Data-driven Modeling Framework Research Articles

Neural dynamical operator: Continuous spatial-temporal model with gradient-based and derivative-free optimization methods

Data-driven modeling techniques have been explored in the spatial-temporal modeling of complex dynamical systems for many engineering applications. However, a systematic approach is still lacking to leverage the information from different types of data, e.g., with different spatial and temporal resolutions, and the combined use of short-term trajectories and long-term statistics. In this work, we build on the recent progress of neural operator and present a data-driven modeling framework called neural dynamical operator that is continuous in both space and time. A key feature of the neural dynamical operator is the resolution-invariance with respect to both spatial and temporal discretizations, without demanding abundant training data in different temporal resolutions. To improve the long-term performance of the calibrated model, we further propose a hybrid optimization scheme that leverages both gradient-based and derivative-free optimization methods and efficiently trains on both short-term time series and long-term statistics. We investigate the performance of the neural dynamical operator with three numerical examples, including the viscous Burgers' equation, the Navier–Stokes equations, and the Kuramoto–Sivashinsky equation. The results confirm the resolution-invariance of the proposed modeling framework and also demonstrate stable long-term simulations with only short-term time series data. In addition, we show that the proposed model can better predict long-term statistics via the hybrid optimization scheme with a combined use of short-term and long-term data.

Advanced feature engineering in microgrid PV forecasting: A fast computing and data-driven hybrid modeling framework

This study introduces an innovative framework designed to forecast the fluctuating short-term generation of photovoltaic (PV) energy in isolated microgrids. The framework relies entirely on solar irradiance data obtained from weather stations located far from the target microgrid. It implements a sophisticated decomposition approach to effectively extract an enriched collection of features from the dataset. Subsequently, a machine learning-based clustering method further enhances the forecasting process by accurately separating the relevant data points. The approach utilizes an advanced two-stage Hybrid Data Linked Model (HDLM) architecture, integrating a Layered Recurrent Neural Framework (LRNF) for prediction and a pattern identification network unit for pattern extraction. This paper demonstrates significant improvements in both the accuracy and effectiveness of estimating PV generation, achieving a mean absolute error of 1.02, a root mean square error of 2.176, and an R-squared score of 0.991. Additionally, the method reduces computing time by 15% after finalizing the input features. A comparative analysis evaluates the superior forecasting capabilities of the HDLM in remote microgrids by benchmarking it against other advanced hybrid deep learning models. The findings highlight the HDLM’s potential to greatly enhance and revolutionize the management and operation of renewable energy systems in remote microgrids.

Empowering Capacitive Devices: Harnessing Transfer Learning for Enhanced Data-Driven Optimization.

Developing data-driven models has found successful applications in engineering tasks, such as material design, process modeling, and process monitoring. In capacitive devices like deionization and supercapacitors, there exists potential for applying this data-driven machine learning (ML) model in optimizing its potential use in energy-efficient separations or energy generation. However, these models are faced with limited datasets, and even in large quantities, the datasets are incomplete, limiting their potential use for successful data-driven modeling. Here, the success of transfer learning in resolving the challenges with limited datasets was exploited. A two-step data-driven ML modeling framework named ImputeNet involving training with ML-imputed datasets and then with clean datasets was explored. Through data imputation and transfer learning, it is possible to develop a data-driven model with acceptable metrics mirroring experimental measurements. By using the model, optimization studies using the genetic algorithm were implemented to analyze the solution under the Pareto optimality. This early insight can be used in the initial stage of experimental measurements to rapidly identify experimental conditions worthy of further investigation. Moreover, we expect that the insights from these results will drive accurate predictive modeling in other fields including healthcare, genomic data analysis, and environmental monitoring with incomplete datasets.

End-to-end data-driven modeling framework for automated and trustworthy short-term building energy load forecasting

End-to-end data-driven modeling framework for automated and trustworthy short-term building energy load forecasting

Learning spatio-temporal patterns with Neural Cellular Automata.

