travelers are also dynamically issued predictive discounts, catered to their expected willingness to pay, to incentivize them to accept longer trip delays. Results show that the proposed approach can improve system efficiency by increasing average vehicle occupancy by up to 1.0 persons/trip and DRS acceptance by up to 38.9% depending on fleet size. Additionally, congestion is eased through the decrease of empty vehicle miles traveled by up to 7.1%.

Paul, Joseph↗

DOE OSTI2025

Revenue-Maximizing Shared Parking and Electric Vehicle Charging Management in Multi-Unit Dwellings

In urban areas, searching for parking and electric vehicle (EV) charging can result in cruising, congestion, and environmental externalities. Recognizing the business opportunity of offering private parking and charging infrastructure access within multi-unit dwellings (MUDs) during daytime, we model a shared parking and EV charging management system. We maximize the revenue of MUD charging hubs in mixed land use, catering to public demand. Our approach accounts for the objectives of the two stakeholders involved: a demand model is fitted on the choices of EV charging users, and the supply model optimizes the allocation of parking and charging requests in an MUD parking lot. A binary integer linear programming model for the allocation of parking and charging spaces with a rolling horizon is integrated with matching rules that handle both parking and charging requests. In our numerical experiments in a neighborhood of Chicago, Illinois, we estimate the performance of the MUD parking and charging system with metrics that include revenue, number of matchings, and utilization rates. At any given time, MUDs with lower prices attract more charging requests, particularly those of longer duration, resulting in higher revenue and greater charging utilization. Dynamic pricing facilitates a more equitable distribution of requests; as MUD parking lots reach capacity and their fees increase, other MUDs become more competitive, attracting additional requests. Comparing our method against first-come-first-served and optimal-solution benchmarks, we demonstrate our model’s effectiveness in dynamically managing mixed parking and charging demand in MUD charging hubs.

electric vehicle, multi-unit dwelling, charging in↗

DOE OSTI2018

Preliminary Findings of the South Africa Power System Capacity Expansion and Operational Modelling Study: Preprint

Wind and solar power contract prices have recently become cheaper than many conventional new-build alternatives in South Africa and trends suggest a continued increase in the share of variable renewable energy (vRE) on South Africa's power system with coal technology seeing the greatest reduction in capacity, see 'Figure 6: Percentage share by Installed Capacity (MW)' in [1]. Hence it is essential to perform a state-of-the-art grid integration study examining the effects of these high penetrations of vRE on South Africa's power system. Under the 21st Century Power Partnership (21CPP), funded by the U.S. Department of Energy, the National Renewable Energy Laboratory (NREL) has significantly augmented existing models of the South African power system to investigate future vRE scenarios. NREL, in collaboration with Eskom's Planning Department, further developed, tested and ran a combined capacity expansion and operational model of the South African power system including spatially disaggregated detail and geographical representation of system resources. New software to visualize and interpret modelling outputs has been developed, and scenario analysis of stepwise vRE build targets reveals new insight into associated planning and operational impacts and costs. The model, built using PLEXOS, is split into two components, firstly a capacity expansion model and secondly a unit commitment and economic dispatch model. The capacity expansion model optimizes new generation decisions to achieve the lowest cost, with a full understanding of capital cost and an approximated understanding of operational costs. The operational model has a greater set of detailed operational constraints and is run at daily resolutions. Both are run from 2017 through 2050. This investigation suggests that running both models in tandem may be the most effective means to plan the least cost South African power system as build plans seen to be more expensive than optimal by the capacity expansion model can produce greater operational cost savings seen only in the operational model.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2023

gLaSDI: Parametric physics-informed greedy latent space dynamics identification

A parametric adaptive physics-informed greedy Latent Space Dynamics Identification (gLaSDI) method is proposed for accurate, efficient, and robust data-driven reduced-order modeling of high-dimensional nonlinear dynamical systems. In the proposed gLaSDI framework, an autoencoder discovers intrinsic nonlinear latent representations of high-dimensional data, while dynamics identification (DI) models capture local latent-space dynamics. Here, an interactive training algorithm is adopted for the autoencoder and local DI models, which enables identification of simple latent-space dynamics and enhances accuracy and efficiency of data-driven reduced-order modeling. To maximize and accelerate the exploration of the parameter space for the optimal model performance, an adaptive greedy sampling algorithm integrated with a physics-informed residual-based error indicator and random-subset evaluation is introduced to search for the optimal training samples on the fly. Further, to exploit local latent-space dynamics captured by the local DI models for an improved modeling accuracy with a minimum number of local DI models in the parameter space, a -nearest neighbor convex interpolation scheme is employed. The effectiveness of the proposed framework is demonstrated by modeling various nonlinear dynamical problems, including Burgers equations, nonlinear heat conduction, and radial advection. The proposed adaptive greedy sampling outperforms the conventional predefined uniform sampling in terms of accuracy. Compared with the high-fidelity models, gLaSDI achieves 17 to 2,658× speed-up with 1 to 5% relative errors.

97 MATHEMATICS AND COMPUTING↗