Extrapolation Capability Research Articles

Improving extrapolation capabilities of a data-driven prediction model for control of an air separation unit

In model predictive control, fully data-driven prediction models can be used besides common (non-)linear prediction models based on first-principles. Although no process knowledge is required while relying only on sufficient data, they suffer in their extrapolation capability which is shown in the present work for the control of an air separation unit. In order to compensate for the deficits in the extrapolation behavior, a further data source, here a digital twin, is deployed for additional data generation. The plant data set is augmented with the artificially generated data giving rise to a hybrid model in terms of data generation. It is shown that this model can significantly improve the prediction quality in former extrapolation areas of the plant data set. Even conclusions about the uncertainty behavior of the prediction model can be found.

The Enhancement of Machine Learning-Based Engine Models Through the Integration of Analytical Functions

The integration of analytical functions into machine learning-based engine models represents a significant advancement in predictive performance and operational efficiency. This paper focuses on the development of hybrid approaches to model engine combustion and temperature indices and on the synergistic effects of combining traditional analytical methods with modern machine learning techniques (such as artificial neural networks) to enhance the accuracy and robustness of such models. The main innovative contribution of this paper is the integration of analytical functions to improve the extrapolation capabilities of the data-driven models. In this work, it is demonstrated that the integrated models achieve superior predictive accuracy and generalization performance across dynamic engine operating conditions, with respect to purely neural network-based models. Furthermore, the analytical corrective functions force the output of the complete model to follow a physical trend and to assume consistent values also outside the domain of values assumed by the input features during the training procedure of the neural networks. This study highlights the potential of this integrative approach based on the implementation of the effects superposition principle. Such an approach also allows us to solve one of the intrinsic issues of data-driven modeling, without increasing the complexity of the training data’s collection and pre-processing.

Addressing high-performance data sparsity in metasurface inverse design using multi-objective optimization and diffusion probabilistic models.

Recent advancements in deep learning, particularly generative networks capable of producing high-freedom structures, have significantly enhanced the precise generation of meta-atoms. However, these methodologies typically rely on an abundance of high-performance data, which remains scarce in many practical design scenarios. To bridge this gap, our study introduces what we believe to be a novel approach that synergistically combines multi-objective optimization algorithms with an enhanced diffusion model featuring an attention mechanism, termed MetaDiffusion-Att. Using the complex design task of dual-polarized, wide-angle incidence, and broadband low-emissivity electromagnetic glass as an application example, we demonstrate the effectiveness of our method through qualitative and quantitative experiments. The introduced multi-objective optimization method significantly captures more high-performance samples while ensuring high degrees of freedom, compared to currently widely used generic dataset construction methods. The MetaDiffusion-Att model, improved by the introduced attention mechanism, significantly outperforms conventional WGAN-GP and conditional VAE methods in generation accuracy and quality under small datasets. Furthermore, the proposed method exhibits extrapolation capabilities, generating new structures with performance surpassing that of the dataset, further enriching the design space. This framework provides a promising solution for the inverse design of metasurfaces in challenging scenarios with sparse high-performance samples.

Predicting the Physical Properties of Dark Matter Subhalos from Baryonic Parameters Using Machine Learning

Dark matter subhalos play an important role in galaxy formation and evolution. However, accurate prediction of dark matter properties remains a challenge of modern-day astronomy. In recent times, machine learning (ML) tools have shown promising results in solving numerous astrophysical problems. In this paper, we use data from the EAGLE simulations to determine the total mass and the half-mass radius of dark matter subhalos using structural properties of gas, star, black hole, and photometric features using gradient boosted decision trees (GBDT) and dense neural network. GBDT does not require data preprocessing, and results in better performance compared to the neural network. According to GBDT, the most important feature for subhalo radius and mass estimation is gas radius and black hole mass respectively. The all-features combined approach results in the highest test accuracy — Pearson’s correlation coefficient = 0.947 and 0.981, coefficient of determination = 0.898 and 0.962, normalized median absolute deviation = 0.111 and 0.114 for radius and mass respectively. We evaluate our model for masses and redshifts beyond its training range and find that GBDT demonstrates significantly better extrapolation capabilities than the neural network. We also test our model on simulations with different resolutions, and find that the discrepancies lie within 10% if the resolution is changed. This novel study incorporates the structural parameters of gas and black hole to determine the dark matter properties using a ML-based approach. The promising results of this study prove that ML tools can improve our current understanding of dark matter, and answer some of the basic cosmological questions.

