Hybrid Modeling Framework Research Articles

A Multi-Model Output Fusion Strategy Based on Various Machine Learning Techniques for Product Price Prediction

In the digital era, precise product price prediction becomes crucial for enhancing competitiveness in the online marketplace. This paper presents a hybrid model framework that enhances the accuracy of online product price predictions by integrating several machine learning algorithms, including Linear Regression, Decision Trees, and Gradient Boosting. The objective of this approach is to leverage the distinct advantages of each model to address their individual limitations and create a robust unified predictive model. This integration allows for improved handling of complex data relationships and diverse market dynamics that are typical in online sales environments. The results demonstrate that the hybrid model achieves superior prediction accuracy, as reflected in reduced Mean Absolute Error (MAE) and Root Mean Square Error (RMSE) metrics, and an exceptionally high R ² value compared to single-model approaches. These outcomes underscore the efficacy of combining multiple predictive models to enhance the precision of price forecasts in the highly competitive online marketplace. This model fusion strategy not only provides more accurate pricing predictions but also offers strategic insights into the optimal pricing strategies for businesses looking to enhance their market position.

Soil moisture estimation in the unsaturated zone using surface wave measurements and hybrid modeling framework

Abstract Soil moisture plays a critical role in influencing various facets of ecosystem dynamics. The preference for measuring soil moisture without physical intrusion has been desirable for precise assessments while minimizing disruptions to soil structural, hydraulic, and biological characteristics. In this study, we explored the potential of surface elastic waves as a proxy to estimate soil moisture profiles to a depth of 1.05 m at intervals of 0.1 m. We conducted a multichannel analysis of surface waves (MASW) survey and measured soil moisture at depths of 0.15 m and 0.35 m. To address the limited availability of soil moisture measurements, we developed a mechanistic soil moisture model as a substitute for measured soil moisture profiles. Our results showed that as soil moisture increased, the propagation of surface waves became more pronounced due to reduced frictional resistance. However, it was not straightforward to link measured surface wave responses and subsurface soil moisture profile. To address these challenges, we developed a convolutional neural network (CNN) with the inputs of the frequency-velocity and frequency-wavenumber images obtained from the measured surface waves. We found that the integration of MASW and CNN proved effective in estimating soil moisture profiles to a depth of 1.05 m at intervals of 0.1 m without causing disturbances to the soil (MAE = 0.0035 m3 m−3). This study suggested that the combined use of surface waves and CNN hold promise in measuring soil moisture profiles without physical disruptions. As such, the proposed approach could serve as a viable alternative to noninvasive soil moisture sensors.

Multi-temperature capable enhanced bidirectional long short term memory-multilayer perceptron hybrid model for lithium-ion battery SOC estimation

In this study, we propose a novel hybrid modeling framework for State of Charge (SOC) estimation across a broad temperature spectrum. First, we build a hybrid model to optimize stacked layers of stacked bidirectional long short term memory networks by introducing dropout mechanisms. At the same time, we also optimize the traditional multi-layer perceptron model to ResMLP, which is improved by introducing residual linkage, and then integrate the two optimization models. Finally, the synergistic effect and attention mechanism of genetic algorithm and particle swarm optimization are used to optimize its parameters. We then rigorously tested the model on nine datasets, including HPPC, DST and BBDST, at different temperatures of 5 °C, 15 °C and 35 °C. Using MAE, RMSE and MAXE benchmarks, our research results show that the proposed hybrid model outperforms the benchmark algorithm, achieving significantly enhanced performance and higher accuracy, and the maximum SOC estimation error is kept below 4.53 %. In addition, experimental evaluation at different temperatures shows the robustness and adaptability of the proposed algorithm.

An integrated approach toward digital design and simulation of the automated overbraiding process for composite manufacturing

The study presents a new integrated hybrid modeling framework that combines kinematic models with Finite Element Analysis (FEA) to simulate the overbraiding process on non-circular and variable cross-section mandrels in composite manufacturing. By combining the computational efficiencies of kinematic models with the detailed physical insights from FEA simulations, this hybrid method provides a holistic solution for designing and prototyping overbraided structures. Specifically applied to a complex rectangular-to-square mandrel, the approach accurately predicts braid angles, validated against physical braiding experiments covering a range of target angles. The achieved results highlight the model's accuracy and emphasize its potential to boost the efficiency and precision of overbraiding in industrial settings, thereby reducing the need for costly and time-consuming physical braiding iterations.