Neural Cellular Automata (NCA) are a powerful combination of machine learning and mechanistic modelling. We train NCA to learn complex dynamics from time series of images and Partial Differential Equation (PDE) trajectories. Our method is designed to identify underlying local rules that govern large scale dynamic emergent behaviours. Previous work on NCA focuses on learning rules that give stationary emergent structures. We extend NCA to capture both transient and stable structures within the same system, as well as learning rules that capture the dynamics of Turing pattern formation in nonlinear PDEs. We demonstrate that NCA can generalise very well beyond their PDE training data, we show how to constrain NCA to respect given symmetries, and we explore the effects of associated hyperparameters on model performance and stability. Being able to learn arbitrary dynamics gives NCA great potential as a data driven modelling framework, especially for modelling biological pattern formation.

A data-driven global flood forecasting system for medium to large rivers.

Losses from catastrophic floods are driving intense efforts to increase preparedness and improve response to disastrous flood events by providing early warnings. Yet accurate flood forecasting remains a challenge due to uncertainty in modeling, calibrating, and validating a useful early warning system. This paper presents the Requisitely Simple (ReqSim) flood forecasting system that includes key variables and processes of basin hydrology and atmospheric forcing in a data-driven modeling framework. The simplicity of the modeling structure and data requirements of the system allows for customization and implementation in any medium to large rain-fed river basin globally, provided there are water level or discharge measurements at the forecast locations. The proposed system's efficacy is demonstrated in this paper through providing useful forecasts for various river basins around the world. This include 3-10-day forecasts for the Ganges and Brahmaputra rivers in South Asia, 2-3-day forecast for the Amur and Yangtze rivers in East Asia, 5-10-day forecasts for the Niger, Congo and Zambezi rivers in West and Central Africa, 6-8-day forecasts for the Danube River in Europe, 2-5-day forecasts for the Parana River in South America, and 2-7-day forecasts for the Mississippi, Missouri, Ohio, and Arkansas rivers in the USA. The study also quantifies the effect of basin size, topography, hydrometeorology, and river flow controls on forecast accuracy and lead times. Results indicate that ReqSim's forecasts perform better in river systems with moderate slopes, high flow persistence, and less flow controls. The simple structure, minimal data requirements, ease of operation, and useful operational accuracy make ReqSim an attractive option for effective real-time flood forecasting in medium and large river basins worldwide.

Data-Driven Modeling and Operation Optimization With Inherent Feature Extraction for Complex Industrial Processes

In response to the tenets of Industry 4.0, operation optimization in industrial processes has become a significant research topic. However, the uncertainties prevailing in the process pose challenges to production operations, especially the feedstock properties. In this work, the operation optimization study is performed on a distillation unit (DU), a typical plant in the industrial process. To enhance production performance, a modeling and operation optimization strategy based on feedstock property and production features is presented. One of the difficulties is how to uncover features from high-dimensional and imperfect data, where imperfect data refers to product quality data that is unavailable online. In the strategy, we inject the inherent characteristic of the process into the data-driven method to extract the feedstock property in a data-based and knowledge-oriented manner. Further, optimal feature representation and process modeling can be achieved by customizing the network structure. The operation optimization problem is formulated to adjust the top temperature of the distillation column (TTDC) to achieve satisfactory production under varying feedstock properties. Experimental results illustrate that the process model based on feedstock property and production features (PM-FP-PF) can better fit the physical process mechanism even based on incomplete information in industrial data. Industrial experiments have shown the proposed strategy has advanced generalization ability to the different feedstock properties. The proposed operation optimization strategy (OOS) improves the product qualification rate and has broad application prospects in industrial processes with similar features. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —Industrial processes suffer from a variety of disturbances that interrupt the smooth operation of the system, such as varying feedstock properties. How to deal with them is the key to improve the product qualification rate. In this work, we propose a data-driven modeling and operation optimization framework to improve product quality under varying feedstock properties. The dynamic variation characteristics of the feedstock properties can be obtained by analyzing the physical properties of the production unit. This is used as a basis for representing and extracting feedstock properties in a data-driven way. Further, a process model based on feedstock property and production features (PM-FP-PF) is built to predict product quality. An operation optimization strategy with production capacity consideration is established. It can determine the optimal operation action required by the current system, mitigating the uncertainty of feedstock property. This operation optimization system has been applied to a distillation unit in the hydrofining process. The application results show that the process model achieves satisfactory estimation accuracy, and the operation optimization strategy has improved production performance.

