Article
Engineering, Multidisciplinary
Yibo Yang, Georgios Kissas, Paris Perdikaris
Summary: This study presents a simple and effective method for quantifying posterior uncertainty in deep operator networks (DeepONets). The approach utilizes a frequentist approach with randomized prior ensembles and introduces an efficient vectorized implementation for fast parallel inference. The proposed method exhibits four main advantages: more robust and accurate predictions compared to deterministic DeepONets, reliable uncertainty estimates for sparse data sets with multi-scale function pairs, effective detection of out-of-distribution and adversarial examples, and seamless quantification of uncertainty due to model bias and data noise. Additionally, the study provides an optimized JAX library called UQDeepONet that can handle large model architectures, ensemble sizes, and data sets with excellent parallel performance on accelerated hardware, enabling uncertainty quantification for DeepONets in realistic large-scale applications.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Environmental Sciences
Amir H. Kohanpur, Siddharth Saksena, Sayan Dey, J. Michael Johnson, M. Sadegh Riasi, Lilit Yeghiazarian, Alexandre M. Tartakovsky
Summary: Estimating uncertainty in flood model predictions is crucial for various applications. This study focuses on uncertainty in physics-based urban flooding models, considering model complexity, uncertainty in input parameters, and the effects of rainfall intensity. The ICPR model is used to quantify floodwater depth prediction uncertainty, with results showing localized uncertainties. Model simplifications lead to overconfident predictions, while increasing model resolution reduces uncertainty but increases computational cost. The multilevel MC method is employed to reduce cost when estimating uncertainty in a high-resolution ICPR model. Utilizing ensemble estimates, the proposed framework improves flood depth forecasting accuracy compared to the ICPR model's mean prediction, even with limited measurements.
WATER RESOURCES RESEARCH
(2023)
Article
Engineering, Multidisciplinary
N. Navaneeth, Tapas Tripura, Souvik Chakraborty
Summary: Deep neural operators are effective for learning solution operators of complex PDEs. The Wavelet Neural Operator is able to capture spatial manifolds effectively. However, relying on conventional solvers for data generation is challenging in practical applications.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2024)
Article
Mechanics
Emanuele Avoledo, Alessandro Tognan, Enrico Salvati
Summary: Substantial advances in fatigue estimation of defective materials can be achieved through the use of Physics-Informed Neural Network (PINN), which can account for multiple defect descriptors while maintaining accurate predictions. This study aims to assess the variability of PINN-estimated fatigue life due to input uncertainties and explore the influence of defect descriptors in fatigue life using sensitivity indices. The findings suggest that traditionally neglected defect descriptors may have a relevant role in specific circumstances.
ENGINEERING FRACTURE MECHANICS
(2023)
Article
Computer Science, Interdisciplinary Applications
Hyomin Shin, Minseok Choi
Summary: We propose a physics-informed learning method based on variational autoencoder (VAE) to solve data-driven stochastic differential equations with limited measurements and known governing equation. Our model integrates VAE with stochastic partial differential equations to infer the randomness of the solution. The efficiency of the proposed model is demonstrated for learning stochastic processes and solving various types of stochastic partial differential equations.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Computer Science, Interdisciplinary Applications
Jared O'Leary, Joel A. Paulson, Ali Mesbah
Summary: This study proposes a framework for training artificial neural networks to learn the hidden physics within stochastic differential equations (SDEs). The framework propagates stochasticity through the known structure of the SDE and utilizes automatic differentiation and mini-batch gradient descent to establish the parameters of the neural networks. The results demonstrate the potential of this method in unraveling the hidden physics of multivariate stochastic dynamical systems.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Engineering, Mechanical
Ryan Nguyen, Shubhendu Kumar Singh, Rahul Rai
Summary: Prognostics is important for the longevity of systems or products. This paper introduces a novel hybrid modeling approach that combines fuzzy logic and generative adversarial networks (GANs) to improve the accuracy of system prognosis. The results show that adding a physics-based aggregation in a fuzzy logic model enhances GAN's ability to model health and provide more accurate predictions.
