Physics-Informed deep operator learning framework for multiphysics heat and mass transport in rotating disk energy systems

A comprehensive empirical study on bug characteristics of deep learning frameworks

Deep learning (DL) frameworks serve as the backbone for a wide range of artificial intelligence applications. However, bugs within DL frameworks can cascade into critical issues in higher-level applications, jeopardizing reliability and security. While numerous techniques have been proposed to detect bugs in DL frameworks, research exploring common API patterns across frameworks and the potential risks they entail remains limited. Notably, many DL frameworks expose similar APIs with overlapping input parameters and functionalities, rendering them vulnerable to shared bugs, where a flaw in one API may extend to analogous APIs in other frameworks. To address this challenge, we propose MirrorFuzz, an automated API fuzzing solution to discover shared bugs in DL frameworks. MirrorFuzz operates in three stages: First, MirrorFuzz collects historical bug data for each API within a DL framework to identify potentially buggy APIs. Second, it matches each buggy API in a specific framework with similar APIs within and across other DL frameworks. Third, it employs large language models (LLMs) to synthesize code for the API under test, leveraging the historical bug data of similar APIs to trigger analogous bugs across APIs. We implement MirrorFuzz and evaluate it on four popular DL frameworks (TensorFlow, PyTorch, OneFlow, and Jittor). Extensive evaluation demonstrates that MirrorFuzz improves code coverage by 39.92% and 98.20% compared to state-of-the-art methods on TensorFlow and PyTorch, respectively. Moreover, MirrorFuzz discovers 315 bugs, 262 of which are newly found, and 80 bugs are fixed, with 52 of these bugs assigned CNVD IDs.

Objective: To design a deep transfer learning framework for modeling fluence map predictions for stereotactic body radiation therapy (SBRT) of adrenal cancer and similar sites that usually have a small number of cases. Approach: We developed a transfer learning framework for adrenal SBRT planning that leverages knowledge in a pancreas SBRT planning model. Treatment plans from the two sites had different dose prescriptions and beam settings but both prioritized gastrointestinal sparing. A base framework was first trained with 100 pancreas cases. This framework consists of two convolutional neural networks (CNN), which predict individual beam doses (BD-CNN) and fluence maps (FM-CNN) sequentially for 9-beam intensity-modulated radiation therapy (IMRT) plans. Forty-five adrenal plans were split into training/validation/test sets with the ratio of 20/10/15. The base BD-CNN was re-trained with transfer learning using 5/10/15/20 adrenal training cases to produce multiple candidate adrenal BD-CNN models. The base FM-CNN was directly used for adrenal cases. The deep learning (DL) plans were evaluated by several clinically relevant dosimetric endpoints, producing a percentage score relative to the clinical plans. Main results: Transfer learning significantly reduced the number of training cases and training time needed to train such a DL framework. The adrenal transfer learning model trained with 5/10/15/20 cases achieved validation plan scores of 85.4/91.2/90.7/89.4, suggesting that model performance saturated with 10 training cases. Meanwhile, a model using all 20 adrenal training cases without transfer learning only scored 80.5. For the final test set, the 5/10/15/20-case models achieved scores of 73.5/75.3/78.9/83.3. Significance: It is feasible to use deep transfer learning to train an IMRT fluence prediction framework. This technique could adapt to different dose prescriptions and beam configurations. This framework potentially enables DL modeling for clinical sites that have a limited dataset, either due to few cases or due to rapid technology evolution.

Accurate prediction and confirmation of mechanical properties are critical for the reliable design and deployment of sustainable aluminum–agro-waste composites (AWCs). This study presents a confirmatory analytical–experimental–deep machine learning (DML) framework for the identification of true material properties under multi-response conditions. Experimental characterization yielded mean tensile strength of 190.61 MPa, compressive strength of 287.16 MPa, flexural strength of 243.94 MPa, wear rate of 5.46 × 10⁻⁶ mm³ /N·m, coefficient of friction of 0.34, and fatigue life of 5.86 × 10⁵ cycles, with low variability observed in strength-related properties and higher dispersion in tribological and fatigue responses. Isolated analytical predictions produced comparable estimates for tensile (189.60 MPa), compressive (296.42 MPa), flexural (255.75 MPa), and fatigue properties (5.97 × 10⁵ cycles), but failed to reliably capture tribological behavior, yielding a non-physical negative wear rate (− 4.06 mm³/N·m) and an overestimated coefficient of friction (0.45). Consolidated analytical modeling improved agreement for tensile (187.60 MPa), compressive (285.63 MPa), flexural (244.88 MPa), and fatigue life (5.86 × 10⁵ cycles), yet significantly deviated in tribological predictions, producing unrealistically high wear rate (0.20 mm³/N·m) and coefficient of friction (2.84). To resolve these discrepancies, DML models—implemented via a deep convolutional neural network (ID-CNN) and a hybrid residual CNN guided by a residual-based loss function—were employed to reconcile analytical (isolated/consolidated) predictions with experimental data. The DML framework successfully minimized analytical–experimental residuals and confirmed true predictive reliability for compressive strength, flexural strength, coefficient of friction, and fatigue life, while consistently identifying wear rate as falsely predicted across analytical frameworks. These findings establish DML as both a predictive and diagnostic tool, enabling discrimination between truly confirmed and analytically unstable properties. The proposed framework offers a scalable, data-informed pathway for optimized composite design, process refinement, and industrial adoption, with potential extension to multi-scale modeling and real-time process monitoring. Residual-based DML loss quantifies and minimizes analytical–experimental prediction errors. • Residual-based DML loss quantifies and minimizes analytical–experimental prediction errors. • Integrated analytical–DML modeling confirms strength, fatigue, and friction properties. • Bulk properties converge, while wear rate shows persistent tribological uncertainty. • The framework supports reliable certification and sustainable composite design.

