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We introduce a novel approach that combines interpretable quantitative stochastic machine learning with multiscale analysis to predict the macroscopic thermal conductivity of graphene-enhanced polymer nanocomposites. Our method effectively addresses uncertainties in input parameters across meso and macro scales within a bottom-up modeling framework. By integrating Representative Volume Elements (RVE) with traditional Finite Element Modeling (FEM), we calculate the effective thermal conductivity through homogenization. We further enhance predictive modeling by employing the XGBoost regression tree method. To clarify the influence of input variables on model outcomes, we incorporate SHapley Additive exPlanations (SHAP) and Local Interpretable Model-agnostic Explanations (LIME). Additionally, sensitivity analyses are conducted to assess the impact of design parameters on material properties. This comprehensive approach improves both global and local interpretability, clarifying feature interactions in data-driven and physical models. It reduces the reliance on extensive analytical modeling and simulations, enhancing prediction accuracy and significantly lowering computational costs. Our method holds significant promise for the design of new composite materials optimized for thermal management.

Polyurethane (PU) possesses excellent thermal properties, making it an ideal material for thermal insulation. Incorporating Phase Change Materials (PCMs) capsules into Polyurethane has proven to be an effective strategy for enhancing building envelopes. This innovative design substantially enhances indoor thermal stability and minimizes fluctuations in indoor air temperature. To investigate the thermal conductivity of the Polyurethane-Phase Change Materials foam composite, we propose a hierarchical multi-scale model utilizing Physics-Informed Neural Networks (PINNs). This model allows accurate prediction and analysis of the material’s thermal conductivity at both the meso-scale and macro-scale. By leveraging the integration of physics-based knowledge and data-driven learning offered by Physics-Informed Neural Networks, we effectively tackle inverse problems and address complex multi-scale phenomena. Furthermore, the obtained thermal conductivity data facilitates the optimization of material design. To fully consider the occupants’ thermal comfort within a building envelope, we conduct a case study evaluating the performance of this optimized material in a detached house. Simultaneously, we predict the energy consumption associated with this scenario. All outcomes demonstrate the promising nature of this design, enabling passive building energy design and significantly improving occupants’ comfort. The successful development of this Physics-Informed Neural Networks-based multi-scale model holds immense potential for advancing our understanding of Polyurethane-Phase Change Material’s thermal properties. It can contribute to the design and optimization of materials for various practical applications, including thermal energy storage systems and insulation design in advanced building envelopes.

We introduce an interpretable stochastic integrated machine learning based multiscale approach for the prediction of the macroscopic thermal conductivity in Polymeric graphene-enhanced composites (PGECs). This method encompasses the propagation of uncertain input parameters from the meso to macro scale, implemented through a foundational bottom-up multi-scale framework. In this context, Representative Volume Elements in Finite Element Modeling (RVE-FEM) are employed to derive the homogenized thermal conductivity. Besides, we employ two sets of techniques: Regression-tree-based methods (Random Forest and Gradient Boosting Machine) and Neural networks-based approaches (Artificial Neural Networks and Deep Neural Networks). To ascertain the relative influence of factors on output estimations, the SHapley Additive exPlanations (SHAP) algorithm is integrated. This interpretable machine learning methodology demonstrates strong alignment with published experimental data. It holds promise as an efficient and versatile tool for designing new composite materials tailored to applications involving thermal management.

We present a web-based framework based on the R shiny package with functional back-end server in machine learning methods. A 4-tiers architecture is programmed to achieve users’ interactive design and visualization via a web browser. Many data-driven methods are integrated into this framework, namely Random Forest, Gradient Boosting Machine, Artificial and Deep neural networks. Moreover, a robust gradient-free optimization technique, the Particle Swarm Optimization, is used to search optimal values in hyper-parameters tuning. K-fold Cross Validation is applied to avoid over-fitting. R2 and RMSE are considered as two key factors to evaluate the trained models. The contributions to the expert system in materials design are: (1) A systematic framework that can be applied in materials prediction with machine learning approaches, (2) A user-friendly web-based platform that is easy and flexible to use and (3) integrated optimization and visualization into the framework with pre set algorithms. This computational framework is designed for researchers and materials engineers who would like to do the preliminary designs before experimental studies. Finally, we demonstrate the performance of the web-based framework through 2 case studies.

