No Arabic abstract
Moving Morphable Component (MMC) based topology optimization approach is an explicit algorithm since the boundary of the entity explicitly described by its functions. Compared with other pixel or node point-based algorithms, it is optimized through the parameter optimization of a Topological Description Function (TDF). However, the optimized results partly depend on the selection of related parameters of Method of Moving Asymptote (MMA), which is the optimizer of MMC based topology optimization. Practically, these parameters are tuned according to the experience and the feasible solution might not be easily obtained, even the solution might be infeasible due to improper parameter setting. In order to address these issues, a Machine Learning (ML) based parameter tuning strategy is proposed in this study. An Extra-Trees (ET) based image classifier is integrated to the optimization framework, and combined with Particle Swarm Optimization (PSO) algorithm to form a closed loop. It makes the optimization process be free from the manual parameter adjustment and the reasonable solution in the design domain is obtained. In this study, two classical cases are presented to demonstrate the efficiency of the proposed approach.
An Iterative Reanalysis Approximation (IRA) is integrated with the Moving Morphable Components (MMCs) based topology optimization (IRA-MMC) in this study. Compared with other classical topology optimization methods, the Finite Element (FE) based solver is replaced with the suggested IRA method. In this way, the expensive computational cost can be significantly saved by several nested iterations. The optimization of linearly elastic planar structures is constructed by the MMC, the specifically geometric parameters of which are taken as design variables to acquire explicitly geometric boundary. In the suggested algorithm, a hybrid optimizer based on the Method of Moving Asymptotes (MMA) approach and the Globally Convergent version of the Method of Moving Asymptotes (GCMMA) is suggested to improve convergence ratio and avoid local optimum. The proposed approach is evaluated by some classical benchmark problems in topology optimization, where the results show significant time saving without compromising accuracy.
Nonlocal operators of fractional type are a popular modeling choice for applications that do not adhere to classical diffusive behavior; however, one major challenge in nonlocal simulations is the selection of model parameters. In this work we propose an optimization-based approach to parameter identification for fractional models with an optional truncation radius. We formulate the inference problem as an optimal control problem where the objective is to minimize the discrepancy between observed data and an approximate solution of the model, and the control variables are the fractional order and the truncation length. For the numerical solution of the minimization problem we propose a gradient-based approach, where we enhance the numerical performance by an approximation of the bilinear form of the state equation and its derivative with respect to the fractional order. Several numerical tests in one and two dimensions illustrate the theoretical results and show the robustness and applicability of our method.
Mode-based model-reduction is used to reduce the degrees of freedom of high dimensional systems, often by describing the system state by a linear combination of spatial modes. Transport dominated phenomena, ubiquitous in technical and scientific applications, often require a large number of linear modes to obtain a small representation error. This difficulty, even for the most simple transports, originates from the inappropriateness of the decomposition structure in time dependent amplitudes of purely spatial modes. In this article an approach is discussed, which decomposes a flow field into several fields of co-moving frames, where each one can be approximated by a few modes. The method of decomposition is formulated as an optimization problem. Different singular-value-based objective functions are discussed and connected to former formulations. A boundary treatment is provided. The decomposition is applied to generic cases and to a technically relevant flow configuration of combustion physics.
In this work, by introducing the seismic impedance tensor we propose a new Rayleigh wave dispersion function in a homogeneous and layered medium of the Earth, which provides an efficient way to compute the dispersion curve -- a relation between the frequencies and the phase velocities. With this newly established forward model, based on the Mixture Density Networks (MDN) we develop a machine learning based inversion approach, named as FW-MDN, for the problem of estimating the S-wave velocity from the dispersion curves. The method FW-MDN deals with the non-uniqueness issue encountered in studies that invert dispersion curves for crust and upper mantle models and attains a satisfactory performance on the dataset with various noise structure. Numerical simulations are performed to show that the FW-MDN possesses the characteristics of easy calculation, efficient computation, and high precision for the model characterization.
Differential geometry (DG) based solvation models are a new class of variational implicit solvent approaches that are able to avoid unphysical solvent-solute boundary definitions and associated geometric singularities, and dynamically couple polar and nonpolar interactions in a self-consistent framework. Our earlier study indicates that DG based nonpolar solvation model outperforms other methods in nonpolar solvation energy predictions. However, the DG based full solvation model has not shown its superiority in solvation analysis, due to its difficulty in parametrization, which must ensure the stability of the solution of strongly coupled nonlinear Laplace-Beltrami and Poisson-Boltzmann equations. In this work, we introduce new parameter learning algorithms based on perturbation and convex optimization theories to stabilize the numerical solution and thus achieve an optimal parametrization of the DG based solvation models. An interesting feature of the present DG based solvation model is that it provides accurate solvation free energy predictions for both polar and nonploar molecules in a unified formulation. Extensive numerical experiment demonstrates that the present DG based solvation model delivers some of the most accurate predictions of the solvation free energies for a large number of molecules.