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In this work, we proposed a robust radial point interpolation method empowered with neural network solvers (RPIM-NNS) for solving highly nonlinear solid mechanics problems. It is enabled by neural network solvers via minimizing an energy-based functional loss. The RPIM-NNS has the following key ingredients: (1) It uses radial basis functions (RBFs) for displacement interpolation at arbitrary points in the problem domain, permitting irregular node distributions. (2) Nodes are placed also beyond the domain boundary, allowing the convenient implementation of boundary conditions of both Dirichlet and Neumann types. (3) It uses strain energy in an integral form as a part of the loss function, ensuring solution stability. (4) A well-developed gradient descendant algorithm in machine learning is employed to find the optimal solution, enabling robustness and ease in handling material and geometrical nonlinearities. (5) The proposed RPIM-NNS is compatible with parallel computing schemes. The performance of this method is tested using nonlinear problems including Cook's membrane and 3D twisting rubber problems, demonstrating its remarkable stability and robustness. This work, which seamlessly integrates the neural network solvers with mechanics governing equations and computational mechanics techniques, offers an excellent alternative for nonlinear solid mechanics problems. MATLAB codes are made available at https://github.com/JinshuaiBai/RPIM%5fNNS for free downloading. [ABSTRACT FROM AUTHOR]

• A new PINN-based topology optimization framework is proposed. • The proposed framework employs PINN to conduct structural analysis to replace FEA. • The proposed framework does not require any labelled data to train PINN. • The proposed framework can effectively optimize the problem domains. • Comparisons and discussions are provided between the topology optimization methods. Physics-Informed Neural Networks (PINNs) have recently attracted exponentially increasing attention in the field of computational mechanics. This paper proposes a novel topology optimization framework: Physics-Informed Neural Network-based Topology Optimization (PINNTO). Unlike existing machine-learning based topology optimization frameworks, PINNTO employs an energy-based PINN to replace Finite Element Analysis (FEA) in the conventional structural topology optimization, to numerically determine the deformation states, which is a key novelty in the proposed methodology. A supervised neural network that respects governing physical laws defined via partial differential equations is trained to develop the corresponding network without any labelled data, with the intention of solving solid mechanics problems. To assess feasibility and potential of the proposed PINNTO framework, a number of topology-optimization-related case studies have been implemented. The subsequent findings illustrate that PINNTO has the ability to attain optimized topologies with neither labelled data nor FEA. In addition, it has the capability to generate comparable designs to those produced by the current successful approaches such as Solid Isotropic Material with Penalization (SIMP). Based on the results of this study, it can also be deduced that PINNTO can acquire optimal topologies for various types of complex domains given that the boundary conditions and loading configurations are correctly imposed for the associated energy-based PINN. Consequently, the proposed PINNTO framework has demonstrated promising capabilities to solve problems under conditions when the usage of FEA is challenged (if not impossible). In summary, the proposed PINNTO framework opens up a new avenue for structural design in this ' data-rich ' age. [ABSTRACT FROM AUTHOR]

Neural Particle Method (NPM) is a newly proposed Physics-Informed Neural Network (PINN) based, truly meshfree method for hydrodynamics modeling. In the NPM, PINN is applied to globally approximate field variables, and the high-order Implicit Runge–Kutta (IRK) method is used to treat the time integration. The NPM can easily achieve incompressibility and deal with the free-surface problem. However, the NPM is currently limited to inviscid hydrodynamics problems and is computationally expensive. In this work, we developed a general NPM (gNPM) for viscous hydrodynamics modeling. In the gNPM, a single pressure is output as the predicted pressure field rather than the multiple pressures in the original NPM. Thus, the size of the neural network is greatly reduced, making the gNPM computationally more efficient. Besides, the spatial derivatives in the governing equations are calculated with respect to the current spatial coordinates rather than the predicted space. In this manner, the gNPM is more straightforward to be implemented. Furthermore, by considering the viscous term in the conservation of momentum, the gNPM can be applied for viscous hydrodynamics modeling. The effectiveness and robustness of the gNPM have been demonstrated through several hydrodynamics benchmark cases with different boundary conditions. We highlight that the proposed gNPM is able to cope with highly uneven particle distributions, while the traditional meshfree method can produce severe failure. • A general Neural Particle Method (gNPM) is proposed for hydrodynamics modeling. • The gNPM is computationally more efficient and easier to be implemented than the NPM. • The effectiveness of the gNPM has been demonstrated through benchmark cases. • The gNPM is more robust than the SPH for uneven particle distributions. [ABSTRACT FROM AUTHOR]

