• The Journal of the Acoustical Society of Korea
• /
• v.42 no.4
• /
• pp.305-312
• /
• 2023

Physics-Informed Neural Network (PINN) is used to invert bubble size distributions from attenuation losses. By considering a linear system for the bubble population inversion, Adaptive Learned Iterative Shrinkage Thresholding Algorithm (Ada-LISTA), which has been solved linear systems in image processing, is used as a neural network architecture in PINN. Furthermore, a regularization based on the linear system is added to a loss function of PINN and it makes a PINN have better generalization by a solution satisfying the bubble physics. To evaluate an uncertainty of bubble estimation, deep ensemble is adopted. 20 Ada-LISTAs with different initial values are trained using the same training dataset. During test with attenuation losses different from those in the training dataset, the bubble size distribution and corresponding uncertainty are indicated by average and variance of 20 estimations, respectively. Deep ensemble Ada-LISTA demonstrate superior performance in inverting bubble size distributions than the conventional convex optimization solver of CVX.

• Nuclear Engineering and Technology
• /
• v.55 no.6
• /
• pp.2305-2314
• /
• 2023

The governing equations of atmospheric dispersion most often taking the form of a second-order partial differential equation (PDE). Currently, typical computational codes for predicting atmospheric dispersion use the Gaussian plume model that is an analytic solution. A Gaussian model is simple and enables rapid simulations, but it can be difficult to apply to situations with complex model parameters. Recently, a method of solving PDEs using artificial neural networks called physics-informed neural network (PINN) has been proposed. The PINN assumes the latent (hidden) solution of a PDE as an arbitrary neural network model and approximates the solution by optimizing the model. Unlike a Gaussian model, the PINN is intuitive in that it does not require special assumptions and uses the original equation without modifications. In this paper, we describe an approach to atmospheric dispersion modeling using the PINN and show its applicability through simple case studies. The results are compared with analytic and fundamental numerical methods to assess the accuracy and other features. The proposed PINN approximates the solution with reasonable accuracy. Considering that its procedure is divided into training and prediction steps, the PINN also offers the advantage of rapid simulations once the training is over.

• Geophysics and Geophysical Exploration
• /
• v.26 no.3
• /
• pp.114-125
• /
• 2023

The physics-informed neural network (PINN) has been proposed to overcome the limitations of various numerical methods used to solve partial differential equations (PDEs) and the drawbacks of purely data-driven machine learning. The PINN directly applies PDEs to the construction of the loss function, introducing physical constraints to machine learning training. This technique can also be applied to wave equation modeling. However, to solve the wave equation using the PINN, second-order differentiations with respect to input data must be performed during neural network training, and the resulting wavefields contain complex dynamical phenomena, requiring careful strategies. This tutorial elucidates the fundamental concepts of the PINN and discusses considerations for wave equation modeling using the PINN approach. These considerations include spatial coordinate normalization, the selection of activation functions, and strategies for incorporating physics loss. Our experimental results demonstrated that normalizing the spatial coordinates of the training data leads to a more accurate reflection of initial conditions in neural network training for wave equation modeling. Furthermore, the characteristics of various functions were compared to select an appropriate activation function for wavefield prediction using neural networks. These comparisons focused on their differentiation with respect to input data and their convergence properties. Finally, the results of two scenarios for incorporating physics loss into the loss function during neural network training were compared. Through numerical experiments, a curriculum-based learning strategy, applying physics loss after the initial training steps, was more effective than utilizing physics loss from the early training steps. In addition, the effectiveness of the PINN technique was confirmed by comparing these results with those of training without any use of physics loss.

• Journal of the Korean Society of Visualization
• /
• v.21 no.1
• /
• pp.119-126
• /
• 2023

Acquiring experimental data for PIV verification or machine learning training data is resource-demanding, leading to an increasing interest in synthetic particle images as simulation data. Conventional synthetic particle image generation algorithms do not follow physical laws, and the use of CFD is time-consuming and requires computing resources. In this study, we propose a new method for synthetic particle image generation, based on a Physics-Informed Neural Networks(PINN). The PINN is utilized to infer the flow fields, enabling the generation of synthetic particle images that follow physical laws with reduced computation time and have no constraints on spatial resolution compared to CFD. The proposed method is expected to contribute to the verification of PIV algorithms.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.28 no.1
• /
• pp.33-58
• /
• 2024

This paper reviews basic concepts for Physics-Informed Neural Networks (PINN) applied to the initial value problems for ordinary differential equations. In particular, using only basic calculus, we derive the error estimates where the error functions (the differences between the true solution and the approximations expressed by neural networks) are dominated by training loss functions. Numerical experiments are conducted to validate our error estimates, visualizing the relationship between the error and the training loss for various first-order differential equations and a second-order linear equation.