Hybrid local energy markets: Incorporating utility function-based peer risk attributes, renewable energy integration, and grid constraints analysis

This study proposes a novel hybrid Local Energy Market (LEM) trading framework meticulously designed for efficient energy trading among distribution network participants. The proposed LEM hybrid modeling framework aims to maximize social welfare by considering the behavior of market participants and incorporating network constraints into the transactional framework. To address the consumption behavior of market participants, the concept of the utility function with peer risk attributes is employed, differentiating between flexible and inflexible demands. Additionally, it adeptly manages various generation types, including diesel generators, wind and solar generators, and storage, each characterized by a unique cost function. The investigation extends to the analysis of the Japan Electric Power Exchange market (JEPX), taking into account the residential electricity demand in Tokyo, Japan, by comparing with community-based (CB) and peer-to-peer (P2P) markets and scrutinizing market player behavior across multiple scenarios. These scenarios include comparisons of different market structures, variations in prices, considerations of grid constraints, and diverse weather scenarios. The proposed framework undergoes rigorous evaluation utilizing the IEEE 33-bus and 69-bus standard test systems, with results demonstrating its practicality, superiority of the proposed market compared to the CB and P2P markets, and providing valuable insights into the intricate interplay between market players’ behavior and the dynamics of diverse market structures, price fluctuations, grid constraints, and weather scenarios.

Intelligent crude oil price probability forecasting: Deep learning models and industry applications

The crude oil price has been subject to periodic fluctuations because of seasonal changes in industrial demand and supply, weather, natural disasters and global political unrest. An accurate forecast of crude oil prices is of utmost importance for decision makers and industry players in the energy sector. Despite this, the volatility of crude oil prices contributes to the uncertainty of the energy industry, which was particularly challenging following the recent global spread of the COVID-19 epidemic and the Russia–Ukraine conflict. This paper proposes a hybrid deep learning (DL) modelling framework to deal with the volatility of crude oil prices, applying ensemble empirical mode decomposition (EEMD), convolutional neural network (CNN) and bidirectional long short-term memory (BiLSTM) integrated with quantile regression (QR); named EEMD-CNN-BiLSTM-QR. Two real-world datasets on crude oil prices from the West Texas Intermediate and Brent Crude Oil markets were employed to validate the EEMD-CNN-BiLSTM-QR hybrid modelling framework. Given that the probability density forecast can capture uncertainty, an in-depth analysis was carried out and prediction accuracy calculated. The findings of this study demonstrate that the proposed EEMD-CNN-BiLSTM-QR DL modelling framework, which uses the probability density forecast method, is superior to other tested models in terms of its ability to forecast crude oil prices. The novelty of this study stems mainly from its use of QR, which allows for the description of the conditional distribution of predicted variables and the extraction of more uncertain information for probability density forecasts.

Non-linear relationship between built environment and active travel: A hybrid model considering spatial heterogeneity

Exploring the mechanisms between the built environment and active travel is crucial for promoting green transportation and fostering the sustainable development of cities. Existing literature focuses on the correlation between the built environment and active travel in urban centers, with limited studies on suburban environments, ignoring the implications of spatial heterogeneity. This paper conducts a comprehensive spatio-temporal analysis of suburban residents’ active travel behavior and explores the nonlinear relationship between suburban built environment and active travel. A novel hybrid modeling framework that combines eXtreme Gradient Boosting and Multi-scale Geographic Weighted Regression is introduced to forecast suburban active travel demand with the consideration of the nonlinearity and spatial heterogeneity in parameter estimates. Shapley additive explanation is used to elucidate the non-linear relationship between built environment variables and active travel. The results indicate that the proposed hybrid model performs the best with high predictive power and interpretability. The density of tourist attractions, transportation facilities, and household properties emerges as the three most influential factors affecting residents’ active travel behavior. Social-economic attributes contribute 15.70% to the prediction, while three categories of built environment variables (accessibility, transportation facilities, and land use) contribute 7.31%, 5.13%, and 71.87%, respectively. The hybrid model appears to be effective in identifying the nonlinear relationship and threshold effects between built environment variables and active travel. Besides, the model provides actionable insights into designing sustainable and efficient suburban environments, supporting targeted planning and policy-making efforts.