Performance evaluation of deep learning based stream nitrate concentration prediction model to fill stream nitrate data gaps at low-frequency nitrate monitoring basins

Accurate and frequent nitrate estimates can provide valuable information on the nitrate transport dynamics. The study aimed to develop a data-driven modeling framework to estimate daily nitrate concentrations at low-frequency nitrate monitoring sites using the daily nitrate concentration and stream discharge information of a neighboring high-frequency nitrate monitoring site. A Long Short-Term Memory (LSTM) based deep learning (DL) modeling framework was developed to predict daily nitrate concentrations. The DL modeling framework performance was compared with two well-established statistical models, including LOADEST and WRTDS-Kalman, in three selected basins in Iowa, USA: Des Moines, Iowa, and Cedar River. The developed DL model performed well with NSE >0.70 and KGE >0.70 for 67% and 79% nitrate monitoring sites, respectively. DL and WRTDS-Kalman models performed better than the LOADEST in nitrate concentration and load estimation for all low-frequency sites. The average NSE performance of the DL model in daily nitrate estimation is 20% higher than that of the WRTDS-Kalman model at 18 out of 24 sites (75%). The WRTDS-Kalman model showed unrealistic fluctuations in the estimated daily nitrate time series when the model received limited observed nitrate data (less than 50) for simulation. The DL model indicated superior performance in winter months' nitrate prediction (60% of cases) compared to WRTDS-Kalman models (33% of cases). The DL model also better represented the exceedance days from the USEPA maximum contamination level (MCL). Both the DL and WRTDS-Kalman models demonstrated similar performance in annual stream nitrate load estimation, and estimated values are close to actual nitrate loads.

Sparse Identification of Fractional Chaotic Systems based on the time-domain data

The complexity inherent in defining and computing fractional derivatives renders the development of a data-driven modeling framework for fractional-order systems more formidable than for their integer-order counterparts. This study introduces a methodology for sparsely identifying fractional chaotic systems by leveraging time-domain data to ascertain the system’s governing equations. Initially, we establish a sparse identification framework specifically tailored for fractional order systems and introduce a joint iterative thresholding method designed to identify these systems’ fractional and integer order components concurrently. Moreover, this study conducts a comparative analysis of two error criteria for model selection. It introduces a strategy predicated on minimizing the distance to balance sparsity and model fitting error optimally. To validate the efficacy and precision of the proposed methodology, numerical simulations were conducted on fractional order simplified Lorenz and Chua’s circuits, affirming the robustness and accuracy of our approach.

Data-Driven Overlapping-Track Profile Modeling in Cold Spray Additive Manufacturing

Cold spray additive manufacturing is an emerging solid-state deposition process that enables large-scale components to be manufactured at high-production rates. Control over geometry is important for reducing the development and growth of defects during the 3D build process and improving the final dimensional accuracy and quality of components. To this end, a machine learning approach has recently gained interest in modeling additively manufactured geometry; however, such a data-driven modeling framework lacks the explicit consideration of a depositing surface and domain knowledge in cold spray additive manufacturing. Therefore, this study presents surface-aware data-driven modeling of an overlapping-track profile using a Gaussian Process Regression model. The proposed Gaussian Process modeling framework explicitly incorporated two relevant geometric features (i.e., surface type and polar length from the nozzle exit to the surface) and a widely adopted Gaussian superposing model as prior domain knowledge in the form of an explicit mean function. It was shown that the proposed model could provide better predictive performance than the Gaussian superposing model alone and the purely data-driven Gaussian Process model, providing consistent overlapping-track profile predictions at all overlapping ratios. By combining accurate prediction of track geometry with toolpath planning, it is anticipated that improved geometric control and product quality can be achieved in cold spray additive manufacturing.

Enhancing Streamflow Prediction Physically Consistently Using Process-Based Modeling and Domain Knowledge: A Review

Streamflow prediction (SFP) constitutes a fundamental basis for reliable drought and flood forecasting, optimal reservoir management, and equitable water allocation. Despite significant advancements in the field, accurately predicting extreme events continues to be a persistent challenge due to complex surface and subsurface watershed processes. Therefore, in addition to the fundamental framework, numerous techniques have been used to enhance prediction accuracy and physical consistency. This work provides a well-organized review of more than two decades of efforts to enhance SFP in a physically consistent way using process modeling and flow domain knowledge. This review covers hydrograph analysis, baseflow separation, and process-based modeling (PBM) approaches. This paper provides an in-depth analysis of each technique and a discussion of their applications. Additionally, the existing techniques are categorized, revealing research gaps and promising avenues for future research. Overall, this review paper offers valuable insights into the current state of enhanced SFP within a physically consistent, domain knowledge-informed data-driven modeling framework.

