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• 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]

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]

• A new data-driven topology optimization (DDTO) framework is proposed. • Sensitivity analysis for discrete noisy material data sets is developed. • Verification of the new DDTO framework by truss structure designs. The application of structural topology optimization with complex engineering materials is largely hindered due to the complexity in phenomenological or physical constitutive modeling from experimental or computational material data sets. In this paper, we propose a new data-driven topology optimization (DDTO) framework to break through the limitation with the direct usage of discrete material data sets in lieu of constitutive models to describe the material behaviors. This new DDTO framework employs the recently developed data-driven computational mechanics for structural analysis which integrates prescribed material data sets into the computational formulations. Sensitivity analysis is formulated by applying the adjoint method where the tangent modulus of prescribed uniaxial stress-strain data is evaluated by means of moving least square approximation. The validity of the proposed framework is well demonstrated by the truss topology optimization examples. The proposed DDTO framework will provide a great flexibility in structural design for real applications. [ABSTRACT FROM AUTHOR]