arXiv subjects

Mayu Muramatsu

Publications and source records attributed to Mayu Muramatsu.

12 recordsLinked to original sources

arXiv2026

Adaptive Encoding Strategy for Quantum Annealing in Mixed-Variable Engineering Optimization

Mixed discrete-continuous optimization is central to engineering design, where discrete choices interact with continuous fields. These problems are difficult due to high-dimensional, complex search spaces. To tackle them, Quantum Annealing (QA) is promising, yet its native binary nature supports only discrete variables, making accurate and efficient encodings of continuous quantities a central challenge. Existing approaches either split the coupled problem, mapping discrete decisions to QA while solving continuous fields classically, or use fixed-bit-depth encodings. The former compromises QA's global search advantages; the latter can underrepresent dynamic range or inflate the number of binary variables. We show that simply increasing bit depth can even degrade performance on current QA hardware, underscoring the need for alternative encodings. In response, we introduce an adaptive encoding strategy for continuous variables in QA that enables efficient treatment of coupled mixed-variable problems. We propose an update strategy for the representable ranges of the continuous variables and demonstrate its utility by integrating it into the minimum complementary energy formulation for structural design optimization, which provides a single, coupled constrained problem. We apply a quadratic penalty method where we update the representation of the continuous variables while targeting the full original objective, preserving QA's global search capability. On a published benchmark, the size optimization of a composite rod, our adaptive encoding improves solution quality under a fixed binary variable budget, demonstrating a superior precision-resource trade-off. Since the framework generalizes beyond structural design, it offers practical guidance for encoding continuous variables for QA and indicates that adaptive representations can enhance precision on current hardware.

cs.CE↗

arXiv2026

Tackling multiphysics problems via finite element-guided physics-informed operator learning

This work presents a finite element-guided physics-informed operator learning framework for multiphysics problems with coupled partial differential equations (PDEs) on arbitrary domains. The proposed framework learns an operator from the input space to the solution space with a weighted residual formulation based on the finite element method, enabling discretization-independent prediction beyond the training resolution without relying on labeled simulation data. The present framework for multiphysics problems is implemented in Folax, a JAX-based operator learning platform, and is verified on nonlinear coupled thermo-mechanical problems. Two- and three-dimensional representative volume elements with varying heterogeneous microstructures, and a close-to-reality industrial casting example under varying boundary conditions are investigated as the example problems. We investigate the potential of several neural operators combined with the proposed finite element-guided approach, including Fourier neural operators (FNOs), deep operator networks (DeepONets), and a newly proposed implicit finite operator learning (iFOL) approach based on conditional neural fields. The results demonstrate that FNOs yield highly accurate solution operators on regular domains, where the global features can be efficiently learned in the spectral domain, and iFOL offers efficient parametric operator learning capabilities for complex and irregular geometries. Furthermore, studies on training strategies, network decomposition, and training sample quality reveal that a monolithic training strategy using a single network is sufficient for accurate predictions, while training sample quality strongly influences performance. Overall, the present approach highlights the potential of physics-informed operator learning with a finite element-based loss as a unified and scalable approach for coupled multiphysics simulations.

cs.LG↗

arXiv2026

Quantum Extreme Reservoir Computing for Phase Classification of Polymer Alloy Microstructures

Quantum machine learning (QML) is expected to offer new opportunities to process high-dimensional data efficiently by exploiting the exponentially large state space of quantum systems. In this work, we apply quantum extreme reservoir computing (QERC) to the classification of microstructure images of polymer alloys generated using self-consistent field theory (SCFT). While previous QML efforts have primarily focused on benchmark datasets such as MNIST, our work demonstrates the applicability of QERC to engineering data with direct materials relevance. Through numerical experiments, we examine the influence of key computational parameters-including the number of qubits, sampling cost (the number of measurement shots), and reservoir configuration-on classification performance. The resulting phase classifications are depicted as phase diagrams that illustrate the phase transitions in polymer morphology, establishing an understandable connection between quantum model outputs and material behavior. These results illustrate QERC performance on realistic materials datasets and suggest practical guidelines for quantum encoder design and model generalization. This work establishes a foundation for integrating quantum learning techniques into materials informatics.

