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LEARNING ONLY ON BOUNDARIES: A PHYSICS-INFORMED NEURAL OPERATOR FOR SOLVING PARAMETRIC PARTIAL DIFFERENTIAL EQUATIONS IN COMPLEX GEOMETRIES

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arXiv 2023年

作者： Fang, Zhiwei Wang, Sifan Perdikaris, Paris Graduate Group in Applied Mathematics Computational Science University of Pennsylvania PhiladelphiaPA19104 United States Department of Mechanichal Engineering Applied Mechanics University of Pennsylvania PhiladelphiaPA19104 United States

Recently deep learning surrogates and neural operators have shown promise in solving partial differential equations (PDEs). However, they often require a large amount of training data and are limited to bounded domains. In this work, we present a novel physics-informed neural operator method to solve parametrized boundary value problems without labeled data. By reformulating the PDEs into boundary integral equations (BIEs), we can train the operator network solely on the boundary of the domain. This approach reduces the number of required sample points from O(Nd) to O(Nd−1), where d is the domain's dimension, leading to a significant acceleration of the training process. Additionally, our method can handle unbounded problems, which are unattainable for existing physics-informed neural networks (PINNs) and neural operators. Our numerical experiments show the effectiveness of parametrized complex geometries and unbounded problems. Copyright © 2023, The Authors. All rights reserved.

关键词： Boundary element method

A statistical mechanics framework for constructing non-equilibrium thermodynamic models

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arXiv 2023年

作者： Leadbetter, Travis Purohit, Prashant K. Reina, Celia Graduate Group in Applied Mathematics and Computational Science University of Pennsylvania PhiladelphiaPA19104 United States Department of Mechanical Engineering and Applied Mechanics University of Pennsylvania PhiladelphiaPA19104 United States

Far-from-equilibrium phenomena are critical to all natural and engineered systems, and essential to biological processes responsible for life. For over a century and a half, since Carnot, Clausius, Maxwell, Boltzmann, and Gibbs, among many others, laid the foundation for our understanding of equilibrium processes, scientists and engineers have dreamed of an analogous treatment of non-equilibrium systems. But despite tremendous efforts, a universal theory of non-equilibrium behavior akin to equilibrium statistical mechanics and thermodynamics has evaded description. Several methodologies have proved their ability to accurately describe complex non-equilibrium systems at the macroscopic scale, but their accuracy and predictive capacity is predicated on either phenomenological kinetic equations fit to microscopic data, or on running concurrent simulations at the particle level. Instead, we provide a framework for deriving stand-alone macroscopic thermodynamics models directly from microscopic physics without fitting in overdamped Langevin systems. The only necessary ingredient is a functional form for a parameterized, approximate density of states, in analogy to the assumption of a uniform density of states in the equilibrium microcanonical ensemble. We highlight this framework's effectiveness by deriving analytical approximations for evolving mechanical and thermodynamic quantities in a model of coiled-coil proteins and double stranded DNA, thus producing, to the authors' knowledge, the first derivation of the governing equations for a phase propagating system under general loading conditions without appeal to phenomenology. The generality of our treatment allows for application to any system described by Langevin dynamics with arbitrary interaction energies and external driving, including colloidal macromolecules, hydrogels, and biopolymers. © 2023, CC BY.

关键词： Statistical mechanics

An Expert's Guide to Training Physics-informed Neural Networks

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arXiv 2023年

作者： Wang, Sifan Wang, Hanwen Sankaran, Shyam Perdikaris, Paris Graduate Group in Applied Mathematics and Computational Science University of Pennsylvania PhiladelphiaPA19104 United States Department of Mechanical Engineering and Applied Mechanics University of Pennsylvania PhiladelphiaPA19104 United States

Physics-informed neural networks (PINNs) have been popularized as a deep learning framework that can seamlessly synthesize observational data and partial differential equation (PDE) constraints. Their practical effectiveness however can be hampered by training pathologies, but also oftentimes by poor choices made by users who lack deep learning expertise. In this paper we present a series of best practices that can significantly improve the training efficiency and overall accuracy of PINNs. We also put forth a series of challenging benchmark problems that highlight some of the most prominent difficulties in training PINNs, and present comprehensive and fully reproducible ablation studies that demonstrate how different architecture choices and training strategies affect the test accuracy of the resulting models. We show that the methods and guiding principles put forth in this study lead to state-of-the-art results and provide strong baselines that future studies should use for comparison purposes. To this end, we also release a highly optimized library in JAX that can be used to reproduce all results reported in this paper, enable future research studies, as well as facilitate easy adaptation to new use-case scenarios. © 2023, CC BY-NC-SA.

