Abstract
The Grad–Shafranov equation for axisymmetric MHD equilibria is a nonlinear, scalar PDE which in principle can have zero, one or more non-trivial solutions. The conditions for the existence ...of multiple solutions has been little explored in the literature so far. We develop a simple analytic model to calculate multiple solutions in the large aspect ratio limit. We compare the results to the recently developed deflated continuation method to find multiple solutions in a realistic geometry and right-hand side of the Grad–Shafranov equation using the finite element method. The analytic model is surprisingly accurate in calculating multiple solutions of the Grad–Shafranov equation for given boundary conditions and the two methods agree well in limiting cases. We examine the effect of plasma shaping and aspect ratio on the multiple solutions and show that shaping generally does not alter the number of solutions. We discuss implications for predictive modelling, equilibrium reconstruction, plasma stability and disruptions.
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Artificial neural networks (ANNs), a subset of Quantitative Structure-Property Relationship (QSPR) methods, offer a promising avenue for addressing challenges in materials science. In ...particular, ANNs can learn intricated patterns within the experimental data, enabling them to predict properties and recognize complex relationships with remarkable accuracy. However, the opacity of ANNs, normally acting as black boxes, raises concerns about their reliability and interpretability. To enhance their transparency and to uncover the underlying relationships between chemical features and material properties, we propose a novel approach that employs Gradient-weighted Class Activation Mapping (Grad-CAM) applied to Convolutional Neural Networks (CNNs). By analyzing these attention maps, we identify the crucial chemical features influencing the prediction of a polymer property, specifically the glass transition temperature (Tg). Our methodology is validated using a dataset of atactic acrylates, allowing us to not only predict Tg values for a control group of polymers but also to quantitatively assess the impact of individual monomer structural elements on these predictions. This work proposes a step towards transparent models in materials science, contributing to a deeper understanding of the intricate relationship between chemical structures and material properties.
Myocardial infarction (MI) accounts for a high number of deaths globally. In acute MI, accurate electrocardiography (ECG) is important for timely diagnosis and intervention in the emergency setting. ...Machine learning is increasingly being explored for automated computer-aided ECG diagnosis of cardiovascular diseases. In this study, we have developed DenseNet and CNN models for the classification of healthy subjects and patients with ten classes of MI based on the location of myocardial involvement. ECG signals from the Physikalisch-Technische Bundesanstalt database were pre-processed, and the ECG beats were extracted using an R peak detection algorithm. The beats were then fed to the two models separately. While both models attained high classification accuracies (more than 95%), DenseNet is the preferred model for the classification task due to its low computational complexity and higher classification accuracy than the CNN model due to feature reusability. An enhanced class activation mapping (CAM) technique called Grad-CAM was subsequently applied to the outputs of both models to enable visualization of the specific ECG leads and portions of ECG waves that were most influential for the predictive decisions made by the models for the 11 classes. It was observed that Lead V4 was the most activated lead in both the DenseNet and CNN models. Furthermore, this study has also established the different leads and parts of the signal that get activated for each class. This is the first study to report features that influenced the classification decisions of deep models for multiclass classification of MI and healthy ECGs. Hence this study is crucial and contributes significantly to the medical field as with some level of visible explainability of the inner workings of the models, the developed DenseNet and CNN models may garner needed clinical acceptance and have the potential to be implemented for ECG triage of MI diagnosis in hospitals and remote out-of-hospital settings.
•This is the first study to explain the inner workings of the DenseNet and CNN models developed for MI detection.•DenseNet is a better model than CNN, for rapid classification of MI.•Model is developed with ten-fold cross-validation. Hence, it is robust and accurate.•Obtained high accuracy of 98.9% for the classification of ten MI classes with DenseNet model.
We present Mars Atmosphere and Volatile EvolutioN (MAVEN) observations of a giant magnetic flux rope in the Martian dayside ionosphere. The flux rope was observed at an altitude of <300 km, ...downstream from strong subsolar crustal magnetic fields. The peak field amplitude was ∼200 nT, resulting in the largest difference between the observed magnetic field strength and a model for crustal magnetic fields of the entire MAVEN primary science phase. MAVEN detected planetary ions, including H+, O+, and
O2+, across the structure. The axial orientation estimated for the flux rope indicates that it likely formed as a result of interactions between the local crustal and overlaid draped interplanetary magnetic fields. Pitch angle distributions of ionospheric photoelectrons imply that this structure is connected to the Martian upper atmosphere. However, the flux rope is not present in observations at the next commensurable orbit crossing (approximately two Martian days later), implying that it eventually detaches from the atmosphere and is carried downstream. The flux rope observations occurred during an interplanetary coronal mass ejection event at Mars, suggesting that the disturbed upstream state played a role in allowing the interplanetary magnetic field to penetrate deeper into the Martian ionosphere than is typical, allowing the formation of the flux rope.