MECHANICAL SYSTEMS AND SIGNAL PROCESSING
(2023)
Article
Automation & Control Systems
Michail Spitieris, Ingelin Steinsland
Summary: This paper introduces an efficient data-driven framework for quantifying the uncertainty in physical parameters and model formulation of computer models. The framework combines physics-informed priors and Bayesian methods to recover the true parameters of physical models and generate accurate predictions. Additionally, our approach is computationally faster than traditional Bayesian calibration methods.
JOURNAL OF MACHINE LEARNING RESEARCH
(2023)
Article
Computer Science, Interdisciplinary Applications
Apostolos F. Psaros, Xuhui Meng, Zongren Zou, Ling Guo, George Em Karniadakis
Summary: Neural networks have revolutionized computational methods by effectively solving challenging problems that cannot be solved using traditional methods. However, quantifying errors and uncertainties in neural network-based inference is more complex than in traditional methods. This study presents a comprehensive framework for effectively and efficiently quantifying total uncertainty in neural networks, including uncertainty modeling, solution methods, and evaluation metrics. Furthermore, an open-source Python library called NeuralUQ is developed to facilitate the deployment of uncertainty quantification in scientific machine learning research and practice.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Engineering, Multidisciplinary
Mingyuan Yang, John T. Foster
Summary: In this paper, a multi-output physics-informed neural network (MO-PINN) is proposed to provide solutions with uncertainty distributions for both forward and inverse PDE problems with noisy data. It is demonstrated that MO-PINN can provide accurate predictions and its solutions are consistent with traditional methods. Additional statistical knowledge can be incorporated to improve the prediction if available.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Computer Science, Interdisciplinary Applications
Alex Alberts, Ilias Bilionis
Summary: Data-driven approaches combined with physical knowledge are powerful techniques for modeling engineering systems. The objective is to efficiently solve for the underlying physical field by combining measurements with known physical laws. To handle the uncertainties arising from unknown elements, such as missing parameters, noisy measurements, or incomplete physical laws, information field theory (IFT) is extended to physics-informed information field theory (PIFT) by incorporating functional priors based on the physical laws. The method remains independent of any specific numerical scheme and can capture multiple modes, allowing for the solution of ill-posed problems.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Engineering, Multidisciplinary
Joseph P. Molnar, Samuel J. Grauer
Summary: We introduce a new approach to flow field tomography using the Navier-Stokes and advection-diffusion equations for regularization. Through the use of physics-informed neural networks (PINNs), we are able to leverage the governing physics to improve the accuracy of flow field reconstructions from sparse line-of-sight integrated measurements. Our results demonstrate that PINNs outperform state-of-the-art algorithms in terms of accuracy, even when used for post-processing. However, high levels of noise can lead to semi-convergence, which we address with a Bayesian PINN that allows for uncertainty quantification and reveals the source of semi-convergence.
MEASUREMENT SCIENCE AND TECHNOLOGY
(2022)
Article
Engineering, Multidisciplinary
Ravi G. Patel, Nathaniel A. Trask, Mitchell A. Wood, Eric C. Cyr
Summary: The paper presents a framework for discovering continuum models from high-fidelity molecular simulation data using neural networks to parameterize governing physics. The approach is effective for various physics, including local and nonlocal diffusion processes and single and multiphase flows, with the learned operator able to generalize to system characteristics not included in the training sets.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2021)
Article
Thermodynamics
Xinchao Jiang, Xin Wang, Ziming Wen, Enying Li, Hu Wang
Summary: This study proposes an ensemble physics-informed neural network (E-PINN) method to handle space-dependent inverse heat conduction problems (IHCPs). Compared with other data-driven uncertainty quantification methods, the suggested method is straightforward to implement and achieves high-quality uncertainty estimates of the quantities of interest (QoIs). Furthermore, an adaptive active sampling strategy based on the uncertainty estimates from E-PINNs is proposed to improve the accuracy of material field inversion problems. Finally, the proposed method is validated through several numerical experiments of IHCPs.
INTERNATIONAL COMMUNICATIONS IN HEAT AND MASS TRANSFER
(2023)
Article
Computer Science, Artificial Intelligence
Clemens Oszkinat, Susan E. Luczak, I. G. Rosen
Summary: In this study, we develop an approach to estimate the blood alcohol content from a transdermal alcohol signal using physics-informed neural networks. By utilizing a generative adversarial network and a residual-augmented loss function, we are able to accurately estimate the distribution of unknown parameters in the transdermal alcohol transport model and separate the blood alcohol signal. We improve the accuracy of estimation by quantifying uncertainty and using posterior latent variables.