Hybrid physics-guided data-driven modeling for generalizable geometric accuracy prediction and improvement in two-photon lithography

Two-photon lithography (TPL) is an additive manufacturing technique to produce three-dimensional (3D) micro- and nano-scale structures. Geometric accuracy is of vital importance to ensure the quality and functionality of additively manufactured 3D structures. However, there exists limited research on modeling and improving the geometric accuracy of TPL. Moreover, there is a lack of understanding of the influence of TPL process parameters (e.g., scanning rate, laser power) and structure design on the resulting geometric accuracy. This paper presents a new hybrid physics-guided data-driven modeling framework for generalizable cross-design and cross-parameter geometric accuracy prediction and improvement. The proposed model decomposes TPL-produced geometric features into two levels: a global trend and a spatial trend. Guided by physical laws that govern voxel dimensions, we construct the global trend as a function of TPL process parameters. Our new findings reveal strong linear relationships among the parameters of the global trend model across structure design dimensions, which enable generalizable predictive modeling. Moreover, the spatial trend captures the spatially varying patterns in geometric features. A large-scale experimental design consisting of six hemisphere sizes and six parameter combinations is carried out to thoroughly test the effectiveness of the proposed method. Our modeling approach demonstrates high accuracy in predicting the geometric error of a target design with knowledge derived from other designs and parameters. The average prediction errors for radius and height are 5.23% and 4.66%, respectively. Furthermore, the proposed compensation strategy is shown to reduce the geometric errors from 22.19% to 3.21% for radius, and from 12.18% to 4.96% for height. Meanwhile, the within-sample variations are greatly reduced, indicating improved process consistency. To the best of our knowledge, this study is among the first to develop a generalizable method for cross-design and cross-parameter geometric accuracy modeling and improvement in TPL.

Big data-driven TBM tunnel intelligent construction system with automated-compliance-checking (ACC) optimization

TBM tunneling in subsea areas with adverse geological conditions presents potential risks due to non-compliant tunneling strategies resulting from manual adjustments and untimely communications. This study proposes an innovative subsea TBM tunnel intelligent construction system, featuring automated-compliance-checking (ACC) optimization, to assess feasibility through a case study. The key ingredient of the system is an integrated data-driven model framework comprising of a geological identification model based on fuzzy set theory and Dempster-Shafer (D-S) fusion theory and a machine learning-based TBM construction strategy ACC optimization model. In addition, a real-time data services scheme is established to manage TBM engineering big data, ensuring its effective utilization. Implemented in the PRDWRA project's F27 fault zone, the system identified greater stratum complexity than previously known, with potential dual faults. Post-ACC optimization, it achieved a 13.6 % increase in advance rate, maintained consistent slurry pressure, and reduced the deviation between optimized and expected values by 57.1 %. Finally, drawing upon statistical data sourced from project stakeholders, the system's deployment yielded a 9 % cycle time reduction, and a 27 % cost saving, with 17 % from reduced construction times and 9 % from lower accident rates. These results confirm the strategy's compliance with construction codes, significantly reducing risk and improving tunneling efficiency. The results confirm that the operational strategy adheres to construction code requirements, substantially reducing construction risks and effectively enhancing tunneling efficiency.

A Bi-Party Engaged Modeling Framework for Renewable Power Predictions With Privacy-Preserving

This paper presents a pioneering study in developing data-driven models for predicting the future renewable power out-put sequence via using numerical weather predictions of multiple sites without breaching the data privacy. A novel bi-party engaged data-driven modeling framework (BEDMF) is developed to enable efficiently learning local and global latent features serving as de-centralized data for data-driven modeling with privacy-preserv-ing. The BEDMF contains two stages, the pretraining stage and fine-tuning. At the pretraining stage of the BEDMF, local latent features are learned via local models and then aggregated to pro-duce the global latent feature via a global model. At the fine-tuning stage, local latent features are learned using local data and global latent feature from the previous iteration. The proposed frame-work enables capturing spatial-temporal patterns among multiple sites to further benefit modeling in renewable power prediction tasks. Meanwhile, the framework preserves the data privacy via isolating data locally in the clients. To verify the advantage of the BEDMF, a comprehensive computational study is conducted to benchmark it against famous baselines. Results show that the BEDMF achieve at least 3% improvements on average.