关键词： Deep learning

ENSEMBLE LEARNING FOR PHYSICS INFORMED NEURAL NETWORKS: A GRADIENT BOOSTING APPROACH

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arXiv 2023年

作者： Fang, Zhiwei Wang, Sifan Perdikaris, Paris Graduate Group in Applied Mathematics and Computational Science University of Pennsylvania PhiladelphiaPA19104 United States Department of Mechanichal Engineering and Applied Mechanics University of Pennsylvania PhiladelphiaPA19104 United States

While the popularity of physics-informed neural networks (PINNs) is steadily rising, to this date, conventional PINNs have not been successful in simulating multi-scale and singular perturbation problems. In this work, we present a new training paradigm referred to as "gradient boosting" (GB), which significantly enhances the performance of physics informed neural networks (PINNs). Rather than learning the solution of a given partial differential equation (PDE) using a single neural network directly, our algorithm employs a sequence of neural networks to achieve a superior outcome. This approach allows us to solve problems presenting great challenges for traditional PINNs. Our numerical experiments demonstrate the effectiveness of our algorithm through various benchmarks, including comparisons with finite element methods and PINNs. Furthermore, this work also unlocks the door to employing ensemble learning techniques in PINNs, providing opportunities for further improvement in solving PDEs. © 2023, CC BY-NC-SA.

关键词： Numerical methods

Human intracortical responses to varying electrical stimulation conditions are separable in low-dimensional subspaces

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Human intracortical responses to varying electrical stimulat...

2022 IEEE International Conference on Systems, Man, and Cybernetics, SMC 2022

作者： Sun, Samantha Levinson, Lila H. Paschall, Courtnie J. Herron, Jeffrey Weaver, Kurt Hauptman, Jason Ko, Andrew Ojemann, Jeffrey Rao, Rajesh P. N. University of Washington Paul G. Allen School of Computer Science & Engineering Department of Bioengineering SeattleWA98195 United States University of Washington Graduate Program in Neuroscience Paul G. Allen School of Computer Science & Engineering SeattleWA98195 United States University of Washington Paul G. Allen School of Computer Science & Engineering Department of Neurological Surgery SeattleWA98195 United States University of Washington Paul G. Allen School of Computer Science & Engineering Department of Radiology SeattleWA98195 United States

ISBN: (数字)9781665452588

ISBN: (纸本)9781665452588

Electrical stimulation is a powerful tool for targeted neurorehabilitation, and recent work in adaptive stimulation where stimulation can be adjusted in real-time has shown promise in improving stimulation outcomes and reducing stimulation-induced side effects. Mapping the relationship between electrical stimulation input and neural activity response can help reveal their interactions and can give us tools to iterate and improve on our stimulation protocols. Here, we introduce methods for identifying low-dimensional subspaces of human intracortical responses to electrical stimulation in invasive electroencephalography. In epilepsy patients (n=4) undergoing clinical monitoring, we applied a stimulation protocol of varying amplitude and frequency in 5-second intervals to capture a range of responses to different stimulation conditions. We characterized these responses using time-frequency spectral power, applied baseline subtraction and outlier removal procedures, and performed principal component analysis across frequencies. We identified that intracortical responses to different stimulation conditions can be represented in a 3-dimensional subspace, accounting for more than 95% of the variance. Using support vector machine classification, we demonstrated separability of intracortical responses in different stimulation conditions across subjects, where this separability was contingent on applying baseline subtraction and outlier removal. Our results represent a first step towards building a predictive model of neural response from stimulation input, an important prerequisite for adaptive closed-loop stimulation for targeted neurorehabilitation. © 2022 IEEE.

关键词： Electroencephalography

Walking Optimization Algorithm for Humanoid Robots Using Genetic Algorithm

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Walking Optimization Algorithm for Humanoid Robots Using Gen...

International Conference on Control, Decision and Information Technologies (CoDIT)

作者： F. S. Chagas L. D. P. de Farias A. A. A. Bechina A. L. L. Ramos P. F. F. Rosa Department of Science and Industry Systems Faculty of Technology Natural Sciences and Maritime Sciences University of South-Eastern Norway Kongsberg Norway Department of Mechanical Engineering Military Institute of Engineering (IME) Rio de Janeiro Brazil Graduate Program in Defense Engineering Military Institute of Engineering (IME) Rio de Janeiro Brazil

ISBN: (数字)9798350373974

ISBN: (纸本)9798350373981

This paper proposes an algorithm to optimize the walking of humanoid robots based on the inverse kinematic model combined with a Genetic Algorithm. The objectives are to improve the sagittal displacement of the robot and reduce possible lateral deviations during a predetermined path. The foot of the humanoid performs a tapered motion, an approximate ellipse. Horizontal and vertical speeds and the angulation of the humanoid trunk are the input parameters of the algorithm. The algorithm utilizes the input information to calculate the inverse kinematics, and then it submits the obtained result to an evaluation function. We develop a virtual simulator and a robotic platform with 14 degrees of freedom to validate the proposed algorithm. We then test a prototype using the best result obtained in the simulations.