Due to the complexity of both material composition and the structure of the catalyst layer (CL) used in the proton-exchange membrane fuel cell (PEMFC), conjugated heat and mass transfer as well as electrochemical processes simultaneously occur through the CL. In this study, a microstructure model of CL was first reconstructed using images acquired by Nano-computed tomography (Nano-CT) of a real sample of CL. Then, the multiphysics dynamic distribution (MPDD) simulation, which is inherently a multiscale approach made of a combination of pore-scale and homogeneous models, was conducted on the reconstructed microstructure model to compute the corresponded heat and mass transport, electrochemical reactions, and water phase-change processes. Considering a computational domain with the size of 4 um and cube shape, this model consisting of mass and heat transport as well as electrochemical reactions reached a stable solution within 3 s as the convergence time. In the presence of sufficient oxygen, proton conduction was identified as the dominant factor determining the strength of the electrochemical reaction. Additionally, it was concluded that current density, temperature, and the distribution of water all exhibit similar distribution trends, which decrease from the interface between CL and the proton-exchange membrane to the interface between CL and the gas-diffusion layer. The present study not only provides an in-depth understanding of the mass and heat transport and electrochemical reaction in the CL microstructure, but it also guides the optimal design and fabrication of CL components and structures, such as improving the local structure to reduce the number of dead pores and large agglomerates, etc.

In dry snow packs experiencing a temperature gradient, heat and mass transport is responsible for the metamorphism of ice crystals. The work presented herein investigates the influence of geometry, density, and temperature on the coupled, simultaneous heat and mass transport in idealized, two dimensional ice lattice cells. Mass transfer rates, mass flux rates, concentration and temperature distributions, and effective diffusion coefficients and thermal conductivities are presented as functions of temperature, geometry, density, and time. The results of the analysis show clearly that both the mass and heat transport are strongly dependent upon the ice lattice geometry. The effective diffusion coefficient is enhanced relative to the diffusion coefficient for water vapor in air for all of the two dimensional geometries studied. In addition, the preferential growth of branch grains has been verified using both static and dynamic, computer generated images of the ice lattice cells undergoing temperature gradient metamorphism.

Abstract We have studied heat and mass transport in two-dimensional, infinite Prandtl number, incompressible thermal convection for a range of Rayleigh numbers (Ra), between 106 and 108, and two different aspect-ratio boxes, between 1·8 and 10. This study has been motivated by recent developments in studying the transition from weak to strong turbulence in thermal convection. We have employed a two-dimensional finite element method in solving the time-dependent convection equations. Passive tracers, up to 900, have been put into the flow fields for monitoring the style and pattern of mass transport. At Ra around 106 convection does not take place in a strictly cellular mode. Thermals are ejected from the hot and cold boundary layers. These boundary-layer instabilities enhance the mass transport in the interior of individual cells. The fate of these instabilities is determined ultimately by the large-scale circulation. The persistent large-scale circulation gives rise to a significant decrease of the heat transport, compared to steady-state boundary-layer predictions. Cross-cell mass transport over large horizontal distances in large aspect ratio domains is inhibited by the primary rising and sinking currents, whose positions would vary over a time scale much longer those associated with boundary-layer instabilities. At high Ra, between 107 and 108, we find a total breakdown of globally connected thermal plumes for base-heated convection. In this hard turbulent regime the plumes become disconnected and efficiency in mass transport is enhanced. The efficiency of mixing is not only governed by the magnitude of the convective velocities but also by the style of convection. With internal heating the large-scale flow becomes smaller and mass transport between neighboring cells is increased by the temporal variabilities in the flow patterns induced by internal heating. Mixing in the Earth's mantle is thus influenced by many factors. Among them are the complexity and strength of time-dependent convection, the aspect-ratio of the global configuration and the amount of internal heating. Key words: Mantle convectionmixinghard turbulence

