Multiscale Problems Research Articles

Imaging Markers Derived From MRI-Based Automated Kidney Segmentation.

Population-wide research on potential new imaging biomarkers of the kidney depends on accurate automated segmentation of the kidney and its compartments (cortex, medulla, and sinus). We developed a robust deep-learning framework for kidney (sub-)segmentation based on a hierarchical, three-dimensional convolutional neural network (CNN) that was optimized for multiscale problems of combined localization and segmentation. We applied the CNN to abdominal magnetic resonance images from the population-based German National Cohort (NAKO) study. There was good to excellent agreement between the model predictions and manual segmentations. The median values for the body-surface normalized total kidney, cortex, medulla, and sinus volumes of 9934 persons were 158, 115, 43, and 24 mL/m2. Distributions of these markers are provided both for the overall study population and for a subgroup of persons without kidney disease or any associated conditions. Multivariable adjusted regression analyses revealed that diabetes, male sex, and a higher estimated glomerular filtration rate (eGFR) are important predictors of higher total and cortical volumes. Each increase of eGFR by one unit (i.e., 1 mL/min per 1.73 m2 body surface area) was associated with a 0.98 mL/m2 increase in total kidney volume, and this association was significant. Volumes were lower in persons with eGFR-defined chronic kidney disease. The extraction of image-based biomarkers through CNN-based renal sub-segmentation using data from a population-based study yields reliable results, forming a solid foundation for future investigations.

A Nonoverlapping Hybrid FDTD-PITD Method Using Upwind Conditions for Multiscale Problems

A Nonoverlapping Hybrid FDTD-PITD Method Using Upwind Conditions for Multiscale Problems

From Domain Decomposition to Model Reduction for Large Nonlinear Structures

The numerical simulation of multiscale and multiphysics problems requires efficient tools for spatial localization and model reduction. A general strategy combining Domain Decomposition and Nonuniform Transformation Field Analysis (NTFA) is proposed herein for the simulation of nuclear fuel assemblies at the scale of a full nuclear reactor. The model at subdomain level solves the full elastic problem but with a reduced nonlinear loading, based on simplified boundary conditions, reduced creep flow rules, projected sign preserving contact conditions, and a NTFA like reduced friction law to get the evolution of each slipping mode. With this loading reduction, the local solution can be explicitly obtained from a small set of precomputed elementary elastic solutions. The numerical tests indicate that considerable cost reduction (a factor of 50 to 1000) can be achieved while preserving engineering accuracy.

Solving a class of multi-scale elliptic PDEs by Fourier-based mixed physics informed neural networks

Deep neural networks have garnered widespread attention due to their simplicity and flexibility in the fields of engineering and scientific calculation. In this study, we probe into solving a class of elliptic partial differential equations (PDEs) with multiple scales by utilizing Fourier-based mixed physics informed neural networks (dubbed FMPINN), its solver is configured as a multi-scale deep neural network. In contrast to the classical PINN method, a dual (flux) variable about the rough coefficient of PDEs is introduced to avoid the ill-condition of neural tangent kernel matrix caused by the oscillating coefficient of multi-scale PDEs. Therefore, apart from the physical conservation laws, the discrepancy between the auxiliary variables and the gradients of multi-scale coefficients is incorporated into the cost function, obtaining a satisfactory solution of PDEs by minimizing the defined loss through some optimization methods. Additionally, a trigonometric activation function is introduced for FMPINN, which is suited for representing the derivatives of complex target functions. Handling the input data by Fourier feature mapping will effectively improve the capacity of deep neural networks to solve high-frequency problems. Finally, to validate the efficiency and robustness of the proposed FMPINN algorithm, we present several numerical examples of multi-scale problems in various dimensional Euclidean spaces. These examples cover low-frequency and high-frequency oscillation cases, demonstrating the effectiveness of our approach. All code and data accompanying this manuscript will be publicly available at https://github.com/Blue-Giant/FMPINN.

Physics-Informed Neural Networks for High-Frequency and Multi-Scale Problems Using Transfer Learning

Physics-Informed Neural Network (PINN) is a data-driven solver for partial and ordinary differential equations (ODEs/PDEs). It provides a unified framework to address both forward and inverse problems. However, the complexity of the objective function often leads to training failures. This issue is particularly prominent when solving high-frequency and multi-scale problems. We proposed using transfer learning to boost the robustness and convergence of training PINN, starting training from low-frequency problems and gradually approaching high-frequency problems through fine-tuning. Through two case studies, we discovered that transfer learning can effectively train PINNs to approximate solutions from low-frequency problems to high-frequency problems without increasing network parameters. Furthermore, it requires fewer data points and less training time. We compare the PINN results using direct differences and L2 relative error showing the advantage of using transfer learning techniques. We describe our training strategy in detail, including optimizer selection, and suggest guidelines for using transfer learning to train neural networks to solve more complex problems.