Extreme time extrapolation capabilities and thermodynamic consistency of physics-inspired neural networks for the 3D microstructure evolution of materials via Cahn–Hilliard flow

Abstract A Convolutional Recurrent Neural Network (CRNN) is trained to reproduce the evolution of the spinodal decomposition process in three dimensions as described by the Cahn–Hilliard equation. A specialized, physics-inspired architecture is proven to provide close accordance between the predicted evolutions and the ground truth ones obtained via conventional integration schemes. The method can accurately reproduce the evolution of microstructures not represented in the training set at a fraction of the computational costs. Extremely long-time extrapolation capabilities are achieved, up to reaching the theoretically expected equilibrium state of the system, consisting of a layered, phase-separated morphology, despite the training set containing only relatively-short, initial phases of the evolution. Quantitative accordance with the decay rate of the free energy is also demonstrated up to the late coarsening stages, proving that this class of machine learning approaches can become a new and powerful tool for the long timescale and high throughput simulation of materials, while retaining thermodynamic consistency and high-accuracy.

Landslide Deformation Analysis and Prediction with a VMD-SA-LSTM Combined Model

The evolution of landslides is influenced by the complex interplay of internal geological factors and external triggering factors, resulting in nonlinear dynamic changes. Although deep learning methods have demonstrated advantages in predicting multivariate landslide displacement, their performance is often constrained by the challenges of extracting intricate features from extended time-series data. To address this challenge, we propose a novel displacement prediction model that integrates Variational Mode Decomposition (VMD), Self-Attention (SA), and Long Short-Term Memory (LSTM) networks. The model first employs VMD to decompose cumulative landslide displacement into trend, periodic, and stochastic components, followed by an assessment of the correlation between these components and the triggering factors using grey relational analysis. Subsequently, the self-attention mechanism is incorporated into the LSTM model to enhance its ability to capture complex dependencies. Finally, each displacement component is fed into the SA-LSTM model for separate predictions, which are then reconstructed to obtain the cumulative displacement prediction. Using the Zhonghai Village tunnel entrance (ZVTE) landslide as a case study, we validated the model with displacement data from GPS point 105 and made predictions for GPS point 104 to evaluate the model’s generalization capability. The results indicated that the RMSE and MAPE for SA-LSTM, LSTM, and TCN-LSTM at GPS point 105 were 0.3251 and 1.6785, 0.6248 and 2.9130, and 1.1777 and 5.5131, respectively. These findings demonstrate that SA-LSTM outperformed the other models in terms of complex feature extraction and accuracy. Furthermore, the RMSE and MAPE at GPS point 104 were 0.4232 and 1.0387, further corroborating the model’s strong extrapolation capability and its effectiveness in landslide monitoring.

A cGAN-based fatigue life prediction of 316 austenitic stainless steel in high-temperature and high-pressure water environments