quant-ph↗

arXiv2025

A Physics-Informed Meta-Learning Framework for the Continuous Solution of Parametric PDEs on Arbitrary Geometries

In this work, we introduce implicit Finite Operator Learning (iFOL) for the continuous and parametric solution of partial differential equations (PDEs) on arbitrary geometries. We propose a physics-informed encoder-decoder network to establish the mapping between continuous parameter and solution spaces. The decoder constructs the parametric solution field by leveraging an implicit neural field network conditioned on a latent or feature code. Instance-specific codes are derived through a PDE encoding process based on the second-order meta-learning technique. In training and inference, a physics-informed loss function is minimized during the PDE encoding and decoding. iFOL expresses the loss function in an energy or weighted residual form and evaluates it using discrete residuals derived from standard numerical PDE methods. This approach results in the backpropagation of discrete residuals during both training and inference. iFOL features several key properties: (1) its unique loss formulation eliminates the need for the conventional encode-process-decode pipeline previously used in operator learning with conditional neural fields for PDEs; (2) it not only provides accurate parametric and continuous fields but also delivers solution-to-parameter gradients without requiring additional loss terms or sensitivity analysis; (3) it can effectively capture sharp discontinuities in the solution; and (4) it removes constraints on the geometry and mesh, making it applicable to arbitrary geometries and spatial sampling (zero-shot super-resolution capability). We critically assess these features and analyze the network's ability to generalize to unseen samples across both stationary and transient PDEs. The overall performance of the proposed method is promising, demonstrating its applicability to a range of challenging problems in computational mechanics.

cs.LG↗

arXiv2025

Hamiltonian simulation for nonlinear partial differential equation by Schrödingerization

Hamiltonian simulation is a fundamental algorithm in quantum computing that has attracted considerable interest owing to its potential to efficiently solve the governing equations of large-scale classical systems. Exponential speedup through Hamiltonian simulation has been rigorously demonstrated in the case of coupled harmonic oscillators. The question arises as to whether Hamiltonian simulations in other physical systems also accelerate exponentially. Schrödingerization is a technique that transforms the governing equations of classical systems into the Schrödinger equation. However, since the Schrödinger equation is a linear equation, Hamiltonian simulation is often limited to linear equations. The research on Hamiltonian simulation methods for nonlinear governing equations remains relatively limited. In this study, we propose a Hamiltonian simulation method for nonlinear partial differential equations (PDEs). The proposed method is named Carleman linearization + Schrödingerization (CLS), which combines Carleman linearization (CL) and warped phase transformation (WPT). CL is first applied to transform a nonlinear PDE into a linear differential equation. This linearized equation is then mapped to the Schrödinger equation via WPT. The original nonlinear PDE can be solved efficiently by the Hamiltonian simulation of the resulting Schrödinger equation. By applying this method, we transform the original governing equation into the Schrödinger equation. Solving the transformed Schrödinger equation then enables the analysis of the original nonlinear equation. As a specific application, we apply this method to the nonlinear reaction--diffusion equation to demonstrate that Hamiltonian simulations are applicable to nonlinear PDEs.

quant-ph↗

arXiv2025

Conditional diffusion model for inverse prediction of process parameters and dendritic microstructures from mechanical properties