DMS-yolov8 A gesture recognition algorithm based on improved yolov81

Aiming at the problems of slow speed and low accuracy of traditional neural network systems for real-time gesture recognition in complex backgrounds., this paper proposes DMS-yolov8-a gesture recognition method to improve yolov8. This algorithm replaces the Bottleneck convolution module in the backbone network of yolov8 with variable row convolution DCNV2, and increases the feature convolution range without increasing the computation amount through a more flexible feeling field. in addition, the self-developed MPCA attention module is added after the feature output layer of the backbone layer, which improves the problem of recognizing the accuracy of difference gestures in complex backgrounds by effectively combining the feature information of the contextual framework, taking into account the multi-scale problem of the gestures in the image, this paper introduces the SPPFCSPS module, which realizes multi-feature fusion and improves real-time accuracy of detection. Finally, the model proposed in this paper is compared with other models, and the proposed DMS-yolov8 model achieves good results on both publicly available datasets and homemade datasets, with the average accuracy up to 97.4% and the average mAP value up to 96.3%, The improvements proposed in this paper are effectively validated.

Gabor-net with multi-scale hierarchical fusion of features for fundus retinal blood vessel segmentation

This paper proposes a fundus retinal blood vessel segmentation model based on a deep convolutional network structure and biological visual feature extraction mechanism. It aims to solve the multi-scale problem of blood vessels in the fundus retinal blood vessel segmentation task in the field of medical image processing on the basis of increasing the biological interpretability of the model. First, the subject feature information of the retinal blood vessel image is obtained by using the non-subsampled Residual Bolck convolution main channel. Secondly, combined with the study of biological vision mechanisms, an information processing model of the Retina-Exogenius-Primary visual cortex (V1) ventral visual pathway was established. Gabor functions of different scales are used to simulate the structure of different levels of the visual pathway, and the scale information at different levels is integrated into the corresponding hierarchical stages of the convolutional main pathway network to enrich the information of small blood vessels and enhance the semantic information of the overall blood vessels. Finally, considering the imbalance of the ratio of vessel and nonvessel pixels, an adaptive optimization scheme using hybrid loss function weights is proposed to enhance the priority of blood vessel pixels in the calculation of the loss function. According to the experimental results on the STARE, DRIVE and CHASE_DB1 data sets, the model still achieves superior performance evaluation indicators overall compared with the existing optimal methods in the fundus retinal blood vessel segmentation task. This research is of great significance to the field of medical image processing and can provide more accurate auxiliary diagnostic information for clinical diagnosis and treatment.

Multiharmonic multiscale modelling in 3-D nonlinear magnetoquasistatics: Composite material made of insulated particles

The use of the classical finite element method (FEM) to solve problems with magnetic composites leads to huge linear systems that are impossible to solve. Instead, homogenization and multiscale methods are often used with the composite material replaced by a homogeneous material with the homogenized constitutive law obtained by solving cell-problems representing the mesoscale material structure. For non-linear time-dependent problems, FEM is often used with a time-transient method (TTM) and the solution is obtained one time-step at a time. However, in cases where a steady-state solution is of interest, the multiharmonic method can be faster and more cost effective for the same accuracy of the time discretization. In addition, when solving magnetoquasistatic multiscale problems with TTM, the dynamic hysteresis in the homogenized fields can slow down or even impede the convergence of the macro-scale problem due to the possibly non-continuously differentiable homogenized material laws. This work presents a novel robust modelling approach for non-linear magnetoquasistatic problems combining multiharmonic method with the multiscale method.

Thermo-mechanical coupled peridynamics simulation of concrete failure under fire scenarios

A coupled thermo-mechanical bond-based peridynamical (PD) method is developed to simulate thermal cracking processes in concrete. Based on the bond-based PD heat conduction and motion equations, the PD differential operator (PDDO) is used to express the classical computational fluid dynamics basic equations in a non-local integral form, establishing a PD model for the thermo-mechanical coupling problems. In this model, concrete is considered a heterogeneous material composed of aggregates and mortar, with material parameters assumed to be temperature-dependent. The multi-rate explicit time integration scheme is proposed to overcome the multi-scale time problem in coupled thermo-mechanical systems. The model is applied to simulate the transient heat transfer problem of a homogeneous plate. The results show good agreement with the analytical solution, providing evidence for the correctness and accuracy of the proposed coupled numerical method. The damage behavior of the borehole heated concrete plate is analyzed, followed by the simulation of the damage to the concrete plate under a fire scenario. The numerical results accurately predict the temperature distribution within the heterogeneous concrete and the resulting material damage. This study provides new theoretical basis for the fire resistance design and high-temperature performance improvement of concrete materials and structures.