Physics-Informed Neural Networks (PINNs) have recently gained increasing attention in the field of topology optimization. The fusion of deep learning and topology optimization has emerged as a prominent area of insightful research, where minimization of the loss function in neural networks can be comparable to minimization of the objective function in topology optimization. Inspired by concepts of PINNs, this paper proposes a novel framework, ' Complete Physics-Informed Neural Network-based Topology Optimization (CPINNTO) ', to address various challenges in topology optimization, particularly related to structural optimization. The key innovation of the proposed framework lies in introducing the first complete machine-learning-based topology optimization framework through integration of two distinct PINNs. Herein, the Deep Energy Method (DEM) PINN is implemented to determine the deformation state of corresponding structures numerically. In addition, derivation of the objective function with respect to design variables is replaced with automatic differentiation in sensitivity-analysis PINN (S-PINN). The feasibility and potential of the CPINNTO framework have been assessed through several case studies while highlighting strengths and limitations of utilizing PINNs in topology optimization. Subsequent findings indicate that CPINNTO can achieve optimal topologies without labeled data nor FEA. The numerical examples demonstrate that CPINNTO is capable of stably obtaining optimal structures for various topology optimization applications, including compliance minimization problems, multi-constrained problems, and three-dimensional problems. Resulting designs exhibit favorable compliance values comparable to the designs obtained via density-based topology optimization. In summary, the proposed CPINNTO framework opens up novel and interesting possibilities for structural topology optimization. • A novel Complete PINN-based topology optimization framework (CPINNTO). • Two PINNs to replace structural and sensitivity analyses in topology optimization. • CPINNTO does not require any labeled data or FEA to train PINNs. • CPINNTO can effectively optimize problem domains of both 2-D and 3-D structures. [ABSTRACT FROM AUTHOR]

The degree of compaction in the levee building materials is a crucial factor that affects the piping phenomena. The density and compaction of the soil strata determine the structural soundness of the levee. Segments with reduced density or compaction can become weak spots during floods. To assess part of the Helena levee (2,500 m) in Arkansas (AR), the United States, an extensive ground-penetrating radar (GPR) fieldwork was conducted. This reliable method will undoubtedly improve the assessment procedure of the levee structure by identifying the weak spots within the structure that result from poor compaction of the levee core layers in a short time with high accuracy. However, interpreting the GPR data can be challenging and requires specialised knowledge. Obtaining meaningful insights typically involves a time-consuming process of extensive manual processing and visual inspection. To address this issue, this article proposes a novel, reliable deep-feature fusion framework for GPR data to identify horizontal variation in the soil compaction of a levee. To address data scarcity, a new type of transfer learning in the same domain is adopted, and four deep learning models (Xception, Inception, EfficientNet and MobileNet) are used to extract features. The combined features are then used to train and test five machine learning classifiers (Neural Network, Support Vector Machine, K-Nearest Neighbour, Logistic Regression, and Naive Bayes). The best combination of deep Learning and machine learning is four models with the neural network classifier which achieved the highest results by obtaining an accuracy of 98.2%, an F1 score of 97.6%, and an area under the curve of 99.9%. The proposed framework faced an additional challenge when subjected to an unseen dataset of 1,511 images reserved primarily for testing. Remarkably, it achieved an accuracy rate of 95.7% with the neural network classifier. This article presents a new research direction that has substantial potential in various domains, including civil engineering, the petroleum sector, road safety, agriculture, and more. • A Reliable deep feature fusion technique for the Ground Penetrating Radar (GPR) Data. • A new type of transfer learning is adopted to address training data scarcity issues. • Feature fusion is performed on four DL models. • Five machine learning classifiers have been employed. • The proposed framework achieved an accuracy of 98.2%, an F1 score of 97.6% and an AUC of 99.9 %. [ABSTRACT FROM AUTHOR]