关键词： Legged locomotion Humanoid robots Prototypes Kinematics Approximation algorithms Genetics Information technology Biological cells Optimization Genetic algorithms

Power Quality Assessment of Oil and Gas Platform with High Penetration of Floating Offshore Wind Power

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Power Quality Assessment of Oil and Gas Platform with High P...

IEEE Annual Southern Power Electronics Conference (SPEC)

作者： Kassiane de Sousa Medeiros João Marcus Soares Callegari Lorrana Faria da Rocha Danilo Iglesias Brandao Graduate Program in Electrical Engineering Universidade Federal de Minas Gerais Belo Horizonte Brazil Department of Electric Energy Norwegian University of Science and Technology Trondheim Norway

This paper aims to analyze the effect on power quality of a Floating Production Storage and Offloading (FPSO) power system under high penetration of wind-based power generation. A set of results simulated in MATLAB/Simulink® is shown to assess different operational scenarios of a typical Brazilian FPSO, from Mero Oil Field. The floating offshore wind power penetration is varied from 10 to 50 MW and the FPSO power quality effects are reported; then the effect of increasing the umbilical distance from 12 to 150 km between the wind farm and FPSO is evaluated; and finally, the reduction in the number of gas turbine generators (3 and 2 generators) is performed. The conclusions are drawn based on steady-state and transient voltage and frequency profiles; active and reactive power flow between loads and generation; the rate of change of frequency and the minimum frequency reached under the disturbance event when a wind generation loss of 10 MW is triggered.

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Social network analysis of manga: similarities to real-world social networks and trends over decades

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arXiv 2023年

作者： Sugishita, Kashin Masuda, Naoki Department of Transdisciplinary Science and Engineering Tokyo Institute of Technology Tokyo152-8550 Japan Department of Mathematics State University of New York at Buffalo BuffaloNY14260-2900 United States Computational and Data-Enabled Science and Engineering Program State University of New York at Buffalo BuffaloNY14260-5030 United States Center for Computational Social Science Kobe University Kobe657-8501 Japan

Manga, Japanese comics, has been popular on a global scale. Social networks among characters, which are often called character networks, may be a significant contributor to their popularity. We collected data from 162 popular manga that span over 70 years and analyzed their character networks. First, we found that many of static and temporal properties of the character networks are similar to those of real human social networks. Second, the character networks of most manga are protagonist-centered such that a single protagonist interacts with the majority of other characters. Third, the character networks for manga mainly targeting boys have shifted to denser and less protagonist-centered networks and with fewer characters over decades. Manga mainly targeting girls showed the opposite trend except for the downward trend in the number of characters. The present study, which relies on manga data sampled on an unprecedented scale, paves the way for further population studies of character networks and other aspects of comics. Copyright © 2023, The Authors. All rights reserved.

关键词： Population statistics

Domain Adaptation in Color-Shifted Datasets Through Adversarial Learning Balancing

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Domain Adaptation in Color-Shifted Datasets Through Adversar...

International Conference on Artificial Intelligence and Data sciences (AiDAS)

作者： Hidayaturrahman Agung Trisetyarso Iman Herwidiana Kartowisastro Widodo Budiharto Computer Science Department BINUS Graduate Program - Doctor of Computer Science Bina Nusatara University Jakarta Indonesia Mathematics Department School of Computer Science Bina Nusatara University Jakarta Indonesia Computer Engineering Department Faculty of Engineering Bina Nusantara University Jakarta Indonesia Computer Science Department School of Computer Science Bina Nusantara University Jakarta Indonesia

Due to the disparity in the levels of difficulty presented by the several tasks, doing domain adaptation in an adversarial way may result in an imbalanced learning process. In the MNIST dataset, this phenomenon also manifests itself in the form of domain adaptation for color-shifted distribution. In this particular situation, the domain classifier has a higher tendency to fit more quickly, but the category classifier fits quite poorly in the learning process. In order to address this problem, a new hyper-parameter has been added to the loss function in order to strike a compromise between the learning speed of the domain and the categorical classifier. By using this technique, the categorical classifier may better match the data while still maintaining the same level of performance as the domain classifier. In order to determine whether or not making use of this hyper-parameter is useful, the phenomena in question is examined using three distinct color-shifted settings. Following the evaluations, it was discovered that the newly introduced hyper-parameter is capable of coping with imbalanced learning while simultaneously engaging in domain adaptation.

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