Engineering with Computers最新文献

This research seeks to explore the heat shift mechanisms in a rotating system that contains a hybrid nanofluid comprising of graphene oxide and copper particles mixed with pure water, using a novel methodology. The fluid flow in a rotating system is described by mathematical equations that involve nonlinear partial differential equations (PDEs). These equations are simplified by using similarity transformations, resulting in a system of ordinary differential equations. In general, it is not feasible to find a closed-form analytical solution for nonlinear ordinary differential equations (ODEs), which implies that determining an exact mathematical expression that characterizes the behavior of the solution to such ODEs is often challenging or impossible. To that end, we have utilized the controlled learning procedure of machine learning algorithms to predict the solutions for the nonlinear nanofluid problem flowing in the rotating system. The surrogated model are developed for different cases and scenarios, to review the might of differences in various physical parameters on the profiles of the fluid. Furthermore, the solutions are supported by performing an extensive statistical analysis based on different errors. It is concluded that machine learning-based method can potentially provide insights into the underlying physics of nonlinear flow problems, which can aid in the progress of more advanced and accurate models for prognosticating the behavior of nonlinear systems.

Tau tangles in the brain cortex spread along the brain network in distinct patterns among Alzheimer's patients. We aim to simulate their network-based spreading within the cortex, tailored to each individual along the Alzheimer's continuum, without assuming any assumptions about the network architecture. A group-level intrinsic spreading network was constructed to model the pathways for the proximal and distal spreading of tau tangles by optimizing the biophysical model based on a discovery dataset of longitudinal tau positron emission tomography images for 78 amyloid-positive individuals. Group-level spreading parameters were also obtained and subsequently adjusted to produce individuated tau trajectories. By simulating these individuated tau spreading models for every individual in the discovery dataset, we successfully captured proximal and distal tau spreading, allowing reliable inferences about the underlying mechanism of tau spreading. Simulating the models also allowed highly accurate prediction of future tau topography for both discovery and independent validation datasets.

The conductive interconnect structure that connects the electrical functional devices is an important micro-nano structure in stretchable electronics. Given the reliance of numerous devices on steady electrical currents for operation, stretchable electronics would benefit from interconnects with minimal resistance variation during deformation. This paper proposes a topology optimization method for the design of stretchable interconnect structures with stable resistance under large deformation. In the proposed method, an equal material method considering geometrically nonlinear and electromechanical coupling effects is developed to evaluate the resistance of a deformed structure. Besides, a new connectivity control method is proposed to ensure the connectivity between the inlet and outlet by making full use of the electrical problem itself. To achieve the design goal of connected interconnect structures with negligible resistance fluctuation during stretching, a topology optimization formulation is established, and the corresponding sensitivity is also analytically derived. Several numerical examples show that the proposed method is capable of computationally and intelligently generating stretchable structures with extremely small variations in resistance during stretching.

Although deep learning has achieved remarkable success in various scientific machine learning applications, its opaque nature poses concerns regarding interpretability and generalization capabilities beyond the training data. Interpretability is crucial and often desired in modeling physical systems. Moreover, acquiring extensive datasets that encompass the entire range of input features is challenging in many physics-based learning tasks, leading to increased errors when encountering out-of-distribution (OOD) data. In this work, motivated by the field of functional data analysis (FDA), we propose generalized functional linear models as an interpretable surrogate for a trained deep learning model. We demonstrate that our model could be trained either based on a trained neural network (post-hoc interpretation) or directly from training data (interpretable operator learning). A library of generalized functional linear models with different kernel functions is considered and sparse regression is used to discover an interpretable surrogate model that could be analytically presented. We present test cases in solid mechanics, fluid mechanics, and transport. Our results demonstrate that our model can achieve comparable accuracy to deep learning and can improve OOD generalization while providing more transparency and interpretability. Our study underscores the significance of interpretable representation in scientific machine learning and showcases the potential of functional linear models as a tool for interpreting and generalizing deep learning.

In this paper, we develop a semi-implicit partitioned finite element and discontinuous Galerkin method for the non-isothermal non-Newtonian fluid structure interaction (NNFSI) problem within the arbitrary Lagrangian–Eulerian (ALE) framework. The structure is composed of the elastic solid material. The entire mathematical model consists of the governing equations of the non-Newtonian fluid and the structure, as well as the boundary conditions on the contacting interface. The rheological behavior of non-Newtonian fluid is described according to the power law constitutive equation. The whole system is split into several sub-equations and then appropriate finite element method or discontinuous Galerkin method is employed for the spatial discretizations of them. As for the deformation of the structure and the change of the fluid area and computational mesh, we employ the moving mesh technique to handle them. The problem involving a hot flexible rod fixed on the hot bottom of an irregular pipe is fully investigated. The influences of the fluid inlet velocity and the behavior of the fluid on the deformation of the rod and the temperature distribution are all analyzed.