In this study, we develop a conditional diffusion model that proposes the optimal process parameters and predicts the microstructure for the desired mechanical properties. In materials development, it is costly to try many samples with different parameters in experiments and numerical simulations. The use of data-driven inverse design method can reduce the cost of materials development. This study develops an inverse analysis model that predicts process parameters and microstructures. This method can be used for any material, but in this study it is applied to polymeric material, which is the matrix resin of carbon fiber reinforced thermoplastics as an example. Matrix resins contain a mixture of dendrites, which are crystalline phases, and amorphous phases even after crystal growth is complete, and it is important to consider the microstructures consisting of the crystalline structure and the remaining amorphous phase to achieve the desired mechanical properties. Typically, the temperature during forming affects the microstructures, which in turn affect the macroscopic mechanical properties. The trained diffusion model can propose not only the processing temperature but also the microstructure when Young's modulus and Poisson's ratio are given. The capability of our conditional diffusion model to represent complex dendrites is also noteworthy.

cs.CE↗

arXiv2024

Dislocation-based crystal plasticity simulation on grain-size dependence of mechanical properties in dual-phase steels

In this study, the effect of ferrite grain size on the mechanical properties and dislocation behavior of dual-phase (DP) steel is investigated using dislocation-based crystal plasticity finite element analysis. DP steel, composed of a soft ferritic phase and a hard martensitic phase, shows mechanical properties that are significantly influenced by ferrite grain size. The mechanism underlying this grain size effect is clarified by analyzing the partitioning and distribution of stress, strain, and dislocations in each phase. Three models with the same volume fraction of martensitic phase but different ferrite grain sizes are subjected to tensile loading. Interestingly, even though only the ferrite grain size is changed, the stress in the martensitic phase exhibited a notable dependence on ferrite grain size. This can be explained as follows. Geometrically necessary (GN) dislocations accumulate on the ferrite side of the ferrite-martensite grain boundary, and the grain boundary occupancy per unit area increases as the ferrite grain size decreases. As a result, smaller ferrite grain sizes make the ferritic phase less deformable owing to the effect of GN dislocations, shifting more deformation to the martensitic phase. This behavior is confirmed by the more uniform strain distribution and partitioning observed with decreasing ferrite grain size. As the martensitic phase takes on greater deformation, the statistically stored dislocation density in the martensitic phase becomes ferrite grain size dependent, which in turn leads to the observed grain size dependence of stress in the martensitic phase.

cs.CE↗

arXiv2024

An Ising Machine Formulation for Design Updates in Topology Optimization of Flow Channels

Topology optimization is an essential tool in computational engineering, for example, to improve the design and efficiency of flow channels. At the same time, Ising machines, including digital or quantum annealers, have been used as efficient solvers for combinatorial optimization problems. Beyond combinatorial optimization, recent works have demonstrated applicability to other engineering tasks by tailoring corresponding problem formulations. In this study, we present a novel Ising machine formulation for computing design updates during topology optimization with the goal of minimizing dissipation energy in flow channels. We explore the potential of this approach to improve the efficiency and performance of the optimization process. To this end, we conduct experiments to study the impact of various factors within the novel formulation. Additionally, we compare it to a classical method using the number of optimization steps and the final values of the objective function as indicators of the time intensity of the optimization and the performance of the resulting designs, respectively. Our findings show that the proposed update strategy can accelerate the topology optimization process while producing comparable designs. However, it tends to be less exploratory, which may lead to lower performance of the designs. These results highlight the potential of incorporating Ising formulations for optimization tasks but also show their limitations when used to compute design updates in an iterative optimization process. In conclusion, this work provides an efficient alternative for design updates in topology optimization and enhances the understanding of integrating Ising machine formulations in engineering optimization.

cs.CE↗

arXiv2024

Implementation of spectral methods on Ising machines: toward flow simulations on quantum annealer