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.

AI hybrid survival assessment for advanced heart failure patients with renal dysfunction

Renal dysfunction (RD) often characterizes the worse course of patients with advanced heart failure (AHF). Many prognosis assessments are hindered by researcher biases, redundant predictors, and lack of clinical applicability. In this study, we enroll 1736 AHF/RD patients, including data from Henan Province Clinical Research Center for Cardiovascular Diseases (which encompasses 11 hospital subcenters), and Beth Israel Deaconess Medical Center. We developed an AI hybrid modeling framework, assembling 12 learners with different feature selection paradigms to expand modeling schemes. The optimized strategy is identified from 132 potential schemes to establish an explainable survival assessment system: AIHFLevel. The conditional inference survival tree determines a probability threshold for prognostic stratification. The evaluation confirmed the system’s robustness in discrimination, calibration, generalization, and clinical implications. AIHFLevel outperforms existing models, clinical features, and biomarkers. We also launch an open and user-friendly website www.hf-ai-survival.com, empowering healthcare professionals with enhanced tools for continuous risk monitoring and precise risk profiling.

Enhanced nitrous oxide emission factors due to climate change increase the mitigation challenge in the agricultural sector.

Effective nitrogen fertilizer management is crucial for reducing nitrous oxide (N2O) emissions while ensuring food security within planetary boundaries. However, climate change might also interact with management practices to alter N2O emission and emission factors (EFs), adding further uncertainties to estimating mitigation potentials. Here, we developed a new hybrid modeling framework that integrates a machine learning model with an ensemble of eight process-based models to project EFs under different climate and nitrogen policy scenarios. Our findings reveal that EFs are dynamically modulated by environmental changes, including climate, soil properties, and nitrogen management practices. Under low-ambition nitrogen regulation policies, EF would increase from 1.18%-1.22% in 2010 to 1.27%-1.34% by 2050, representing a relative increase of 4.4%-11.4% and exceeding the IPCC tier-1 EF of 1%. This trend is particularly pronounced in tropical and subtropical regions with high nitrogen inputs, where EFs could increase by 0.14%-0.35% (relative increase of 11.9%-17%). In contrast, high-ambition policies have the potential to mitigate the increases in EF caused by climate change, possibly leading to slight decreases in EFs. Furthermore, our results demonstrate that global EFs are expected to continue rising due to warming and regional drying-wetting cycles, even in the absence of changes in nitrogen management practices. This asymmetrical influence of nitrogen fertilizers on EFs, driven by climate change, underscores the urgent need for immediate N2O emission reductions and further assessments of mitigation potentials. This hybrid modeling framework offers a computationally efficient approach to projecting future N2O emissions across various climate, soil, and nitrogen management scenarios, facilitating socio-economic assessments and policy-making efforts.

Probabilistic assessment of rockburst risk in TBM-excavated tunnels with multi-source data fusion

In recent years, tunnel boring machines (TBMs) have become extensively utilized in underground engineering projects. However, as a prevalent type of dynamic geological hazard, rockburst poses a serious threat to the safety of personnel, equipment, and property. To ensure the safe advancement of TBMs, we integrate the data of microseismic monitoring, TBM excavation, and surrounding rock and establish multiple probabilistic assessment models of rockburst risk using probabilistic ensemble learning and quantum particle swarm optimization. In order to identify the most optimal model for geological engineers, a comprehensive evaluation system is devised based on metrics like accuracy, Cohen’s kappa, and F1-score. This system provides a thorough assessment of the models’ global and local generalization performance. The results indicate that the classification and regression tree-extremely randomized trees (CART-ERT) hybrid model achieves the highest score, demonstrating superior generalization performance with an accuracy of 93.06% and a Cohen’s kappa of 0.9074. Moreover, the F1-scores for no rockburst, low rockburst, moderate rockburst, and strong rockburst are 0.9412, 0.9444, 0.9189, and 0.9189, respectively. Based on the operational framework of the CART-ERT hybrid model, a user-friendly graphical user interface (GUI) system is developed. This significantly enhances the practicality and deployability of the model. Through application in a TBM diversion tunnel project in Xinjiang, the on-site early-warning accuracy of rockburst with the GUI system reaches 90%. Notably, the GUI system maintains high early-warning sensitivity and reliability for high-intensity rockburst such as moderate and strong ones. Lastly, to enhance the model’s interpretability, a variable importance measure (VIM) analysis on 14 features extracted from three types of heterogeneous data is conducted to assess their contributions to the early warning of rockburst. We discover that the cumulative energy change rate of microseismic events exhibits the highest importance score, indicating its crucial role in rockburst early warning.

