論文

We propose a novel finite element-based physics-informed operator learning framework that allows for predicting spatiotemporal dynamics governed by partial differential equations (PDEs). The Galerkin discretized weak formulation is employed to incorporate physics into the loss function, termed finite operator learning (FOL), along with the implicit Euler time integration scheme for temporal discretization. A transient thermal conduction problem is considered to benchmark the performance, where FOL takes a temperature field at the current time step as input and predicts a temperature field at the next time step. Upon training, the network successfully predicts the temperature evolution over time for any initial temperature field at high accuracy compared to the solution by the finite element method (FEM) even with a heterogeneous thermal conductivity and arbitrary geometry. The advantages of FOL can be summarized as follows: First, the training is performed in an unsupervised manner, avoiding the need for large data prepared from costly simulations or experiments. Instead, random temperature patterns generated by the Gaussian random process and the Fourier series, combined with constant temperature fields, are used as training data to cover possible temperature cases. Additionally, shape functions and backward difference approximation are exploited for the domain discretization, resulting in a purely algebraic equation. This enhances training efficiency, as one avoids time-consuming automatic differentiation in optimizing weights and biases while accepting possible discretization errors. Finally, thanks to the interpolation power of FEM, any arbitrary geometry with heterogeneous microstructure can be handled with FOL, which is crucial to addressing various engineering application scenarios.

This study aims to develop a multiscale bridging method for investigating nanocrystalline metals based on macro-scale deformation. For this purpose, we propose a hierarchical multiscale computational method that can focus on some of the elements in a finite element model for scale bridging to atomistic-scale models. This method assumes that atomistic-scale nanocrystalline models are related to the integration points in a finite element and deform based on the macro-scale deformation. Nanocrystalline aluminum was chosen for the validation of the multiscale method. The finite element method (FEM) and the molecular dynamics (MD) method were used for continuum-scale and atomistic-scale simulations, respectively. We utilized the notion of the CauchyBorn rule (CBR) for communicating deformation information from the continuum scale to the atomistic scale. We studied three different cases with two nanocrystalline models and two loading cases to compare differences resulting from crystal structures and loading. Based on the crystal structure change during relaxation, nonequilibrium grain boundaries (NEGBs) were shown to play a role as deformation mechanisms in the plastic regime and induce the onset and migration of crystal defects, including deformation twins, as reported in the experiment. Furthermore, the crystal orientation dependence of the onset of crystal defects was confirmed by the comparison of the results from the two different nanocrystalline models. The qualitative agreement of the results with experimental observations is also confirmed. The proposed ‘FEM-MD’ method can bridge a large-scale gap, for example, from a nano-scale to a continuum-scale such that an MD model can be coupled to a millimeter or centimeter scale compared to other embedding methods. The present method is ideal for investigating the dislocation behavior of nanocrystalline materials, which contain multi-grained nanostructure at finite temperature, undergoing various loading scenarios at the macro-scale.

A novel model to be applied to next-generation accelerators, Ising machines, is formulated on the basis of the phase-field model of the phase-separation structure of a diblock polymer. Recently, Ising machines including quantum annealing machines, attract overwhelming attention as a technology that opens up future possibilities. On the other hand, the phase-field model has demonstrated its high performance in material development, though it takes a long time to achieve equilibrium. Although the convergence time problem might be solved by the next-generation accelerators, no solution has been proposed. In this study, we show the calculation of the phase-separation structure of a diblock polymer as the equilibrium state using phase-field model by an actual Ising machine. The proposed new model brings remarkable acceleration in obtaining the phase-separation structure. Our model can be solved on a large-scale quantum annealing machine. The significant acceleration of the phase-field simulation by the quantum technique pushes the material development to the next stage.

In this study, using some machine learning methods, we develop a framework that deals with forward analysis to predict a property from a polymer alloy's phase separation structure and inverse design to generate the structure from the property. We only consider Young's modulus as the property in this study. The forward analysis is performed using a convolutional neural network (CNN) and the inverse design is realized by a random search toward a model combining a generative adversarial network (GAN) and a CNN. This framework is applicable to other properties at a low computational cost, and latent variables belonging to the GAN are useful for feature extraction.