Peridynamic modeling of seepage in multiscale fractured rigid porous media

AbstractThe numerical simulation of seepage in fractured porous media holds significant relevance for subsurface energy development. The presence of fractures at various scales profoundly influences the hydraulic properties of porous media during seepage. A peridynamic (PD)‐based frame is proposed for the seepage problem analysis of multiscale fractured porous media, in which micro‐fractures are implicitly represented like the porous media, macro‐fractures are explicitly represented. For fluid flow modeling, the peridynamic bonds are divided into three types: pore seepage bond, fracture seepage bond, and fluid exchange bond. The micro‐permeabilities of different bonds are derived by Darcy's law, Poiseuille's law, and fluid exchange model, respectively. The proposed peridynamic model can naturally simulate the seepage problem of porous rock with multiscale fractures in a unified framework. Then, four cases of pore seepage and fracture seepage are analyzed using the proposed model, fractured porous media seepage with micro‐fractures and macro‐fractures are respectively considered. The predicted results are compared with the available theoretical solutions, the close agreement shows that the wide validity and applicability of the proposed model in multiscale seepage problems.

Optimizing nanoporous metallic actuators through multiscale calculations and machine learning

Nanoporous materials (NMs) immersed in electrolytes can achieve approximately 1 % deformation at a low operating voltage of about 1 V. The actuation renders them promising artificial muscles. The actuation performance significantly hinges on the structure and size of nanopores and ligaments in NMs. Consequently, designing an optimal configuration is imperative for excellent performance. The actuation mechanism of NMs involves the coupling of multiple fields at various length scales, posing a formidable challenge to conventional simulation and design approaches. To surmount this challenge, we have developed a computational framework capable of conducting concurrent and sequential multiscale calculations. By utilizing artificial neural network (ANN) surrogate models trained on data obtained through the finite element method (FEM), the framework achieves optimized values for both actuation strain and effective Young's modulus within a designated design space. The constitutive model, which establishes the relationship between surface stress and charges in FEM, is derived from the surface eigenstress model and symbolic regression. This involves utilizing data calculated through joint density functional theory. This framework not only ensures the desired properties but also demonstrates its potential for effectively addressing other multiscale optimization problems.

Mitigating spectral bias for the multiscale operator learning

Neural operators have emerged as a powerful tool for learning the mapping between infinite-dimensional parameter and solution spaces of partial differential equations (PDEs). In this work, we focus on multiscale PDEs that have important applications such as reservoir modeling and turbulence prediction. We demonstrate that for such PDEs, the spectral bias towards low-frequency components presents a significant challenge for existing neural operators. To address this challenge, we propose a hierarchical attention neural operator (HANO) inspired by the hierarchical matrix approach. HANO features a scale-adaptive interaction range and self-attentions over a hierarchy of levels, enabling nested feature computation with controllable linear cost and encoding/decoding of multiscale solution space. We also incorporate an empirical H1 loss function to enhance the learning of high-frequency components. Our numerical experiments demonstrate that HANO outperforms state-of-the-art (SOTA) methods for representative multiscale problems.

Multi-level optimization strategies for large-scale nonlinear process systems

With growing needs to develop and improve climate-friendly processes, optimization strategies are essential at all levels of decision-making in chemical and energy processes, including process development, process synthesis and design, as well as process operations, control, scheduling, and planning. Challenges include the formulation of well-posed and well-conditioned process models, and development and application of efficient, reliable optimization algorithms. Here we describe a synthesis of optimization concepts and algorithms that enable large-scale nonlinear programming, nonintrusive decomposition strategies and the inclusion of a wide class of surrogate models. All of these are crucial to address challenging nonconvex, multi-scale problems in Computer Aided Process Engineering (CAPE). These elements are demonstrated through dynamic optimization strategies for novel energy generation, demand-based optimization for specialty chemicals, and optimization with integrated heterogeneous models for carbon capture processes.

Gas mask wearing detection based on Faster R-CNN

Gas masks are essential respiratory protective equipment commonly used by laborers who work in harsh environments. However, respiratory diseases and accidents can occur due to the absence of gas masks. To prevent these accidents, this paper developed an object detector that uses convolutional neural networks (CNNs) to detect whether workers are wearing gas masks. To achieve this goal, a gas mask detection dataset was constructed derived from real industrial scenarios and Faster R-CNN was improved for gas mask wearing detection. Firstly, to address the multi-scale problem in real scenes, the Feature Pyramid Network was introduced into Faster R-CNN to effectively fuse features between different levels and improve the detection ability of small objects. Secondly, the Online Hard Sample Mining algorithm was used to alleviate the class imbalance problems in the dataset. Finally, Mixup and Mosaic were used in the training process to augment the data and make the model better adapt to different scenes and complex backgrounds. After multiple experiments, the combination of the three optimization strategies improved the mAP 0.5 : 0.95 by 23.2%. This work is an initial attempt at gas mask wearing detection and there is still much room for improvement in terms of model and dataset.