We investigate the possibility and current limitations of flow computations using quantum annealers by solving a fundamental flow problem on Ising machines. As a fundamental problem, we consider the one-dimensional advection-diffusion equation. We formulate it in a form suited to Ising machines (i.e., both classical and quantum annealers), perform extensive numerical tests on a classical annealer, and finally test it on an actual quantum annealer. To make it possible to process with an Ising machine, the problem is formulated as a minimization problem of the residual of the governing equation discretized using either the spectral method or the finite difference method. The resulting system equation is then converted to the Quadratic Unconstrained Binary Optimization (QUBO) form though quantization of variables. It is found in the numerical tests using a classical annealer that the spectral method requiring smaller number of variables has a particular merit over the finite difference method because the accuracy deteriorates with the increase of the number of variables. We also found that the computational error varies depending on the condition number of the coefficient matrix. In addition, we extended it to a two-dimensional problem and confirmed its fundamental applicability. From the numerical test using a quantum annealer, however, it turns out that the computation using a quantum annealer is still challenging due largely to the structural difference from the classical annealer, which leaves a number of issues toward its practical use.

physics.flu-dyn↗

arXiv2024

A finite element-based physics-informed operator learning framework for spatiotemporal partial differential equations on arbitrary domains

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 proposed framework employs a loss function inspired by the finite element method (FEM) with the implicit Euler time integration scheme. A transient thermal conduction problem is considered to benchmark the performance. The proposed operator learning framework takes a temperature field at the current time step as input and predicts a temperature field at the next time step. The Galerkin discretized weak formulation of the heat equation is employed to incorporate physics into the loss function, which is coined finite operator learning (FOL). Upon training, the networks successfully predict the temperature evolution over time for any initial temperature field at high accuracy compared to the FEM solution. The framework is also confirmed to be applicable to 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 a large data set 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. Second, 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 when optimizing weights and biases while accepting possible discretization errors. Finally, thanks to the interpolation power of FEM, any arbitrary geometry can be handled with FOL, which is crucial to addressing various engineering application scenarios.

cs.LG↗

arXiv2024

Investigation on optimal microstructure of dual-phase steel with high strength and ductility by machine learning

In this study, we developed an inverse analysis framework that proposes a microstructure for dual-phase (DP) steel that exhibits high strength and ductility. The inverse analysis method proposed in this study involves repeated random searches on 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 DP steel microstructures. GAN was trained using images of DP steel microstructures generated by the phase-field method. CNN was trained using images of DP steel microstructures, the maximum stress and the working limit strain calculated by the dislocation-crystal plasticity finite element method. The constructed framework made an efficient search for microstructures possible because of a low-dimensional search space by a latent variable of GAN. The multiple deformation modes were considered in this framework, which allowed the required microstructures to be explored under complex deformation modes. A microstructure with a fine grain size was proposed by using the developed framework.

cs.CE↗

arXiv2023

Heterogeneous biological membranes regulate protein partitioning via fluctuating diffusivity

Cell membranes phase separate into ordered ${\rm L_o}$ and disordered ${\rm L_d}$ domains depending on their compositions. This membrane compartmentalization is heterogeneous and regulates the localization of specific proteins related to cell signaling and trafficking. However, it is unclear how the heterogeneity of the membranes affects the diffusion and localization of proteins in ${\rm L_o}$ and ${\rm L_d}$ domains. Here, using Langevin dynamics simulations coupled with the phase-field (LDPF) method, we investigate several tens of milliseconds-scale diffusion and localization of proteins in heterogeneous biological membrane models showing phase separation into ${\rm L_o}$ and ${\rm L_d}$ domains. The diffusivity of proteins exhibits temporal fluctuations depending on the field composition. Increases in molecular concentrations and domain preference of the molecule induce subdiffusive behavior due to molecular collisions by crowding and confinement effects, respectively. Moreover, we quantitatively demonstrate that the protein partitioning into the ${\rm L_o}$ domain is determined by the difference in molecular diffusivity between domains, molecular preference of domain, and molecular concentration. These results pave the way for understanding how biological reactions caused by molecular partitioning may be controlled in heterogeneous media. Moreover, the methodology proposed here is applicable not only to biological membrane systems but also to the study of diffusion and localization phenomena of molecules in various heterogeneous systems.

cond-mat.soft↗