This study examined the applicability of factorization machines with quantum annealing (FMQA) to the field of landslide risk assessment for two specific black-box optimization problems, hyperparameter optimization (HPO) for metamodeling and metamodel-based simulation optimization (MBSO) targeting granular flow simulation using discrete element method (DEM). These two optimization problems are solved successively: HPO is first performed to determine the hyperparameters of the Gaussian process regression (GPR) metamodel, which is then used as a low-cost, fast approximate solver of granular flow simulations for MBSO. After conducting a series of granular flow simulations using DEM, a metamodel is created that outputs a risk index of interest, the run-out distance, from its input parameters by employing GPR with two hyperparameters, length-scale and signal variance. Subsequently, HPO is performed to obtain the optimal set of hyperparameters by applying FMQA and other optimization methods using another set of hyperparameters determined using the gradient-ascent method as the reference solution. Finally, using the metamodel created by each optimization method as an approximate solver for DEM simulations, MBSO is performed to find the optimal target output, the maximum run-out distance, in the space of physical input parameters for risk assessment. A comparison of the performance of FMQA with that of other methods shows that FMQA is competitive in terms of efficiency and stability with state-of-the-art algorithms such as Bayesian optimization.

Materials development requires numerous numbers of trial and error experiments. To reduce the experimental cost, numerical simulations which predict material microstructures and mechanical properties have a great potential to estimate the microstructures that should be produced for obtaining materials with the desired properties. There is a need to develop dual-phase (DP) steel with higher strength and ductility because DP steel is widely used due to its significant mechanical properties. DP steel consists of a soft phase (ferrite) and a hard phase (martensite), and the mechanical properties depend on the ratio of the two phases. The mechanical properties of DP steels are affected by the spatial distribution of martensite and ferrite, which requires a comprehensive consideration of a variety of microstructures. The problem is how to estimate microstructures of DP steel with the desired mechanical property because a comprehensive investigation of microstructures makes computational cost significantly expensive. For the purpose of reduction of the computational costs, we aim to develop a framework with low computational cost. The developed framework finds the optimal microstructure of DP steel by repeated random searches for a model that combines a generative adversarial network (GAN), which generates microstructures, and a convolutional neural network (CNN), which predicts the maximum stress and working limit strain from microstructures. Due to a low-dimensional search space provided by a latent variable of GAN, the proposed framework enables an efficient search for microstructures possible. To explore the desired microstructures under complex deformation modes, the multiple deformation modes are considered in this study. This framework is applicable not only for the microstructure of DP steel but also any other material microstructures. We are exhaustively able to explore the microstructure with desired properties of metallic or other composite materials in low-dimensional space thanks to this framework and contributes to accelerating materials development.

In this study, we developed a new method of topology optimization for truss structures by quantum annealing. To perform quantum annealing analysis with real variables, representation of real numbers as a sum of random number combinations is employed. The nodal displacement is expressed with binary variables. The Hamiltonian H is formulated on the basis of the elastic strain energy and position energy of a truss structure. It is confirmed that truss deformation analysis is possible by quantum annealing. For the analysis of the optimization method for the truss structure, the cross-sectional area of the truss is expressed with binary variables. The iterative calculation for the changes in displacement and cross-sectional area leads to the optimal structure under the prescribed boundary conditions.

In this study, we focus on random terms with a significant effect on the calculation time and the sidebranch structure of dendrites. We quantitatively evaluate the effect of the random terms on dendrites by changing the term introduced into the evaluation equation, the distribution of the random term, and variance. We introduced the terms: and ∇q. In the phase-field equation, we use to represent interfacial noise. In the heat conduction equation, we use ∇ q to represent thermal noise. We compare the results of calculation using only with those using only ∇ q and analyze the effect of each random term introduced on the shape of dendrites. In terms of the probability distribution for generating random numbers, the uniform and Gaussian distributions are used for comparison. The magnitude of the noise Fu, which controls the variance of noise, is used with 3 or 4 patterns of values to the extent that the calculation results do not diverge. Each value of Fu differs by a factor of 10. Sidebranch length, contour length, and area are used as indices for evaluating dendrites. The succinonitril is used for comparing the simulation and experimental results for dendrites to design the optimal random number model. On the basis of the introduced terms, we clarify that each term requires a different order of the variance. The probability density function of random numbers does not affect the shape of dendrites. On the other hand, the calculation time which is used the random numbers following the uniform distribution is more than twice as fast as when using random numbers that follow a Gaussian distribution. The variance of a random term has the greatest effect on the shape of dendrites.