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS
(2023)
Article
Engineering, Multidisciplinary
Luca Bonfiglio, Paris Perdikaris, Jose del Aguila, George E. Karniadakis
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
(2018)
Article
Engineering, Marine
Jose del Aguila Ferrandis, Stefano Brizzolara, Chryssostomos Chryssostomidis
Article
Engineering, Ocean
Jose del Aguila Ferrandis, Luca Bonfiglio, Ricardo Zamora Rodriguez, Chryssostomos Chryssostomidis, Odd Magnus Faltinsen, Michael Triantafyllou
JOURNAL OF OFFSHORE MECHANICS AND ARCTIC ENGINEERING-TRANSACTIONS OF THE ASME
(2020)
Article
Multidisciplinary Sciences
J. del Aguila Ferrandis, M. S. Triantafyllou, C. Chryssostomidis, G. E. Karniadakis
Summary: Predicting vessel motions in extreme sea states is a challenging problem in naval hydrodynamics, which can be addressed by training neural networks. LSTM neural networks outperform standard RNNs in this task, demonstrating good accuracy in predicting vessel motions for unseen wave elevations.
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
(2021)
Proceedings Paper
Engineering, Marine
Jose del Aguila Ferrandis, Julie Chalfant, Chathan M. Cooke, Chryssostomos Chryssostomidis
2019 IEEE ELECTRIC SHIP TECHNOLOGIES SYMPOSIUM (ESTS 2019): EMERGING TECHNOLOGIES FOR FUTURE ELECTRIC SHIPS
(2019)
Proceedings Paper
Engineering, Marine
Jose del Aguila Ferrandis, Ricardo Zamora Rodriguez, Chryssostomos Chryssostomidis, Luca Bonfiglio
PROCEEDINGS OF THE ASME 37TH INTERNATIONAL CONFERENCE ON OCEAN, OFFSHORE AND ARCTIC ENGINEERING, 2018, VOL 1
(2018)
Article
Computer Science, Interdisciplinary Applications
Tian Liang, Lin Fu
Summary: In this work, a new shock-capturing framework is proposed based on a new candidate stencil arrangement and the combination of infinitely differentiable non-polynomial RBF-based reconstruction in smooth regions with jump-like non-polynomial interpolation for genuine discontinuities. The resulting scheme achieves high order accuracy and resolves genuine discontinuities with sub-cell resolution.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Lukas Lundgren, Murtazo Nazarov
Summary: In this paper, a high-order accurate finite element method for incompressible variable density flow is introduced. The method addresses the issues of saddle point system and stability problem through Schur complement preconditioning and artificial compressibility approaches, and it is validated to have high-order accuracy for smooth problems and accurately resolve discontinuities.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Gabriele Ciaramella, Laurence Halpern, Luca Mechelli
Summary: This paper presents a novel convergence analysis of the optimized Schwarz waveform relaxation method for solving optimal control problems governed by periodic parabolic PDEs. The analysis is based on a Fourier-type technique applied to a semidiscrete-in-time form of the optimality condition, which enables a precise characterization of the convergence factor at the semidiscrete level. The behavior of the optimal transmission condition parameter is also analyzed in detail as the time discretization approaches zero.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Jonas A. Actor, Xiaozhe Hu, Andy Huang, Scott A. Roberts, Nathaniel Trask
Summary: This article introduces a scientific machine learning framework that uses a partition of unity architecture to model physics through control volume analysis. The framework can extract reduced models from full field data while preserving the physics. It is applicable to manifolds in arbitrary dimension and has been demonstrated effective in specific problems.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Nozomi Magome, Naoki Morita, Shigeki Kaneko, Naoto Mitsume
Summary: This paper proposes a novel strategy called B-spline based SFEM to fundamentally solve the problems of the conventional SFEM. It uses different basis functions and cubic B-spline basis functions with C-2-continuity to improve the accuracy of numerical integration and avoid matrix singularity. Numerical results show that the proposed method is superior to conventional methods in terms of accuracy and convergence.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Timothy R. Law, Philip T. Barton
Summary: This paper presents a practical cell-centred volume-of-fluid method for simulating compressible solid-fluid problems within a pure Eulerian setting. The method incorporates a mixed-cell update to maintain sharp interfaces, and can be easily extended to include other coupled physics. Various challenging test problems are used to validate the method, and its robustness and application in a multi-physics context are demonstrated.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Xing Ji, Fengxiang Zhao, Wei Shyy, Kun Xu
