不確実性下での設計に対するMulti-Fidelity不確定性定量化とSurrogate-Based Memeticアルゴリズム

学位の種別: 課程博士審査委員会委員 : （主査）東京大学教授 土屋 武司, 東京大学教授 鈴木 真二, 東京大学教授 李家 賢一, 東京大学准教授 大山 聖, 東北大学准教授 下山 幸治University of Tokyo(東京大学

Physics-Informed Proper Orthogonal Decomposition for Data Reconstruction

Many engineering problems are governed by complex governing equations that are difficult and typically require high computational costs to solve. Machine learning and surrogate modelling aid such an endeavour by providing a cheap-to-evaluate prediction model that acts as a replacement of the original model. While most research focuses on predicting scalar values (e.g., lift and drag), predicting the solution field is also of interest in many practical engineering and scientific applications. This paper proposes a Physics-Informed Proper Orthogonal Decomposition (POD) technique that improves the solution field prediction by enforcing governing equations as a loss penalty. The proposed idea utilizes a reduced-order modeling technique based on POD to decompose solution snapshots into singular vectors and values. A Gaussian Process Regression is then utilized to predict the singular values from variable parameters. The predicted singular values from the data of the problem are then adjusted via optimization to minimize the physics-informed loss and achieve better prediction. In this paper, we illustrate the efficacy of the proposed method on simple two-dimensional partial differential equations. The result clearly shows that the proposed physics-informed POD outperforms the conventional POD in terms of approximation error

Design exploration of additively manufactured chiral auxetic structure using explainable machine learning

A design exploration of hexachiral structures using explainable machine learning (ML) is performed in this work. The hexachiral structures are fabricated using resin via vat photopolymerization (VPP). The ML model is used to build the function that explains the association between Poisson’s ratio and the hexachiral design parameters. The data set for ML model construction is first collected by using the Halton sequence and simulated using the finite element method (FEM). To validate the data set, the results obtained from the FEM simulation are compared with those obtained from the compression test. The Gaussian Process Regression (GPR) models for Poisson’s ratio and porosity are constructed to extract important design insight. A Global Sensitivity Analysis (GSA) and Shapley Additive Explanations (SHAP) are used to analyze the sensitivity of the porosity and Poisson’s ratio to the hexachiral design parameters. GSA result shows that the strut’s thickness is the most decisive parameter that affects the Poisson’s ratio. The application of SHAP also reveals that the relationship between the strut thickness and Poisson’s ratio is nonlinear. Finally, the minimum Poisson’s ratio value is achieved by design with minimum strut thickness, minimum node radius, and maximum strut length

Shapley Additive Explanations for Knowledge Discovery via Surrogate Models

It is sometimes desirable to delve further into how the inputs affect the output in design optimization and uncertainty analysis. Surrogate models such as Gaussian Process Regression and support vector regression are useful for such tasks and can be further enhanced by introducing advanced post-processing methods. This paper investigates Shapley Additive Explanation (SHAP) as a tool to aid surrogate-assisted data-driven analysis. In particular, surrogate-enabled SHAP analysis allows visualization of the input-output relationship in a meaningful way using summary SHAP plots and SHAP dependence plots. Some important information that can be extracted and visualized from SHAP includes the importance of input variables (i.e., global sensitivity analysis), nonlinearity level, and level of interactions. The benefits of Shapley values for engineering analysis using surrogate models are demonstrated in three engineering test problems

Gaussian Process Regression for Seismic Fragility Assessment: Application to Non-Engineered Residential Buildings in Indonesia

Indonesia is located in a high-seismic-risk region with a significant number of non-engineered houses, which typically have a higher risk during earthquakes. Due to the wide variety of differences even among parameters within one building typology, it is difficult to capture the total risk of the population, as the typical structural engineering approach to understanding fragility involves tedious numerical modeling of individual buildings—which is computationally costly for a large population of buildings. This study uses a statistical learning technique based on Gaussian Process Regression (GPR) to build the family of fragility curves. The current research takes the column height and side length as the input variables, in which a linear analysis is used to calculate the failure probability. The GPR is then utilized to predict the fragility curve and the probability of collapse, given the data evaluated at the finite set of experimental design. The result shows that GPR can predict the fragility curve and the probability of collapse well, efficiently allowing rapid estimation of the population fragility curve and an individual prediction for a single building configuration. Most importantly, GPR also provides the uncertainty band associated with the prediction of the fragility curve, which is crucial information for real-world analysis

Composite Kernel Functions for Surrogate Modeling using Recursive Multi-Fidelity Kriging

In this paper, we propose the use of the composite kernel function (CKL) technique for the multi-fidelity Kriging (MFK) surrogate model. The principle of MFK-CKL is to automatically learn the best combination of single kernels in both low- and high-fidelity Kriging to create a more accurate Kriging model. The combination is in the form of a weighted sum in which the weights are treated as extra hyperparameters. We implement the CKL into the recursive co-Kriging approach. It is relatively straightforward to do the same for other MFK approaches. Demonstrations on a set of non-algebraic problems show the high efficacy of MFK with CKL, outperforming the single kernel approach in terms of approximation error. Besides, the use of CKL successfully eliminates the non-trivial process of manual kernel selection in multi-fidelity Kriging