• Proceedings of the Korea Water Resources Association Conference
• /
• 2023.05a
• /
• pp.97-97
• /
• 2023

최근 재해분야에서 인공신경망(ANN), 기계학습(ML), 딥러닝(DL) 등 AI 기술이 활용성이 점차 증가하고 있으며, 센싱정보와 연계한 시설물 안전관리, 원격탐사와 연계한 재해감시(녹조, 산사태, 산불 등), 수문시계열(수위, 유량 등) 예측, 레이더·위성강수 자료의 보정과 예측, 상하수도 관망누수예측 등 다양한 분야에서 AI 기술이 적용되고 그 활용성이 검증된 바 있다. 본 연구에서는 ML, DL, 물리기반신경망(Pysics-informed Neural Networks, PINNs)을 이용한 다양한 재해분석 사례를 소개하고, 그 활용성과 한계에 대해서 논의하고자 한다. 주요사례로는 (1) SAR영상과 기계학습을 이용한 재해피해지역(울진 산불) 감지, (2) 국가 디지털 정보를 이용한 산사태 위험지역 판별(인제 산사태) (3) 기계학습 및 딥러닝 기법을 이용한 위성강수 자료의 보정·예측 및 유출해석, (4) 수리해석을 위한 수치해석분야에서의 PINNs의 적용성(1차원 Saint-Venant 식 해석) 평가 연구결과를 공유한다. 특히, 자료의 입·출력 자료만으로 학습된 인공신경망 모형 대신 지배방정식(물리방정식)을 만족하도록 강제한 PINNs의 경우, 인공신경망 모형보다 우수한 모의능력을 보여주었으며, 향후 복잡한 수리모델링 등 수치해석분야에서 그 활용가능성이 매우 높을 것으로 판단된다.

• Journal of Korea Water Resources Association
• /
• v.56 no.12
• /
• pp.939-953
• /
• 2023

Shallow water equations (SWE) serve as fundamental equations governing the movement of the water. Traditional numerical approaches for solving these equations generally face various challenges, such as sensitivity to mesh generation, and numerical oscillation, or become more computationally unstable around shock and discontinuities regions. In this study, we present a novel approach that leverages the power of physics-informed neural networks (PINNs) to approximate the solution of the SWE. PINNs integrate physical law directly into the neural network architecture, enabling the accurate approximation of solutions to the SWE. We provide a comprehensive methodology for formulating the SWE within the PINNs framework, encompassing network architecture, training strategy, and data generation techniques. Through the results obtained from experiments, we found that PINNs could be an accurate output solution of SWE when its results were compared with the analytical method. In addition, PINNs also present better performance over the Artificial Neural Network. This study highlights the transformative potential of PINNs in revolutionizing water resources research, offering a new paradigm for accurate and efficient solutions to the SVE.

• Structural Engineering and Mechanics
• /
• v.17 no.6
• /
• pp.819-828
• /
• 2004

A new process for estimating the natural frequency and the corresponding damping ratio in large structures is discussed. In a practical situation, it is very difficult to analyze large structures precisely because they are too complex to model using the finite element method and too heavy to excite using the exciting force method; in particular, the measured signals are seriously influenced by ambient noise. In order to identify the structural impulse response associated with the information of natural frequency and the corresponding damping ratio in large structures, the analysis process, a so-called "multiresolution blind system identification algorithm" which combines Mallat algorithm and the bicepstrum method. High time-frequency concentration is attained and the phase information is kept. The experimental result has demonstrated that the new analysis process exploiting the natural frequency and the corresponding damping ratio of structural response are useful tools in structural analysis application.

• Nuclear Engineering and Technology
• /
• v.55 no.9
• /
• pp.3409-3416
• /
• 2023

Licensing the next-generation of nuclear reactor designs requires extensive use of Modeling and Simulation (M&S) to investigate system response to many operational conditions, identify possible accidental scenarios and predict their evolution to undesirable consequences that are to be prevented or mitigated via the deployment of adequate safety barriers. Deep Learning (DL) and Artificial Intelligence (AI) can support M&S computationally by providing surrogates of the complex multi-physics high-fidelity models used for design. However, DL and AI are, generally, low-fidelity 'black-box' models that do not assure any structure based on physical laws and constraints, and may, thus, lack interpretability and accuracy of the results. This poses limitations on their credibility and doubts about their adoption for the safety assessment and licensing of novel reactor designs. In this regard, Physics Informed Neural Networks (PINNs) are receiving growing attention for their ability to integrate fundamental physics laws and domain knowledge in the neural networks, thus assuring credible generalization capabilities and credible predictions. This paper presents the use of PINNs as surrogate models for accidental scenarios simulation in Nuclear Power Plants (NPPs). A case study of a Loss of Heat Sink (LOHS) accidental scenario in a Nuclear Battery (NB), a unique class of transportable, plug-and-play microreactors, is considered. A PINN is developed and compared with a Deep Neural Network (DNN). The results show the advantages of PINNs in providing accurate solutions, avoiding overfitting, underfitting and intrinsically ensuring physics-consistent results.