This paper presents an open digital ecosystem based on a web-framework with a functional back-end server for user-centric energy retrofits. This data-driven web framework is proposed for building energy renovation benchmarking as part of an energy advisory service development for the Västerbotten region, Sweden. A 4-tier architecture is developed and programmed to achieve users’ interactive design and visualization via a web browser. Six data-driven methods are integrated into this framework as backend server functions. Based on these functions, users can be supported by this decision-making system when they want to know if a renovation is needed or not. Meanwhile, influential factors (input values) from the database that affect energy usage in buildings are to be analyzed via quantitative analysis, i.e., sensitivity analysis. The contributions to this open ecosystem platform in energy renovation are: 1) A systematic framework that can be applied to energy efficiency with data-driven approaches, 2) A user-friendly web-based platform that is easy and flexible to use, and 3) integrated quantitative analysis into the framework to obtain the importance among all the relevant factors. This computational framework is designed for stakeholders who would like to get preliminary information in energy advisory. The improved energy advisor service enabled by the developed platform can significantly reduce the cost of decision-making, enabling decision-makers to participate in such professional knowledge-required decisions in a deliberate and efficient manner. This work is funded by the AURORAL project, which integrates an open and interoperable digital platform, demonstrated through regional large-scale pilots in different countries of Europe by interdisciplinary applications.

Polyurethane (PU) exhibits exceptional thermal properties, making it an ideal material for thermal insulation. Incorporating Phase Change Materials (PCMs) capsules into Polyurethane (PU) has proven to be highly effective in enhancing building envelopes. This innovative design greatly enhances the stability of indoor thermal environments and reduces fluctuations in indoor air temperature. To investigate the thermal conductivity of this composite material, we have developed a comprehensive multiscale model of a PU-PCM foam composite. By obtaining thermal conductivity data, we can optimize the material's design for maximum effectiveness. To fully assess the thermal comfort of occupants within a building envelope, we have conducted a case study based on the performance of this optimized material. Specifically, we focused on a single room where PU-PCM composites were applied. Simultaneously, we predicted the energy consumption associated with this scenario. The results of our study clearly demonstrate the promising nature of this design, as it enables passive building energy design and significantly improves the comfort experienced by occupants.

Polyurethane (PU) is an ideal thermal insulation material due to its excellent thermal properties. The incorporation of Phase Change Materials (PCMs) capsules into Polyurethane (PU) has been shown to be effective in building envelopes. This design can significantly increase the stability of the indoor thermal environment and reduce the fluctuation of indoor air temperature. We develop a multiscale model of a PU-PCM foam composite and study the thermal conductivity of this material. Later, the design of materials can be optimized by obtaining thermal conductivity. We conduct a case study based on the performance of this optimized material to fully consider the thermal comfort of the occupants of a building envelope with the application of PU-PCMs composites in a single room. At the same time, we also predict the energy consumption of this case. All the outcomes show that this design is promising, enabling the passive design of building energy and significantly improving occupants' comfort.