A hybrid model coupling process-driven and data-driven models for improved real-time flood forecasting

Accurate and reliable incoming flood forecasting is an important prerequisite for flood warning, flood risk analysis and reservoir flood control operation. This paper proposes a hybrid model for real-time flood forecasting that couples process-driven hydrological models (HMs) with data-driven models (DDMs). The generic hybrid model framework adds DDMs as the post-processing procedure for residual correction to the original results of HMs, and considers multiple uncertainties in input data, parameter and model structure simultaneously. The performance of the hybrid model is evaluated comprehensively in terms of deterministic forecast accuracy, interval forecast reliability, and the reliability and sharpness of probabilistic forecast. Taking the multireservoir system at the east Pi River as a study case, the results indicate that: (1) Compared to the benchmark model (ensemble XAJ model), the hybrid model with additional residual analysis show a significant improvement. The average continuous ranked probability score (CRPS) metric values calculated by the Stacking-Hybrid model improved by 71.5 %, 67.0 % and 38.1 % in the three data samples. Furthermore, the adaptability of the Stacking-Hybrid model for residual correction during short-duration intense rainfall events has been validated, with the relative error of the peak discharge improved to within ± 10 %. (2) The Stacking-Hybrid model, which also takes into account structure uncertainty, is able to better exploit the combined advantages and improve the stability of the model performance compared to those that only apply a single DDM. (3) When the number of iterations within the BOA reaches 300, the parameter optimization process is capable to search for the hyperparameters that bring out the best performance of the DDMs. (4) When the ensemble size reaches 200, the uncertainty of HM parameters can be fully defined, and the consumed computational resources can be controlled within an acceptable bound while ensuring stable model performance. Overall, the hybrid model that takes into account multiple sources of uncertainty generates both interval and probabilistic forecast in addition to deterministic forecast, which can provide richer risk information for subsequent flood warning and reservoir operation, making the flood prevention decisions more reliable and scientific.

Molecular dynamics simulation of CoCrFeMnNi with twin boundaries under high-speed impact

Based on the hybrid modeling framework of atomic scale and continuum, molecular dynamics (MD) was the method to study the shock wave, elastic-plastic dual-wave, and microstructure of CoCrFeMnNi high entropy alloy (HEA) with twin boundary under high-speed impact. The interaction between dislocation and twin interfaces is significant to the plastic deformation of HEA, but research on them as initial defects is still limited. Therefore, this article simulates and analyzes the impact velocity and twin spacing and proves that HEA with twin boundaries can synergistically improve strength and flexibility by comparing the wave simulation process and variation of spalling strength between HEA with TB and crystal Ni. The simulation results show that TB affects the propagation of shock waves in HEA and provides deformation sites for the generation of dislocations. Unlike single-crystal HEA, there is a smoother impact response process, and the maximum tensile stress during the fracture stage can reach 41 GPa, which is about 34.12% higher than that of single-crystal HEA. The research results may contribute to a better understanding of HEA with TB and help apply complex load scenarios such as explosive loads.

Large Language Model Inference Acceleration Based on Hybrid Model Branch Prediction

As the size of deep learning models continues to expand, the elongation of inference time has gradually evolved into a significant challenge to efficiency and practicality for autoregressive models. This work introduces a hybrid model acceleration strategy based on branch prediction, which accelerates autoregressive model inference without requiring retraining and ensures output consistency with the original model. Specifically, the algorithm employs two models with different parameter sizes aimed at the same task. The smaller model generates a series of potential tokens that are then parallelly validated by the larger model to determine their acceptability. By orchestrating the workflow of the large and small models through a branch-prediction strategy, the algorithm conceals the validation time of the larger model when predictions are successful, thereby accelerating inference. We propose a binomial distribution-based prediction function that blends theoretical principles with empirical evidence, specifically designed for the nuanced requirements of accelerating inference within a hybrid model framework. The entire algorithm was designed and implemented on the llama model for text generation and translation tasks. The experimental results indicate significant improvements. The proposed algorithm achieves a 1.2× to 3.4× increase in inference speed compared to the original model, consistently outperforming the speculative sampling inference acceleration algorithm.