This paper introduces the application of Physics-Informed Neural Network (PINN), a novel class of scientific machine learning techniques, for analyzing the static bending response of nanobeams as essential structural elements in micro/nanoelectromechanical systems, including nanoprobes, atomic force microscope sensors, nanoswitches, nanoactuators, and nanoscale biosensors on a three-parameter nonlinear elastic foundation. The study combines Euler–Bernoulli beam theory and Eringen’s nonlocal continuum theory to derive the governing differential equation using the minimum total potential energy principle. PINN is utilized for approximating the differential equation solution and identifying the nanobeam’s nonlocal parameter through an inverse problem with measurement data. The loss function incorporates terms representing the initial and boundary conditions, along with the differential equation residual at specific points in the domain and boundary. The research demonstrates PINN’s efficacy in analyzing nanobeam behavior on nonlinear elastic foundations, providing valuable insights into responses under different loading and boundary conditions. The proposed approach's accuracy and efficiency are validated through comparisons with existing literature. Additionally, the study investigates the effects of activation functions, collocation points’ number and distribution, nonlocal parameter, foundation stiffness coefficients, loading types, and various boundary conditions on nanobeam bending behavior.

We introduce a novel immersed-like numerical framework that combines isogeometric analysis with smoothed particle hydrodynamics for simulating air-blast–structure interaction. The solid domain is represented by a Lagrangian point cloud, which is immersed into a background Eulerian fluid domain. The smoothed particle hydrodynamics framework is employed to solve the equations of motion of the solid point cloud, whereas isogeometric analysis is used for the fluid mechanics equations on the background domain. The coupling strategy relies on a penalty-based volumetric coupling scheme that penalizes the velocity difference between the two domains, and involves a minimal amount of modification to existing codes, resulting in a straightforward implementation. The immersed nature of the proposed approach, combined with volumetric coupling, eliminates the need for explicit tracking of fluid–structure interfaces and imposes no limitations on solid domain motion and topology. Ample mathematical details are provided, and the proposed method is verified and validated against established numerical tools and experimental studies. The results affirm the method’s accuracy, robustness, and ease with which it seamlessly integrates two distinct computational techniques.

Physics informed neural network (PINN) frameworks have been developed as a powerful technique for solving partial differential equations (PDEs) with potential data integration. However, when applied to advection based PDEs, PINNs confront challenges such as parameter sensitivity in boundary condition enforcement and diminished learning capability due to an ill-conditioned system resulting from the strong advection. In this study, we present a multiscale stabilized PINN formulation with a weakly imposed boundary condition (WBC) method coupled with transfer learning that can robustly model the advection diffusion equation. To address key challenges, we use an advection-flux-decoupling technique to prescribe the Dirichlet boundary conditions, which rectifies the imbalanced training observed in PINN with conventional penalty and strong enforcement methods. A multiscale approach under the least squares functional form of PINN is developed that introduces a controllable stabilization term, which can be regarded as a special form of Sobolev training that augments the learning capacity. The efficacy of the proposed method is demonstrated through the resolution of a series of benchmark problems of forward modeling, and the outcomes affirm the potency of the methodology proposed.

This contribution presents a model order reduction framework for real-time efficient solution of trimmed, multi-patch isogeometric Kirchhoff-Love shells. In several scenarios, such as design and shape optimization, multiple simulations need to be performed for a given set of physical or geometrical parameters. This step can be computationally expensive in particular for real world, practical applications. We are interested in geometrical parameters and take advantage of the flexibility of splines in representing complex geometries. In this case, the operators are geometry-dependent and generally depend on the parameters in a non-affine way. Moreover, the solutions obtained from trimmed domains may vary highly with respect to different values of the parameters. Therefore, we employ a local reduced basis method based on clustering techniques and the Discrete Empirical Interpolation Method to construct affine approximations and efficient reduced order models. In addition, we discuss the application of the reduction strategy to parametric shape optimization. Finally, we demonstrate the performance of the proposed framework to parameterized Kirchhoff-Love shells through benchmark tests on trimmed, multi-patch meshes including a complex geometry. The proposed approach is accurate and achieves a significant reduction of the online computational cost in comparison to the standard reduced basis method.

Because the complete set of Trefftz functions for the 3D biharmonic equation is not yet well established, a multiple-direction Trefftz method (MDTM) and an in-plane biharmonic functions method (IPBFM) are deduced in the paper. Inspired by the Trefftz method for the 2D biharmonic equation, a novel MDTM incorporates planar directors into the 2D like Trefftz functions to solve the 3D biharmonic equation. These functions being a series of biharmonic polynomials of different degree, automatically satisfying the 3D biharmonic equation, are taken as the bases to expand the solution. Then, we derive a quite large class solution of the 3D biharmonic equation in terms of 3D harmonic functions, and 2D biharmonic functions in three sub-planes. The 2D biharmonic functions are formulated as the Trefftz functions in terms of the polar coordinates for each sub-plane. Introducing a projective variable, we can obtain the projective type general solution for the 3D Laplace equation, which is used to generate the 3D Trefftz type harmonic functions. Several numerical examples confirm the efficiency and accuracy of the proposed MDTM and IPBFM.