arXiv subjects

Masanobu Horie

Publications and source records attributed to Masanobu Horie.

5 recordsLinked to original sources

arXiv2026

Full-component reconstruction of three-dimensional fluid stress tensors

Forces govern how fluids deform biological tissues, regulate cardiovascular function, and determine the performance and failure of soft materials. Recent advances in flow birefringence, including the use of suspended anisotropic nanomaterials to optically encode stress in fluids, have made direct stress measurement experimentally accessible in projection. However, direct experimental access to all six components of the three-dimensional (3D) fluid stress tensor has remained unattainable because optical measurements provide only path-integrated observables. Recovering local 3D stresses from such data constitutes an intrinsically underdetermined tensor tomography problem, where two optical observables must determine six independent stress components. Here we introduce U-FlowPET, an unsupervised physics-informed framework that integrates photoelastic tomography with the governing equations of fluid mechanics to reconstruct the full 3D stress tensor without relying on constitutive assumptions, geometric symmetry, or labeled training data. Rather than learning from labeled reference stress fields, the method identifies physically admissible stress fields that satisfy momentum balance and continuity while remaining consistent with measured optical projections. We validate the approach using analytical, numerical, and experimental datasets. In axisymmetric pipe flow with an analytical solution, all six stress components are reconstructed with normalized mean absolute errors below 4%. Robust reconstruction is further demonstrated in curved-pipe flow without symmetry assumptions and in experimental pipe-flow data despite measurement noise. By enabling direct 3D stress-field reconstruction from optical data alone, U-FlowPET extends fluid analysis from observing motion to quantifying force and establishes a new framework for stress-based diagnostics in biological flows and functional materials.

physics.flu-dyn↗

arXiv2025

Reconstruction of three-dimensional fluid stress field via photoelasticity using physics-informed convolutional encoder-decoder

Measuring stress fields in fluids and soft materials is crucial in various fields such as mechanical engineering, medicine, and bioengineering. However, conventional methods that calculate stress fields from velocity fields struggle to measure complex fluids where the stress constitutive equation is unknown. To address this, we propose a novel approach that combines photoelastic measurements -- which can non-invasively visualize internal stresses -- with machine learning to measure stress fields. The machine learning model, which we named physics-informed convolutional encoder-decoder (PICED), integrates a convolutional neural network (CNN)-based encoder-decoder model with a physics-informed neural network (PINN). Using this approach, three-dimensional stress fields can be predicted with high accuracy for multiple interpolated data points in a rectangular channel flow.

physics.flu-dyn↗

arXiv2024

Graph Neural PDE Solvers with Conservation and Similarity-Equivariance

Utilizing machine learning to address partial differential equations (PDEs) presents significant challenges due to the diversity of spatial domains and their corresponding state configurations, which complicates the task of encompassing all potential scenarios through data-driven methodologies alone. Moreover, there are legitimate concerns regarding the generalization and reliability of such approaches, as they often overlook inherent physical constraints. In response to these challenges, this study introduces a novel machine-learning architecture that is highly generalizable and adheres to conservation laws and physical symmetries, thereby ensuring greater reliability. The foundation of this architecture is graph neural networks (GNNs), which are adept at accommodating a variety of shapes and forms. Additionally, we explore the parallels between GNNs and traditional numerical solvers, facilitating a seamless integration of conservative principles and symmetries into machine learning models. Our findings from experiments demonstrate that the model's inclusion of physical laws significantly enhances its generalizability, i.e., no significant accuracy degradation for unseen spatial domains while other models degrade. The code is available at https://github.com/yellowshippo/fluxgnn-icml2024.

cs.LG↗

arXiv2023

Physics-Embedded Neural Networks: Graph Neural PDE Solvers with Mixed Boundary Conditions

Graph neural network (GNN) is a promising approach to learning and predicting physical phenomena described in boundary value problems, such as partial differential equations (PDEs) with boundary conditions. However, existing models inadequately treat boundary conditions essential for the reliable prediction of such problems. In addition, because of the locally connected nature of GNNs, it is difficult to accurately predict the state after a long time, where interaction between vertices tends to be global. We present our approach termed physics-embedded neural networks that considers boundary conditions and predicts the state after a long time using an implicit method. It is built based on an E(n)-equivariant GNN, resulting in high generalization performance on various shapes. We demonstrate that our model learns flow phenomena in complex shapes and outperforms a well-optimized classical solver and a state-of-the-art machine learning model in speed-accuracy trade-off. Therefore, our model can be a useful standard for realizing reliable, fast, and accurate GNN-based PDE solvers. The code is available at https://github.com/yellowshippo/penn-neurips2022.

cs.LG↗

arXiv2021

Isometric Transformation Invariant and Equivariant Graph Convolutional Networks

Graphs are one of the most important data structures for representing pairwise relations between objects. Specifically, a graph embedded in a Euclidean space is essential to solving real problems, such as physical simulations. A crucial requirement for applying graphs in Euclidean spaces to physical simulations is learning and inferring the isometric transformation invariant and equivariant features in a computationally efficient manner. In this paper, we propose a set of transformation invariant and equivariant models based on graph convolutional networks, called IsoGCNs. We demonstrate that the proposed model has a competitive performance compared to state-of-the-art methods on tasks related to geometrical and physical simulation data. Moreover, the proposed model can scale up to graphs with 1M vertices and conduct an inference faster than a conventional finite element analysis, which the existing equivariant models cannot achieve.

cs.LG↗