A dynamic exploratory hybrid modelling framework for simulating complex and uncertain system

Complex disaster systems involve various components and mechanisms that could interact in complex ways and change over time, leading to significant deep uncertainty. Due to deep uncertainty, decision-makers have severe inadequacy of knowledge and often encounter unpredictable surprises that may emerge in the future, thus making it difficult to specify appropriate models and parameters to describe the system of interest. In this paper, we propose a dynamic exploratory hybrid modeling framework that fits data, models, and computational experiments together to simulate complex systems with deep uncertainty. In the framework, one needs to develop multiple plausible models from a hybrid modeling perspective and perform enormous computational experiments to explore the diversity of future scenarios. Real-time data is then incorporated into diverse forecasts to dynamically adjust the simulation system. This ultimately enables an ongoing modeling and analysis process in which deep uncertainty would be gradually mitigated. Our approach has been applied to a human-involved car-following system simulation under complex traffic conditions. The results show that the proposed approach can improve the prediction accuracy while enhancing the sensitivity of the simulation system to uncertain changes in the system of interest.

Predicting Antibiotic Resistance and Assessing the Risk Burden from Antibiotics: A Holistic Modeling Framework in a Tropical Reservoir.

Predicting the hotspots of antimicrobial resistance (AMR) in aquatics is crucial for managing associated risks. We developed an integrated modeling framework toward predicting the spatiotemporal abundance of antibiotics, indicator bacteria, and their corresponding antibiotic-resistant bacteria (ARB), as well as assessing the potential AMR risks to the aquatic ecosystem in a tropical reservoir. Our focus was on two antibiotics, sulfamethoxazole (SMX) and trimethoprim (TMP), and on Escherichia coli (E. coli) and its variant resistant to sulfamethoxazole-trimethoprim (EC_SXT). We validated the predictive model using withheld data, with all Nash-Sutcliffe efficiency (NSE) values above 0.79, absolute relative difference (ARD) less than 25%, and coefficient of determination (R2) greater than 0.800 for the modeled targets. Predictions indicated concentrations of 1-15 ng/L for SMX, 0.5-5 ng/L for TMP, and 0 to 5 (log10 MPN/100 mL) for E. coli and -1.1 to 3.5 (log10 CFU/100 mL) for EC_SXT. Risk assessment suggested that the predicted TMP could pose a higher risk of AMR development than SMX, but SMX could possess a higher ecological risk. The study lays down a hybrid modeling framework for integrating a statistic model with a process-based model to predict AMR in a holistic manner, thus facilitating the development of a better risk management framework.

A hybrid modeling framework for generalizable and interpretable predictions of ICU mortality across multiple hospitals

The development of reliable mortality risk stratification models is an active research area in computational healthcare. Mortality risk stratification provides a standard to assist physicians in evaluating a patient’s condition or prognosis objectively. Particular interest lies in methods that are transparent to clinical interpretation and that retain predictive power once validated across diverse datasets they were not trained on. This study addresses the challenge of consolidating numerous ICD codes for predictive modeling of ICU mortality, employing a hybrid modeling approach that integrates mechanistic, clinical knowledge with mathematical and machine learning models . A tree-structured network connecting independent modules that carry clinical meaning is implemented for interpretability. Our training strategy utilizes graph-theoretic methods for data analysis, aiming to identify the functions of individual black-box modules within the tree-structured network by harnessing solutions from specific max-cut problems. The trained model is then validated on external datasets from different hospitals, demonstrating successful generalization capabilities, particularly in binary-feature datasets where label assessment involves extrapolation.