The thermo-mechanical-chemical coupling effect presents significant challenges in accurately predicting the fatigue life of 316 austenitic stainless steel in high-temperature and high-pressure water environments (referred to hereafter as environmental fatigue). The complexity of environmental fatigue experiments results in limited and dispersed data, further making the life prediction difficult. Traditional fatigue life prediction models are often constrained by specific loading conditions and do not adequately account for the complex environmental influences. To address these issues, this paper proposes a novel environmental fatigue life prediction model of 316 stainless steel utilizing conditional Generative Adversarial Networks. The proposed model incorporates critical environmental factors, loading conditions and stacking fault energy, allowing direct prediction of environmental fatigue life. A comparative analysis on the predicted and experimental results reveals that the cGAN-based model significantly improves the prediction accuracy, reducing the fatigue life prediction error from a factor of 5 to within 3. To quantify the uncertainty in fatigue life prediction, the Monte Carlo Dropout method is employed to enable a probabilistic assessment of fatigue life. Furthermore, four environmental and loading conditions are established to evaluate the model’s extrapolation capability. The results demonstrate that the probabilistic fatigue assessment effectively captures data distribution and achieves high prediction accuracy.

Prediction of Fan Array Performance with Polynomial and Support Vector Regression Models

The increasing utilisation of demand-controlled ventilation strategies leads to the frequent operation of fans under part-load conditions. To accurately predict the energy demand of a ventilation system with a fan array in the early design stages, models that calculate reliable results across the whole operating range are required. We present the comparison of a polynomial and a machine learning approach through support vector regression (SVR) to predict the fan performance over a wide range of typical operating points. For fitting and validation, we use experimental data. We investigate the extrapolation performance of both approaches. The SVR model achieves a slightly better representation of the experimental data with a lower error, especially when only sparse data are available. Both approaches yield similar results when the evaluation is conducted within the experimentally captured domain but deviates outside the domain. At operating points that are far from the experimentally captured domain, the polynomial models yield fan efficiencies that are physically plausible, while the SVR models drastically overpredict the fan efficiency. To rate the influence of such deviations towards modelling the actual energy demand, both approaches are applied to an operation simulation of a simplified office building. Both approaches yield similar results despite differing extrapolation capabilities.

A physics‐constrained hybrid residual neural network for the prediction of moisture content in a closed‐cycle drying system

AbstractClosed‐cycle drying technology has the advantages of safety, energy saving, and environmental protection, and has a wide application prospect. Due to the multi‐physics and multi‐scale nature of heat/mass transfer in the closed‐cycle drying process, as well as the characteristics of drying medium circulation and energy integration, it is difficult to obtain the product moisture content prediction model in closed‐cycle process based on rigorous closed‐cycle drying process mechanism model. However, accurate monitoring of product moisture content in the closed‐cycle drying process is the key to improving drying quality and process optimization. Aiming at the challenges in predicting moisture content, this paper proposes a physics‐constrained hybrid residual neural network (PC‐HRNN) for soft sensor modelling within a designed closed‐cycle drying system. The characteristic of this proposed method lies in its effective fusion of physics, knowledge, and data. First, a hybrid residual neural network (HRNN) is constructed based on the integration of a physics model and a data‐driven model. The HRNN takes the knowledge from the physics model as its auxiliary features and learns the prediction residuals of the physics model through a neural network model. Then, a new loss function that takes into account physical laws is introduced into HPNN to standardize model training and improve the generalization performance of the model. The experimental results show that the PC‐HRNN model improves prediction accuracy and model robustness, reduces the demand for data, and demonstrates stronger extrapolation capabilities under limited data.

Prediction of ground state charge radius using support vector regression

Abstract We systematically investigate the prediction of nuclear charge radii using a support vector regression (SVR) model in machine learning(ML), specifically employing a radial basis function (RBF) kernel. Our model is designed to capture the global structure of the radius surface through the utilization of feature spaces encompassing both (N, Z) and (N, Z, A). We achieved a root mean square deviation of 0.019 fm with respect to 885 measured charge radii (Z ⩾ 8). By incorporating the atomic mass number as an additional feature, the model successfully reproduces the charge radii of ( 40 − 50 Ca), ( 74 − 96 Kr), ( 120 − 148 Ba), and ( 183 − 199 Au) isotopes. Furthermore, our ML method demonstrated an extrapolation capability with a deviation of 0.016 fm relative to 10 022 calculated charge radii based on the Weizsacker–Skyrme model. The SVR model’s performance is further tested across different regions of the charge radii table, demonstrating significant agreement with experimental data and underscoring the efficacy of the RBF kernel in nuclear charge radii prediction.