A-posteriori analysis of a data-driven filtered wrinkled flamelet model for thermodiffusively unstable premixed flames

State-of-the-art turbulent combustion models do not account for the effects of intrinsic flame instabilities, which are known to have a non-negligible effect, under technically relevant conditions, in thermodiffusively unstable flames such as those of hydrogen-based fuels. In this work, a data-driven modeling framework for filtered, laminar, self-wrinkling flames subject to intrinsic instabilities is presented and proposed as a stepping stone for the development of turbulent combustion models for large eddy simulation. In this context, data-driven refers to the use of small- and medium-sized resolved simulations, explicitly filtered in physical space, as data sources for the development of filtered tables. For consistency, all the unclosed terms of the filtered governing equations are then written according to the filtered tabulated chemistry formalism. The a-posteriori analysis of the modeling framework indicates that medium-scale simulations, which conversely to the small-scale ones feature at least one characteristic flame-finger, are needed for the generation of the data-driven tables. Furthermore, a laminar wrinkling factor, accounting for the sub-filter cellular wrinkling, should also be used. The presented results show promise for the extension of this modeling framework to the simulation of turbulent flames, as well as to multi-step chemistry and detailed thermo-transport modeling. Statement of SignificanceIt is nowadays well-known that intrinsic flame instabilities have a leading order impact on the propagation of premixed flames in thermodiffusively unstable mixtures, such as lean hydrogen-air premixed flames. This work presents the first a-posteriori analysis of a combustion model for filtered, albeit laminar, large-scale, intrinsically unstable premixed flames. The novelty of the presented data-driven model lies in the use of data obtained from filtering direct numerical simulations performed for paradigmatic small and medium-scale cases, instead of standard one-dimensional flamelets.

Analysis of car–following behaviors based on data–driven and theory–driven car–following models: Heterogeneity and asymmetry

The data–driven car–following model can realistically depict driving behavior, and is widely used in simulating the longitudinal movements of vehicles. However, it has some unexpected results such as uncontrollable output and potential security risks, making it challenging to apply practically. To address this issue, this paper proposes a combination model that integrates the theory–driven model (IDM) with the data–driven model (PSO–Bi–LSTM). This novel integration is referred to as the IDM–Bi–LSTM combination car–following model. This combination model offers two key features. First, to accurately predict vehicle trajectories, rather than manually configuring the number of neurons in the hidden layer and iterations, we employ the Particle Swarm Optimization (PSO) algorithm to optimize these parameters in the data–driven model. Consequently, we establish a PSO–Bi–LSTM data–driven model framework. Second, our combination model integrates the prediction outcomes of the IDM model with those of the PSO–Bi–LSTM neural network. This amalgamation retains the controllability and security offered by the theory–driven model, while also leveraging the prediction accuracy of the data–driven model. To evaluate the effectiveness of our model, we conduct numerical simulations of heterogeneous driving behaviors. The results reveal a significant reduction in error for the combination car–following model, exhibiting reductions of 60.2% and 54.4% compared to the individual IDM theory–driven model and PSO–Bi–LSTM data–driven model, respectively. Additionally, the simulation outcomes for asymmetric driving behavior further confirm the superior performance of the combination model.

Computationally efficient neural hybrid automaton framework for learning complex dynamics

This paper proposes a computationally efficient and effective data-driven modeling framework for dynamical systems. The proposed modeling framework employs a collection of shallow neural networks known as Extreme Learning Machines (ELMs) to model local system behaviors along with data-driven inferred transitions among local models to establish a neural hybrid automaton model. First, the sampled system inputs are mapped to the corresponding feature spaces to obtain data-driven partitions, which subsequently define the transitions and invariants of the neural hybrid automaton model through a novel data-driven mode clustering process. Then, a collection of ELMs are trained to approximate the local dynamics. The learning processes integrate a segmented data merging procedure for location identification and a local dynamics modeling process. The proposed neural hybrid automaton models can capture behaviors of complex dynamical systems with high modeling precision but significantly lower computational complexities in computationally expensive tasks such as training and verification, which are traditionally considered to be computationally expensive tasks for neural network models. A computationally efficient set-valued reachability analysis method which is commonly used in safety verification is then developed based on interval analysis and a novel Split and Combine process. Finally, applications to modeling the limit cycle and human handwritten motions are presented to show the effectiveness and efficiency of our approach.