A novel hybrid modelling framework for GPP estimation: Integrating a multispectral surface reflectance based [formula omitted] simulator into the process-based model

Terrestrial gross primary productivity (GPP) is the key element in the carbon cycle process. Accurate GPP estimation hinges on the maximum carboxylation rate (Vcmax,025). The high uncertainty in deriving ecosystem-level Vcmax,025 has long hampered efforts toward the performance of the GPP model. Recently studies suggest the strong relationship between spectral reflectance and Vcmax,025. We proposed the multispectral surface reflectance-driven Vcmax,025 simulator using the fully connected deep neural network and built the hybrid modelling framework for GPP estimation by integrating the data-driven Vcmax,025 simulator in the process-based model. The performance of hybrid GPP model was evaluated at 95 flux sites. The result shows that the multispectral surface reflectance-driven Vcmax,025 simulator acquires the satisfactory estimation, with correlation coefficient (R), root mean square error (RMSE) and median absolute percentage error (MdAPE) ranging from 0.34 to 0.80, 14 to 43 μmol m−2 s−1 and 21 % to 66 % across different land cover types, respectively. The hybrid framework generates good GPP estimates with R, RMSE and MdAPE varying from 0.76 to 0.89, 1.79 to 6.16 μmol m−2 s−1 and 27 % to 90 %, respectively. Compared with EVI-driven method, the multispectral surface reflectance significantly improves the Vcmax,025 and GPP estimates, with MdAPE declining by 0.6 %–18 % and 1 % to 21 %, respectively. The Shapley value analysis reveals that red (620–670 nm), near-infrared (841–876 nm) and shortwave infrared (1628–1652 nm and 2105–2155 nm) are the key bands for Vcmax,025 estimation. This study highlights the potential of multispectral surface reflectance for quantifying ecosystem-level Vcmax,025. The new hybrid framework fully extracts the information of all available spectral bands using deep learning to reduce parameter uncertainty while maintains the description of photosynthetic process to ensure its physical reasonability. It can serve as a powerful tool for accurate global GPP estimation.

COSMIC-dFBA: A novel multi-scale hybrid framework for bioprocess modeling

Metabolism governs cell performance in biomanufacturing, as it fuels growth and productivity. However, even in well-controlled culture systems, metabolism is dynamic, with shifting objectives and resources, thus limiting the predictive capability of mechanistic models for process design and optimization. Here, we present Cellular Objectives and State Modulation In bioreaCtors (COSMIC)-dFBA, a hybrid multi-scale modeling paradigm that accurately predicts cell density, antibody titer, and bioreactor metabolite concentration profiles. Using machine-learning, COSMIC-dFBA decomposes the instantaneous metabolite uptake and secretion rates in a bioreactor into weighted contributions from each cell state (growth or antibody-producing state) and integrates these with a genome-scale metabolic model. A major strength of COSMIC-dFBA is that it can be parameterized with only metabolite concentrations from spent media, although constraining the metabolic model with other omics data can further improve its capabilities. Using COSMIC-dFBA, we can predict the final cell density and antibody titer to within 10% of the measured data, and compared to a standard dFBA model, we found the framework showed a 90% and 72% improvement in cell density and antibody titer prediction, respectively. Thus, we demonstrate our hybrid modeling framework effectively captures cellular metabolism and expands the applicability of dFBA to model the dynamic conditions in a bioreactor.

Error approximation and bias correction in dynamic problems using a recurrent neural network/finite element hybrid model

This work proposes a hybrid modeling framework based on recurrent neural networks (RNNs) and the finite element (FE) method to approximate model discrepancies in time-dependent, multi-fidelity problems, and use the trained hybrid models to perform bias correction of the low-fidelity models. The hybrid model uses FE basis functions as a spatial basis and RNNs for the approximation of the time dependencies of the FE basis' degrees of freedom. The training data sets consist of sparse, non-uniformly sampled snapshots of the discrepancy function, pre-computed from trajectory data of low- and high-fidelity dynamic FE models. To account for data sparsity and prevent overfitting, data upsampling and local weighting factors are employed, to instigate a trade-off between physically conforming model behavior and neural network regression. The proposed hybrid modeling methodology is showcased in three highly non-trivial engineering test-cases, all featuring transient FE models, namely, heat diffusion out of a heat sink, eddy-currents in a quadrupole magnet, and sound wave propagation in a cavity. The results show that the proposed hybrid model is capable of approximating model discrepancies to a high degree of accuracy and accordingly correct low-fidelity models.