Artificial Intelligence Hybrid Survival Assessment System for Robot-Assisted Proctectomy: A Retrospective Cohort Study.

Robotic-assisted proctectomy (RAP) has emerged as the predominant surgical approach for patients with rectal cancer in recent years; although good postoperative patient recovery with accurate prediction is a guarantee of adaptive surveillance management, there is still a lack of easy-to-use prognostic tools and risk scores designed specifically for those patients undergoing RAP. This study used the electronic health records of 506 RAP participants, including a National Specialist Center for da Vinci Robotic Colorectal Surgery (NSCVRCS) meta cohort, and an independent external validation Sun Yat-sen Memorial Hospital cohort. In the NSCVRCS meta cohort, patients were divided into a discovery cohort (70%, n = 268), where the best-fit model was applied to model our prediction system, RAP-AIscore. Subsequently, an internal validation process for RAP-AIscore was conducted using a replication cohort (30%, n = 116). The study designed and implemented a large-scale artificial intelligence (AI) hybrid framework to identify the best strategy for building a survival assessment system, the RAP-AIscore, from 132 potential modeling scenarios through a combination of iterative cross-validation, Monte Carlo cross-validation, and bootstrap resampling. The 10 variables most relevant to clinical interpretability were identified on the basis of the AI hybrid optimal model values, which helps provide reliable prognostic survival guidance for new patients. The consistent evaluation of discrimination, calibration, generalization, and prognostic value across cohorts reaffirmed the accuracy and robust extrapolation capability of this system. The 10 feature variables most associated with clinical interpretability on the basis of Shapley values were identified, facilitating reliable prognostic survival guidance for new patients. This study introduces a promising and informative tool, the RAP-AIscore, which can be explained through nomograms for interpreting clinical outcomes. It facilitates postoperative risk stratification management and enhances clinical management of prognosis for RAP patients.

A new approach to multiaxial fatigue life prediction: A multi-dimensional multi-scale composite neural network with multi-depth

Many multiaxial fatigue life prediction methods tend to increase additional parameters and model depth as the complexity of the loading path increases. This leads to issues such as poor model robustness, limited flexibility, and single-dimensional approaches. In this study, a multi-dimensional multi-scale composite neural network with multi-depth is proposed to address these challenges and enhance prediction accuracy. Initially, physical and sensitive features serve as input data for the proposed model, to enhance the richness of input features. Subsequently, a multi-dimensional feature extraction module is deployed to extract feature information from the composite data. To process these features, an improved multi-domain query cascaded transformer network (IMQCT) is employed as the feature processing module of the proposed model. The proposed model is verified to have better prediction accuracy and extrapolation capability by using experimental data from nine materials and comparing its performance with six machine learning models.

A frequency domain enhanced multi-view neural network approach to multiaxial fatigue life prediction for various metal materials

Fatigue damages and failure widely exist in engineering structures, particularly in industries such as aerospace, automotive, and construction, where components are often subjected to complex multiaxial loading conditions. Accurate prediction of fatigue life is critical for ensuring the safety and longevity of these structures. In this study, a novel multi-view deep learning model incorporating frequency domain analysis for fatigue life prediction is proposed. The proposed model integrates a Convolutional Neural Network (CNN), a Long Short-Term Memory Network (LSTM), and FNet that combines frequency domain analysis, in a parallel structure to extract features from the loading paths of materials. These extracted features are then connected to a fully connected neural network to predict fatigue life. The model was validated using fatigue data collected from 6 different materials, encompassing 17 loading paths and 336 samples. Additionally, ablation experiments were conducted, and the extrapolation capabilities were evaluated using specifically designed test sets. The results demonstrate that the proposed model exhibits excellent predictive performance and extrapolation capabilities. We anticipate that the multi-view approach, along with its accuracy and applicability, can offer potential applications in engineering fields that require reliable, data-driven models to assess material durability under complex loading scenarios.