Deep learning (DL) frameworks are essential to DL-based software systems, and framework bugs may lead to substantial disasters, thus requiring effective testing. Researchers adopt DL models or single interfaces as test inputs and analyze their execution results to detect bugs. However, floating-point errors, inherent randomness, and the complexity of test inputs make it challenging to analyze execution results effectively, leading to existing methods suffering from a lack of suitable test oracles. Some researchers utilize metamorphic testing to tackle this challenge. They design Metamorphic Relations (MRs) based on input data and parameter settings of a single framework interface to generate equivalent test inputs, ensuring consistent execution results between original and generated test inputs. Despite their promising effectiveness, they still face certain limitations. (1) Existing MRs overlook structural complexity, limiting test input diversity. (2) Existing MRs focus on limited interfaces, which limits generalization and necessitates additional adaptations. (3) Their detected bugs are related to the result consistency of single interfaces and far from those exposed in multi-interface combinations and runtime metrics (e.g., resource usage). To address these limitations, we propose ModelMeta, a model-level metamorphic testing method for DL frameworks with four MRs focused on the structure characteristics of DL models. ModelMeta augments seed models with diverse interface combinations to generate test inputs with consistent outputs, guided by the QR-DQN strategy. It then detects bugs through fine-grained analysis of training loss/gradients, memory/GPU usage, and execution time. We evaluate the effectiveness of ModelMeta on three popular DL frameworks (i.e., MindSpore, PyTorch, and ONNX) with 17 DL models from ten real-world tasks ranging from image classification to object detection. Results demonstrate that ModelMeta outperforms state-of-the-art baselines from the perspective of test coverage and diversity of generated test inputs. Regarding bug detection, ModelMeta has identified 31 new bugs, of which 27 have been confirmed, and 11 have been fixed. Among them, seven bugs existing methods cannot detect, i.e., five wrong resource usage bugs and two low-efficiency bugs. These results demonstrate the practicality of our method.

Developers of deep learning applications (shortened as application developers) commonly use deep learning frameworks in their projects. However, due to time pressure, market competition, and cost reduction, developers of deep learning frameworks (shortened as framework developers) often have to sacrifice software quality to satisfy a shorter completion time. This practice leads to technical debt in deep learning frameworks, which results in the increasing burden to both the application developers and the framework developers in future development.In this paper, we analyze the comments indicating technical debt (self-admitted technical debt) in 7 of the most popular open-source deep learning frameworks. Although framework developers are aware of such technical debt, typically the application developers are not. We find that: 1) there is a significant number of technical debt in all the studied deep learning frameworks. 2) there is design debt, defect debt, documentation debt, test debt, requirement debt, compatibility debt, and algorithm debt in deep learning frameworks. 3) the majority of the technical debt in deep learning framework is design debt (24.07% - 65.27%), followed by requirement debt (7.09% - 31.48%) and algorithm debt (5.62% - 20.67%). In some projects, compatibility debt accounts for more than 10%. These findings illustrate that technical debt is common in deep learning frameworks, and many types of technical debt also impact the deep learning applications. Based on our findings, we highlight future research directions and provide recommendations for practitioners.

Detection of moisture content in salted sea cucumbers by hyperspectral and low field nuclear magnetic resonance based on deep learning network framework

Image-based 3D reconstruction and permeability modelling of rock using enhanced interpretable deep residual learning