Key Points
MAVEN observed a giant flux rope near the subsolar point of the Martian ionosphere, downstream from the strong crustal fields
The observed giant ionospheric flux rope was formed via interactions between the local crustal and overlaid draped magnetic fields
The event was observed during the ICME passage by Mars, indicating that the ICME played a role in forming the observed giant flux rope
Protein-Protein Interactions (PPIs) involves in various biological processes, which are of significant importance in cancer diagnosis and drug development. Computational based PPI prediction methods ...are more preferred due to their low cost and high accuracy. However, existing protein structure based methods are insufficient in the extraction of protein structural information. Furthermore, most methods are less interpretable, which hinder their practical application in the biomedical field. In this paper, we propose MGPPI, which is a Multiscale graph convolutional neural network model for PPI prediction. By incorporating multiscale module into the Graph Neural Network (GNN) and constructing multi convolutional layers, MGPPI can effectively capture both local and global protein structure information. For model interpretability, we introduce a novel visual explanation method named Gradient Weighted interaction Activation Mapping (Grad-WAM), which can highlight key binding residue sites. We evaluate the performance of MGPPI by comparing with state-of-the-arts methods on various datasets. Results shows that MGPPI outperforms other methods significantly and exhibits strong generalization capabilities on the multi-species dataset. As a practical case study, we predicted the binding affinity between the spike (S) protein of SARS-COV-2 and the human ACE2 receptor protein, and successfully identified key binding sites with known binding functions. Key binding sites mutation in PPIs can affect cancer patient survival statues. Therefore, we further verified Grad-WAM highlighted residue sites in separating patients survival groups in several different cancer type datasets. According to our results, some of the highlighted residues can be used as biomarkers in predicting patients survival probability. All these results together demonstrate the high accuracy and practical application value of MGPPI. Our method not only addresses the limitations of existing approaches but also can assists researchers in identifying crucial drug targets and help guide personalized cancer treatment.
In this paper, in order to penalize for lack of divergence-free solution, we propose a sparse grad-div stabilized algorithm for the incompressible magnetohydrodynamics equations, which just adds a ...minimally intrusive module that implements grad-div stabilization with a sparse block structure matrix. Unconditional stability and error estimates of the proposed algorithm are provided and numerical tests are carried out. Compared to other grad-div stabilizations, the sparse grad-div stabilized algorithm is more efficient with some large values of grad-div parameters.
In this paper, we present a new static and time-dependent MagnetoHydroDynamic (MHD) equilibrium code, TokaMaker, for axisymmetric configurations of magnetized plasmas, based on the well-known ...Grad-Shafranov equation. This code utilizes finite element methods on an unstructured triangular grid to enable capturing accurate machine geometry and simple mesh generation from engineering-like descriptions of present and future devices. The new code is designed for ease of use without sacrificing capability and speed through a combination of Python, Fortran, and C/C++ components. A detailed description of the numerical methods of the code, including a novel formulation of the boundary conditions for free-boundary equilibria, and validation of the implementation of those methods using both analytic test cases and cross-code validation is shown. Results show expected convergence across tested polynomial degree for analytic and cross-code test cases.
•A developed CNN model proposed to predict the ETC of gradient porous ceramics.•Integrating self-attention mechanism into our model leads to a higher accuracy.•Grad-CAM applied to visually explain ...the optimization mechanism of our model.•Gradient QSGS developed to generate porous structure with gradient porosity.
Accurate and stable prediction of the effective thermal conductivity (ETC) of porous ceramic materials is of great significance for their application in areas such as optimizing the design of thermal barrier coatings and improving energy conversion efficiency. Porous ceramic materials exhibit complex porous structures with gradient porosity distributions that pose a great challenge for effective medium theory (EMT) and conventional convolutional neural networks (CNN) in attempting to accurately and stably predict the ETC of porous media. In this study, a CNN model that integrates self-attention and a multiscale feature-fusion mechanism is proposed to predict the ETC of porous media with greater accuracy and stability. The integration of the self-attention and multiscale feature-fusion mechanisms enhances the CNN's ability to learn long-range dependencies and preserve detailed information. The optimization of the CNN's accuracy and stability is visually illustrated using gradient-weighted class activation mapping (Grad-CAM) for ETC. Additionally, by employing the proposed gradient quartet structure generation set (QSGS), a gradient porous ceramic media dataset comprising 10 000 images was built to train the CNN model. Finally, the prediction results and relative error distribution of the ETC were compared across different models. Our model demonstrated improvements in statistical metrics, including a 33.7 % decrease in mean error, 25.2 % decrease in median error, and 59.6 % decrease in maximum error. The decreases in these metrics and Grad-CAM for the ETC strongly demonstrates that the model proposed in this work greatly improved the accuracy and stability of predicting the ETC of ceramic materials with gradient porosity distributions.
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