Utilizing machine learning algorithms for predicting risk factors for bone metastasis from right-sided colon carcinoma after complete mesocolic excision: a 10-year retrospective multicenter study

BackgroundBone metastasis (BM) occurs when colon cancer cells disseminate from the primary tumor site to the skeletal system via the bloodstream or lymphatic system. The emergence of such bone metastases typically heralds a significantly poor prognosis for the patient. This study's primary aim is to develop a machine learning model to identify patients at elevated risk of bone metastasis among those with right-sided colon cancer undergoing complete mesocolonectomy (CME).Patients and methodsThe study cohort comprised 1,151 individuals diagnosed with right-sided colon cancer, with a subset of 73 patients presenting with bone metastases originating from the colon. We used univariate and multivariate regression analyses as well as four machine learning algorithms to screen variables for 38 characteristic variables such as patient demographic characteristics and surgical information. The study employed four distinct machine learning algorithms, namely, extreme gradient boosting (XGBoost), random forest (RF), support vector machine (SVM), and k-nearest neighbor algorithm (KNN), to develop the predictive model. Additionally, the model was assessed using receiver operating characteristic (ROC) curves, calibration curves, and decision curve analysis (DCA), while Shapley additive explanation (SHAP) was utilized to visualize and analyze the model.ResultsThe XGBoost algorithm performed the best performance among the four prediction models. In the training set, the XGBoost algorithm had an area under curve (AUC) value of 0.973 (0.953–0.994), an accuracy of 0.925 (0.913–0.936), a sensitivity of 0.921 (0.902–0.940), and a specificity of 0.908 (0.894–0.922). In the validation set, the XGBoost algorithm had an AUC value of 0.922 (0.833–0.995), an accuracy of 0.908 (0.889–0.926), a sensitivity of 0.924 (0.873–0.975), and a specificity of 0.883 (0.810–0.956). Furthermore, the AUC value of 0.83 for the external validation set suggests that the XGBoost prediction model possesses strong extrapolation capabilities. The results of SHAP analysis identified alkaline phosphatase (ALP) levels, tumor size, invasion depth, lymph node metastasis, lung metastasis, and postoperative neutrophil-to-lymphocyte ratio (NLR) levels as significant risk factors for BM from right-sided colon cancer subsequent to CME.ConclusionThe prediction model for BM from right-sided colon cancer developed using the XGBoost machine learning algorithm in this study is both highly precise and clinically valuable.

Classified dataset, regression and machine learning modeling for prediction of phase transformation temperatures in steels

The prediction of the characteristic Martensite Start (Ms) temperature and Austenitic Nose Tip Temperature (ANTT) in steels is of scientific and technological importance; however, it faces significant challenges due to multiphysical complexity.In this study, we introduced a structured framework for data classification and hierarchical iterations aimed at predicting Ms (Martensite start temperature) and ANTT (Austenite non-transforming temperature). This framework was incorporated into two optimization models, leading to enhancements in accuracy, extrapolation capabilities, and generalization performance. First, we classified the collected Ms datasets hierarchically based on the alloying elements presented in steels, including carbon, austenite stabilizers, non-austenitization elements, and data credibility. Regression analyses of Ms temperatures concerning chemical compositions were then carried out using phenomenological variables from binary systems to multi-component systems in alignment with the spirit of CALPHAD modeling, which is renowned for its robust extrapolation abilities. By iteratively fitting the hierarchically classified datasets and implementing hierarchical iterations, we developed the CALPHAD-guided phenomenological variable (CGPV) Ms regression model. This model achieved improved accuracy levels, with R2 values of 0.9 for training and 0.87 for testing, surpassing most conventional regression models that do not account for compositional interactions. Furthermore, the CALPHAD-guided machine learning (CGML) model, constructed based on the classified datasets and hierarchical iterations but without utilizing phenomenological variables, demonstrated strong performance with R2 values of 0.98 and 0.86 for training and testing, respectively. The CGML model was demonstrated not only to reliably filter out problematic data in a dataset but also to unveil the unnoticed coupling between carbon and other alloying elements on Ms. Finally, the CGML method has been readily transferred to predict ANTT with high accuracy as well.