BackgroundNasopharyngeal carcinoma (NPC), an endemic malignancy in Southeast Asia and southern China, necessitates precise delineation of the gross tumor volume (GTV) for radiotherapy to optimize patient prognosis. Positron emission tomography (PET) imaging offers valuable metabolic insights to guide radiotherapy planning but is hampered by manual GTV segmentation, which is labor-intensive and prone to inter- and intra-observer variability. Conventional segmentation methods are inherently limited, and comparative evaluations of deep learning (DL) frameworks for PET-based primary NPC lesion segmentation remain scarce. Thus, this study aimed to optimize the delineation of primary NPC radiotherapy target volumes by leveraging PET-image-based DL segmentation technology, with the goal of enhancing both the precision and efficiency of lesion delineation.MethodsResearchers retrospectively collected PET imaging data from 212 NPC patients at the Affiliated Hospital of Guangdong Medical University. The patients were randomly divided into training (170 patients) and testing (42 patients) datasets. A radiation oncologist and a nuclear medicine physician collaboratively delineated the cancer lesion boundaries through consensus. After data preprocessing, three DL models (Res-Unet, Nn-Unet, and Nn-Former) were used to automatically segment the lesions. Training was based on the training dataset. During evaluation, the models’ segmentation performance was comprehensively assessed using Dice similarity coefficient (DSC) and Hausdorff distance (HD). A visual analysis of the results was also conducted to intuitively understand the models’ segmentation capabilities.ResultsIn the training set, Nn-Unet achieved the highest DSC of 0.869, whereas in the testing set, its DSC was 0.833. The DSC for Nn-Former hovered around 0.8 in both the training and testing sets. In contrast, Res-Unet demonstrated the lowest DSC values among the three models, particularly in the testing set (DSC =0.794). Statistical analysis revealed that the DSC of Nn-Unet was significantly higher than that of both Res-Unet and Nn-Former in the training set (P<0.01 for both comparisons). Regarding the 95% HD and average surface distance (ASD) values, Nn-Unet outperformed the other two models in both the training and testing sets. However, Res-Unet exhibited a much higher HD value in the testing set compared to the training set. The Loss curves for all models gradually decreased as training progressed, indicating that the models were learning relevant features of NPC lesions. The final Loss value for Res-Unet was approximately 0.7, whereas Nn-Unet and Nn-Former had final Loss values below 0.8.ConclusionsThe PET-image-based automatic segmentation model for the primary tumor of NPC established in this study demonstrates the clinical potential of Nn-Unet in primary lesion of NPC segmentation tasks.

Traditional differential expression genes (DEGs) identification models have limitations in small sample size datasets because they require meeting distribution assumptions, otherwise resulting high false positive/negative rates due to sample variation. In contrast, tabular data model based on deep learning (DL) frameworks do not need to consider the data distribution types and sample variation. However, applying DL to RNA-Seq data is still a challenge due to the lack of proper labeling and the small sample size compared to the number of genes. Data augmentation (DA) extracts data features using different methods and procedures, which can significantly increase complementary pseudo-values from limited data without significant additional cost. Based on this, we combine DA and DL framework-based tabular data model, propose a model TabDEG, to predict DEGs and their up-regulation/down-regulation directions from gene expression data obtained from the Cancer Genome Atlas database. Compared to five counterpart methods, TabDEG has high sensitivity and low misclassification rates. Experiment shows that TabDEG is robust and effective in enhancing data features to facilitate classification of high-dimensional small sample size datasets and validates that TabDEG-predicted DEGs are mapped to important gene ontology terms and pathways associated with cancer.

A finite element formulation for a convection–diffusion equation based on Cattaneo’s law

Background and objective: Despite fast evolution cycles in deep learning methodologies for medical imaging in radiotherapy, auto-segmentation solutions rarely run in clinics due to the lack of open-source frameworks feasible for processing DICOM RT Structure Sets. Besides this shortage, available open-source DICOM RT Structure Set converters rely exclusively on 2D reconstruction approaches leading to pixelated contours with potentially low acceptance by healthcare professionals. PyRaDiSe, an open-source, deep learning framework independent Python package, addresses these issues by providing a framework for building auto-segmentation solutions feasible to operate directly on DICOM data. In addition, PyRaDiSe provides profound DICOM RT Structure Set conversion and processing capabilities; thus, it applies also to auto-segmentation-related tasks, such as dataset construction for deep learning model training.Methods: The PyRaDiSe package follows a holistic approach and provides DICOM data handling, deep learning model inference, pre-processing, and post-processing functionalities. The DICOM data handling allows for highly automated and flexible handling of DICOM image series, DICOM RT Structure Sets, and DICOM registrations, including 2D-based and 3D-based conversion from and to DICOM RT Structure Sets. For deep learning model inference, extending given skeleton classes is straightforwardly achieved, allowing for employing any deep learning framework. Furthermore, a profound set of pre-processing and post-processing routines is included that incorporate partial invertibility for restoring spatial properties, such as image origin or orientation.Results: The PyRaDiSe package, characterized by its flexibility and automated routines, allows for fast deployment and prototyping, reducing efforts for auto-segmentation pipeline implementation. Furthermore, while deep learning model inference is independent of the deep learning framework, it can easily be integrated into famous deep learning frameworks such as PyTorch or Tensorflow. The developed package has successfully demonstrated its capabilities in a research project at our institution for organs-at-risk segmentation in brain tumor patients. Furthermore, PyRaDiSe has shown its conversion performance for dataset construction.Conclusions: The PyRaDiSe package closes the gap between data science and clinical radiotherapy by enabling deep learning segmentation models to be easily transferred into clinical research practice. PyRaDiSe is available on https://github.com/ubern-mia/pyradise and can be installed directly from the Python Package Index using pip install pyradise.