Data-driven surrogate modeling for global sensitivity analysis and the design optimization of medical waste shredding systems

Excessive medical waste is generated in various medical facilities, especially post-Covid. Recently, sterilization-based shredding systems are being widely used to treat medical waste; however, such systems are commonly over-designed, due to load variation among various treatment facilities. To overcome this challenge, a data-driven surrogate model framework is proposed to perform sensitivity analysis and design optimization based on different loading environments and capacity requirements. The stress estimation surrogate model was generated using the Latin hypercube sampling (LHS), which can represent the overall information of the design area with a limited sample. Furthermore, the data-driven model significantly reduced the computational time as increased numbers of samples were generated from the data-driven surrogate model, instead of finite element analysis (FEA). Two distinct design capacities of the shredding system were used for assessing the effectiveness of the present framework. The results demonstrated that surrogate model-based sensitivity analysis is an efficient approach to developing system designs based on various input and output conditions. The proposed approach mitigates the tremendous potential of the surrogate model, significantly reduces computational costs associated with sensitivity analysis, and yields promising accuracy for the optimization process. This method suggests a computationally efficient optimization method for different shredding capacities. Additionally, the proposed method does not remain at simply optimizing the existing system but provides optimization values for various capacity systems using the data of the existing design, therefore it can be applied to any mechanical system for designing an optimized and compact system.

Developing a data-driven modeling framework for simulating a chemical accident in freshwater

Chemical accidents in freshwater pose threats to public health and aquatic ecosystems. Process-based models (PBMs) have been used to identify spatiotemporal chemical distributions in natural water. However, their computationally expensive simulations can hinder timely incident responses, which are crucial for minimizing negative impacts. Therefore, this study proposes a site-specific data-driven model (DDM) to supplement PBM-based chemical accident simulations. A convolutional neural network (CNN) was employed as the DDM because of its outstanding performance in capturing spatial patterns. Our model was developed to facilitate chemical accident simulations in the Namhan River, South Korea. The model datasets were generated using the PBM simulation outputs from toluene accident scenarios. Our DDM showed a Nash-Sutcliffe-efficiency of 0.94 and a root-mean-square-error of 0.023 μg/L for the validation set. Its computational time was approximately 64 times faster than that of PBMs. In addition, this study interpreted the DDM results using SHapley Additive exPlanations (SHAP). The SHAP findings highlighted the influential role of distance from the accident site in this study. Overall, this study demonstrated the applicability of our modeling approach in freshwater chemical accidents by providing rapid spatial distribution results complementing PBM simulations.

Data-driven physical fields reconstruction of supercritical-pressure flow in regenerative cooling channel using POD-AE reduced-order model

In order to effectively estimate the physical fields of active cooling channel with supercritical pressure hydrocarbon fuel, a novel data-driven reduced-order model framework is firstly proposed in the present work, which is established via combining reduced-order modeling method based on proper orthogonal decomposition and autoencoder neural network (POD-AE) with Kriging surrogate model. This framework mainly contains offline stage and online stage. Preliminary dimension reduction and feature capture of high-dimensional physical fields data is conducted using POD in the offline stage, and low-dimensional reduced-order models (ROMs) are constructed by the linear combination of orthogonal bases and feature coefficients. Specially, feature coefficients of ROMs are used to trained an AE, and then lower-dimensional secondary reduced-order models (2nd-ROMs) are established by secondary compression for ROMs using the trained AE. Furthermore, the Kriging model is trained for implicitly mapping boundary conditions or temperature data from the sensors on the bottom surface to the established 2nd-ROMs. In the online stage, physical fields estimation under new boundary conditions or wall temperature monitoring based on temperature data of sensors can be quickly fulfilled using this framework. Fifty groups of test conditions are considered to demonstrate the accuracy and efficiency of the POD-AE ROM framework. The results prove that it shows good efficiency, accuracy in estimating and monitoring the physical fields of the cooling channel with supercritical pressure n-dodecane within sample space. Compared with the traditional POD-based ROM framework, the proposed framework still achieved acceptable accuracy under all testing conditions when the original data was compressed to extremely low dimensions. And the calculation time only slightly increased.