Ultraviolet cured-in-place-pipe (UV-CIPP) materials are commonly used in trenchless pipeline rehabilitation. Their bending strength is a crucial indicator to evaluate the curing quality. Studies show that this indicator is affected by multiple factors, including the curing time, UV lamp curing power, curing distance, and material thickness. Laboratory experiments have limitations in analyzing the effect of multiple factors on the bending strength of UV-CIPP materials and quantitatively predicting the optimum curing parameters. Aiming at resolving these shortcomings, resolve machine learning techniques were applied to predict the bending strength. In this regard, the surface curing reaction temperature monitoring data and three-point bending data of 30 groups of UV-CIPP material under the influence of different curing parameters were used as a dataset to predict the bending strength of UV-CIPP material. The results show that the influence degree of each factor on the bending strength of the UV-CIPP material, from high to low, is as follows: UV lamp power (−0.439), the temperature at the illuminated side (−0.392), curing time (−0.323), the temperature at the back side (−0.233), curing distance (0.143) and material thickness (−0.140). The best penalty parameter c (44.435) and width g (0.072) of the kernel function in the support vector machine (SVM) model were obtained using the genetic algorithm (GA) optimization, and the results were compared with the grey wolf optimizer (GWO) and particle swarm optimization (PSO). The performed analyses revealed that the developed GA-SVM model exhibits the best prediction results compared to other machine learning algorithms. The optimum bending strength of the UV-CIPP material used in this test is 294.77 MPa, which corresponds to the curing time, UV lamp power, curing distance, material thickness, light side temperature, and back side temperature of 7.59 min, 157.33 mW/cm², 189.99 mm, 4.38 mm, 79.49 °C, and 76.59 °C, respectively.

Extensive research and development have been dedicated to nano-reinforced polymer composites, owing to their exceptional physical and chemical properties. Recent studies have focused on quantifying the impact of nanofillers on the properties of these composites. Properties such as macroscopic thermal conductivity play a vital role in various engineering applications, including aerospace engineering, automotive industry, energy storage equipment, and electronic devices. The composition of the embedded polymeric filler in the composite matrix significantly influences the overall macroscopic properties of the material. However, previous studies primarily relied on deterministic models that disregarded uncertainties and did not account for the presence of uncertainties in these materials. Consequently, the predicted results deviated from the experimental findings. Moreover, the computational costs associated with stochastic multiscale modeling are high, prompting the use of alternative methods to propagate uncertain parameters across scales. With advancements in high-performance computing and artificial intelligence, machine learning has gained popularity as a modeling tool in numerous applications. Machine learning (ML) is often employed to construct surrogate models by establishing mappings between specific rules and algorithms to build input-output models using available data. ML models are particularly useful for nonlinear inputs, especially when sufficient data are accessible to establish robust relationships. In this study, we propose a stochastic multiscale approach based on ensemble learning to predict the macroscopic thermal conductivity of nanoreinforced polymer composites. We developed eight types of machine learning models: Multivariate Adaptive Regression Splines (MARS), Support Vector Machines (SVM), Regression Trees (RT), Bagging Trees (Bagging), Random Forest (RF), Gradient Boosting Machine (GBM), Cubist, and Deep Neural Networks (DNN). These models are integral to the stochastic modeling process, allowing us to construct representations of all uncertain input variables and the desired output parameterization, specifically the macroscopic thermal conductivity of the composite material. To find the global optimum and significantly reduce computational costs, we employ Particle Swarm Optimization (PSO) for hyperparameter tuning. We also conduct an analysis of the computational costs and model complexity, examining the advantages and disadvantages of each method. The results demonstrate that the proposed stochastic ensemble machine learning method, which considers uncertainties, exhibits excellent performance. This method plays a crucial role in computational modeling, aiding in the design of new composite materials for applications related to thermal management. 

We propose a computational framework using surrogate models through five steps, which can systematically and comprehensively address a number of related stochastic multi-scale issues in composites design. We then used this framework to conduct an implementation in nano-composite. Uncertain input parameters at different scales are propagated within a bottom-up multi-scale framework. Representative volume elements in the context of finite element modelling (RVE-FEM) are used to finally obtain the homogenised thermal conductivity. The input parameters are selected by a top-down scanning method and subsequently are converted as uncertain inputs. Machine learning approaches are exploited for computational efficiency, where particle swarm optimisation (PSO) and ten-fold cross validation (CV) are employed for hyper-parameter tuning. Our machine learning prediction results agree well with published experimental data, which proves our computational framework can be a versatile and efficient method to design new complex nano-composites.