Robust domain decomposition methods for high-contrast multiscale problems on irregular domains with virtual element discretizations

Our research focuses on the development of domain decomposition preconditioners tailored for second-order elliptic partial differential equations. Our approach addresses two major challenges simultaneously: i) effectively handling coefficients with high-contrast and multiscale properties, and ii) accommodating irregular domains in the original problem, the coarse mesh, and the subdomain partition. The robustness of our preconditioners is crucial for real-world applications, such as the efficient and accurate modeling of subsurface flow in porous media and other important domains.The core of our method lies in the construction of a suitable partition of unity functions and coarse spaces utilizing local spectral information. Leveraging these components, we implement a two-level additive Schwarz preconditioner. We demonstrate that the condition number of the preconditioned systems is bounded with a bound that is independent of the contrast. Our claims are further substantiated through selected numerical experiments, which confirm the robustness of our preconditioners.

Forces on a singing wineglass rim

The characterization of friction is a multiscale problem involving a balance between asperity contacts and fluid film forces, most commonly modeled with a velocity-dependent coefficient of friction. Periodic stick–slip phenomena are often associated with the friction force that causes mechanical vibration. This type of vibration can cause noise to radiate via structural modes of a system. Notable examples include journal bearings, brake squeal, turkey calls, and wineglasses. Singing wineglasses have been used for centuries as musical instruments, so musical acousticians have studied the structural vibrations and acoustic output. However, the tri-axial force applied to the rim has not been measured. A test rig was designed to measure the vertical, tangential, and radial dynamic forces applied to the spinning glass rim and simultaneously capture the radiated noise. The sound radiated from the wineglass was observed to depend on the relative velocity at the rim and applied vertical load, so a stability region for a clear sound was determined. Additionally, the strongest radiating modes and harmonics in the pressure were found in the concurrently measured nonlinear force. This work may be extended to confirm the force measurement by existing friction models, a water medium, and more complicated systems.

A Pre-splitting Green’s Function based Hybrid Fast Algorithm for Multiscale Problems

Based on the splitting form of the Green’s function, a hybrid fast algorithm is proposed for efficient analysis of multiscale problems. In this algorithm, the Green’s function is a priori split into two parts: a spectrally band-limited part and a spatially localized part. Then, the fast Fourier transforms (FFT) utilizing the global Cartesian grid and the matrix compression method aided by an adaptive octree grouping are implemented for these two parts, respectively. Compared with the traditional methods which only employ the FFT for acceleration, the proposed hybrid fast algorithm is capable of maintaining low memory consumption in multiscale problems without compromising time cost. Moreover, the proposed algorithm does not need cumbersome geometric treatment to implement the hybridization, and can be established in a concise and straightforward manner. Several numerical examples discretized with multiscale meshes are provided to demonstrate the computational performance of proposed hybrid fast algorithm.

A Review of Physics Informed Neural Networks for Multiscale Analysis and Inverse Problems

A Review of Physics Informed Neural Networks for Multiscale Analysis and Inverse Problems

A CutFE-LOD method for the multiscale elliptic problems on complex domains

In this paper, we construct a new combined multiscale finite element method to solve the elliptic problem which has both a highly oscillating diffusion coefficient and a very complicated boundary. To design a numerical method for this kind of problems is difficult because that the microscopically geometrical information of the boundary and oscillation information of the coefficient should be taken into account simultaneously, which usually requires a very fine mesh. The main idea of the proposed method is to adopt unfitted fine scale meshes on the complicated boundary by using the cut finite element, and adopt the coarse scale meshes for the other part by using the recently developed local orthogonal decomposition (LOD) technique. Through this way, the introduced method can deal with arbitrarily complex boundaries and cut down some unnecessary computational effort. To ensure that the discrete systems are well-posed, we utilize the penalty technique on the artificial interface between coarse and fine meshes as well as on the boundary. The ghost penalty technique is used on the boundary to avoid the ill-condition of the system matrix. The error estimate and the condition number of the system matrix for the proposed method are derived without any periodic assumptions on the coefficient and boundary shape. Especially, the result is independent of the way that the boundary cut the mesh. Numerical experiments further confirm the theoretical results and demonstrate the accuracy and efficiency of the proposed method.

Food oral processing as a multiscale soft matter physics problem

Food oral processing as a multiscale soft matter physics problem