Hybrid modeling for in silico optimization of a dynamic perfusion cell culture process.

The bio-pharmaceutical industry heavily relies on mammalian cells for the production of bio-therapeutic proteins. The complexity of implementing and high cost-of-goods of these processes are currently limiting more widespread patient access. This is driving efforts to enhance cell culture productivity and cost reduction. Upstream process intensification (PI), using perfusion approaches in the seed train and/or the main bioreactor, has shown substantial promise to enhance productivity. However, developing optimal process conditions for perfusion-based processes remain challenging due to resource and time constraints. Model-based optimization offers a solution by systematically screening process parameters like temperature, pH, and culture media to find the optimum conditions in silico. To our knowledge, this is the first experimentally validated model to explain the perfusion dynamics under different operating conditions and scales for process optimization. The hybrid model accurately describes Chinese hamster ovary (CHO) cell culture growth dynamics and a neural network model explains the production of mAb, allowing for optimization of media exchange rates. Results from six perfusion runs in Ambr® 250 demonstrated high accuracy, confirming the model's utility. Further, the implementation of dynamic media exchange rate schedule determined through model-based optimization resulted in 50% increase in volumetric productivity. Additionally, two 5 L-scale experiments validated the model's reliable extrapolation capabilities to large bioreactors. This approach could reduce the number of wet lab experiments needed for culture process optimization, offering a promising avenue for improving productivity, cost-of-goods in bio-pharmaceutical manufacturing, in turn improving patient access to pivotal medicine.

A Novel Hybrid Deep Learning Framework for Evaluating Field Evapotranspiration Considering the Impact of Soil Salinity

AbstractAccurate evaluation of evapotranspiration (ET) is crucial for efficient agricultural water management. Data‐driven models exhibit strong predictive ET capabilities, yet significant limitations like naive extrapolation hamper wider generalization. In this perspective, we explore a novel hybrid deep learning (DL) framework to integrate domain knowledge and demonstrate its potential for evaluating ET under the influence of soil salinity. Specifically, we integrated physical constraints from process models (Penman‐Monteith or Shuttleworth‐Wallace) and salinity‐induced stomatal stress mechanisms into the DL algorithm, and evaluated its performance by comparing four diverse scenarios. Results demonstrate that hybrid DL framework offers a promising alternative for ET estimation, achieving comparable accuracy to pure DL during training and validation. Nonetheless, due to the limited available measurements, data‐driven model may not adequately capture plant responses to salt stress, leading to significant prediction biases observed during independent testing. Encouragingly, the hybrid DL model (DL‐SS) integrating Shuttleworth‐Wallace and salinity‐induced stomatal stress mechanisms demonstrated enhanced interpretability, generalizability, and extrapolation capabilities. During testing, DL‐SS consistently showed optimal performance, yielding root mean square error (RMSE) values of 37.4 W m−2 for sunflower and 39.2 W m−2 for maize. Compared to traditional Jarvis‐type approaches (JPM and JSW) and pure DL model during testing, DL‐SS achieved substantial reductions in RMSE values: 51%, 33%, and 43% for sunflower, and 45%, 31%, and 35% for maize, respectively. These findings highlight the importance of integrating prior scientific knowledge into data‐driven models to enhance extrapolation capability of ET modeling, especially in salinized regions where conventional models may struggle.