Summary: This paper presents the development of a third-order compact gas-kinetic scheme for compressible Euler and Navier-Stokes solutions, constructed particularly for an unstructured tetrahedral mesh. The scheme demonstrates robustness in high-speed flow computation and exhibits excellent adaptability to meshes with complex geometrical configurations.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Alsadig Ali, Abdullah Al-Mamun, Felipe Pereira, Arunasalam Rahunanthan
Summary: This paper presents a novel Bayesian statistical framework for the characterization of natural subsurface formations, and introduces the concept of multiscale sampling to localize the search in the stochastic space. The results show that the proposed framework performs well in solving inverse problems related to porous media flows.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Jacob Rains, Yi Wang, Alec House, Andrew L. Kaminsky, Nathan A. Tison, Vamshi M. Korivi
Summary: This paper presents a novel method called constrained optimized DMD with Control (cOptDMDc), which extends the optimized DMD method to systems with exogenous inputs and can enforce the stability of the resulting reduced order model (ROM). The proposed method optimally places eigenvalues within the stable region, thus mitigating spurious eigenvalue issues. Comparative studies show that cOptDMDc achieves high accuracy and robustness.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Andrea La Spina, Jacob Fish
Summary: This work introduces a hybridizable discontinuous Galerkin formulation for simulating ideal plasmas. The proposed method couples the fluid and electromagnetic subproblems monolithically based on source and employs a fully implicit time integration scheme. The approach also utilizes a projection-based divergence correction method to enforce the Gauss laws in challenging scenarios. Numerical examples demonstrate the high-order accuracy, efficiency, and robustness of the proposed formulation.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Junhong Yue, Peijun Li
Summary: This paper proposes two numerical methods (IP-FEM and BP-FEM) to study the flexural wave scattering problem of an arbitrary-shaped cavity on an infinite thin plate. These methods successfully decompose the fourth-order plate wave equation into the Helmholtz and modified Helmholtz equations with coupled conditions on the cavity boundary, providing an effective solution to this challenging problem.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
William Anderson, Mohammad Farazmand
Summary: We develop fast and scalable methods, called RONS, for computing reduced-order nonlinear solutions. These methods have been proven to be highly effective in tackling challenging problems, but become computationally prohibitive as the number of parameters grows. To address this issue, three separate methods are proposed and their efficacy is demonstrated through examples. The application of RONS to neural networks is also discussed.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Marco Caliari, Fabio Cassini
Summary: In this paper, a second order exponential scheme for stiff evolutionary advection-diffusion-reaction equations is proposed. The scheme is based on a directional splitting approach and uses computation of small sized exponential-like functions and tensor-matrix products for efficient implementation. Numerical examples demonstrate the advantage of the proposed approach over state-of-the-art techniques.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Sebastiano Boscarino, Seung Yeon Cho, Giovanni Russo
Summary: This work proposes a high order conservative semi-Lagrangian method for the inhomogeneous Boltzmann equation of rarefied gas dynamics. The method combines a semi-Lagrangian scheme for the convection term, a fast spectral method for computation of the collision operator, and a high order conservative reconstruction and a weighted optimization technique to preserve conservative quantities. Numerical tests demonstrate the accuracy and efficiency of the proposed method.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Jialei Li, Xiaodong Liu, Qingxiang Shi
Summary: This study shows that the number, centers, scattering strengths, inner and outer diameters of spherical shell-structured sources can be uniquely determined from the far field patterns. A numerical scheme is proposed for reconstructing the spherical shell-structured sources, which includes a migration series method for locating the centers and an iterative method for computing the inner and outer diameters without computing derivatives.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)