Thermomechanical characterisation and plane stress linear viscoelastic modelling of ethylene-tetra-fluoroethylene foils

Ethylene-tetra-fluoroethylene (ETFE) is a polymer employed in tension membrane structures with mechanical properties that strongly depend on time and temperature effects. A comprehensive understanding of the mutual influence of these variables and a unified viscoelastic constitutive model design can enable wider exploitation of ETFE in sustainable lightweight construction. This study presents a thermomechanical characterisation of ETFE foils through quasi-static tensile experiments spanning two orders of magnitude of strain rates, creep, relaxation, shear and dynamic cyclic tests in a wide range of temperatures suitable for building applications, from −20∘ C\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$-20^{\\circ }\ ext{ C}$\\end{document} to 60∘ C\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$60^{\\circ }\ ext{ C}$\\end{document}. The experimental results in different material orientations are used to identify the limits of the linear viscoelastic domain, define the direction-dependent creep compliance master curves and calibrate the parameters of a plane stress orthotropic linear viscoelastic model, employing the Boltzmann superposition and the time-temperature superposition principles. The model has been numerically implemented using a recursive integration algorithm and its code is provided open source. A validation on independently acquired data shows the accuracy of the constitutive model in predicting ETFE behaviour within the linear viscoelastic regime usually adopted during structural design, with excellent extrapolation capabilities outside the range of the calibration data.

Phyformer: A degradation physics-informed self-data driven approach to machinery prognostics

Machinery degradation prognostics methods have been suffering the “dilemma” that both physics and data-driven methods have their own limitations. On one hand, constructing accurate close-form mathematical physics models are prohibitively difficult for a complex system. On the other hand, for pure data driven models such as deep learning models, due to the lack of physics guidance, their extrapolation capability decays over time and even yield unexplainable predictions that violate common cognition. Therefore, relaxing the pursuit for the perfect and accurate degradation model, and instead coupling general degradation model with deep learning model, fully leveraging the advantages from both physics-based prognostics and data-driven prognostics, is a promising way to solve the “dilemma”. Driven by this motivation, this paper proposes Phyformer, a general degradation physics-informed self-data-driven method for machinery prognostics. A backbone deep learning model based on auto-correlation and Transformer architecture is developed for time series data prediction. Multiple local physical models that are constructed with data in sliding time windows are embedded into the backbone model in the form of loss function. Only the historical data of the machine itself are used to extrapolate the future, which is significant especially for high-end equipment since their run-to-fail data are scarce. Then the predicted data are mapped to degradation stage by an unsupervised clustering model Gath-Geva adaptively without the requirement of knowing the number of degradation stages in advance. Due to the above nature, Phyformer is high flexibility, easy to be deployed in different applications, working condition-independent and simple. Two typical prognostics tasks are studied, which use direct and indirect condition monitoring data as input, respectively. Comparisons with other state-of-the-art machinery prognostics models show the advances of Phyformer.

Adsorption Modeling Based on Classical Density Functional Theory and PC-SAFT: Temperature Extrapolation and Fluid Transfer.

Adsorption is at the heart of many processes from gas separation to cooling. The design of adsorption-based processes requires equilibrium adsorption properties. However, data for adsorption equilibria are limited, and therefore, a model is desirable that uses as little data as possible for its parametrization, while allowing for data interpolation or even extrapolation. This work presents a physics-based model for adsorption isotherms and other equilibrium adsorption properties. The model is based on one-dimensional classical density functional theory (1D-DFT) and the perturbed-chain statistical associating fluid theory (PC-SAFT). The physical processes inside the pores are considered in a thermodynamically consistent approach that is computationally efficient. Once parametrized with a single isotherm, the model is able to extrapolate to other temperatures and outperforms the extrapolation capabilities of state-of-the-art models, such as the empirical isotherm models from Langmuir or Toth. Furthermore, standard combining rules can be used to transfer parameters adjusted to an adsorbent/fluid pair to other fluids. These features are demonstrated for the adsorption of N2, CH4, and CO2 in metal-organic frameworks. Thereby, the presented model can calculate temperature-dependent isotherms for various fluids by using data limited to a single isotherm as input.