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Frame invariance and scalability of neural operators for partial differential equations [article]

Muhammad I. Zafar, Jiequn Han, Xu-Hui Zhou, Heng Xiao
2021
In this work, invariance properties and computational complexity of two neural operators are examined for transport PDE of a scalar quantity.  ...  Partial differential equations (PDEs) play a dominant role in the mathematical modeling of many complex dynamical processes.  ...  Government is authorised to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright notation thereon. The computational resources used for this  ... 
doi:10.48550/arxiv.2112.14769 fatcat:5mwcznhn4zdn5m4eg3r6hbrq2e

Physics-Guided Deep Learning for Dynamical Systems: A Survey [article]

Rui Wang, Rose Yu
2022 arXiv   pre-print
While deep learning (DL) provides novel alternatives for efficiently recognizing complex patterns and emulating nonlinear dynamics, its predictions do not necessarily obey the governing laws of physical  ...  Thus, the study of physics-guided DL emerged and has gained great progress.  ...  Neural Differential Equations [24] developed a continuous depth NN for solving ordinary differential equations, Neural ODE.  ... 
arXiv:2107.01272v5 fatcat:k6hhdt6csnfebgkzrpuoeqkwzi

A Local Spectral Exterior Calculus for the Sphere and Application to the Shallow Water Equations [article]

Clauson Carvalho da Silva, Christian Lessig, Boyko Dodov, Henk Dijkstra, Themis Sapsis
2020 arXiv   pre-print
These are well localized in space and frequency and provide (Stevenson) frames for the homogeneous Sobolev spaces Ḣ^-r+1( Ω_ν^r , S^2 ) of differential r-forms.  ...  These extend scalable frames to weighted sampling expansions and provide an alternative to quadrature rules for the discretization of needlet-like scale-discrete wavelets.  ...  CL would like to thank Mathieu Desbrun for helpful discussion on the relationship between Discrete Exterior Calculus and the present work. Funding by AIR Worldwide is gratefully acknowledged.  ... 
arXiv:2005.03598v1 fatcat:a4ml376umjamrb57htwwuimb44

Fast Object Tracking on a Many-Core Neural Network Chip

Lei Deng, Zhe Zou, Xin Ma, Ling Liang, Guanrui Wang, Xing Hu, Liu Liu, Jing Pei, Guoqi Li, Yuan Xie
2018 Frontiers in Neuroscience  
Results show that a single chip is able to accommodate the whole tracking model, and a fast tracking speed of nearly 800 FPS (frames per second) can be achieved.  ...  Then, we design a many-core neural network architecture with several computation and transformation operations to support the model.  ...  ACKNOWLEDGMENTS This work was partially supported by National Science Foundation of China (Grant No. 61475080, 61603209, and 61876215) and National Science Foundation (Grant No. 1725447 and 1730309)  ... 
doi:10.3389/fnins.2018.00841 pmid:30505264 pmcid:PMC6250745 fatcat:7gemdjzjfff23mnna2r4kmok4e

A PDE-free, neural network-based eddy viscosity model coupled with RANS equations [article]

Ruiying Xu, Xu-Hui Zhou, Jiequn Han, Richard P. Dwight, Heng Xiao
2022 arXiv   pre-print
Most turbulence models used in Reynolds-averaged Navier-Stokes (RANS) simulations are partial differential equations (PDE) that describe the transport of turbulent quantities.  ...  The success of the coupling paves the way for neural network-based emulation of Reynolds stress transport models.  ...  The turbulence quantities are described by two partial differential equations (PDEs) coupled with the source term.  ... 
arXiv:2202.08342v1 fatcat:mdvbiuar4jhczpky6mwb6di3pu

Self-Supervision by Prediction for Object Discovery in Videos [article]

Beril Besbinar, Pascal Frossard
2021 arXiv   pre-print
In addition to disentangling the notion of objects and the motion dynamics, our compositional structure explicitly handles occlusion and inpaints inferred objects and background for the composition of  ...  One scalable solution is to make the model generate the supervision for itself by leveraging some part of the input data, which is known as self-supervised learning.  ...  For object inpainting, the function F 4 (·) in Equation (10) is a selection operator based on a if-statement to copy values of pixels in occluded regions from previous frames, whereas F 5 (·) in Equation  ... 
arXiv:2103.05669v1 fatcat:trixe3eoqza5tilaku5q447q6e

Multimedia Security: A Survey of Chaos-Based Encryption Technology [chapter]

Zhaopin Su, Guofu Zhang, Jianguo Jiang
2012 Multimedia - A Multidisciplinary Approach to Complex Issues  
Differential attack test can be achieved through measuring the percentage p of different pixel numbers (see Equation 1 and Equation 2) between two encrypted images, I 1 and I 2 (the width and height  ...  blocks or bit-planes are partially encrypted by a stream cipher based on a modified chaotic neural network .  ...  To make the most of this phenomenon, the rapidly increasing volume and usage of digitised content requires constant reevaluation and adaptation of multimedia methodologies, in order to meet the relentless  ... 
doi:10.5772/36036 fatcat:eeknyvo6j5hl7p6i6a23pjhot4

Neural Jacobian Fields: Learning Intrinsic Mappings of Arbitrary Meshes [article]

Noam Aigerman, Kunal Gupta, Vladimir G. Kim, Siddhartha Chaudhuri, Jun Saito, Thibault Groueix
2022 arXiv   pre-print
The field of matrices is then projected onto the tangent bundle of the given mesh, and used as candidate jacobians for the predicted map.  ...  The framework is based on reducing the neural aspect to a prediction of a matrix for a single given point, conditioned on a global shape descriptor.  ...  A INVARIANCE TO THE CHOICE OF FRAMES Claim. Our framework is completely invariant to the (arbitrary) choice of frames {B 𝑖 } .  ... 
arXiv:2205.02904v1 fatcat:igrv2g723vfn5f3zcbdjnskgnm

Scalable Surrogate Deconvolution for Identification of Partially-Observable Systems and Brain Modeling [article]

Matthew F Singh, Anxu Wang, Todd S Braver, ShiNung Ching
2020 bioRxiv   pre-print
We show that the proposed technique is highly scalable, low in computational complexity, and performs competitively with the current gold-standard in partially-observable system estimation: the joint Kalman  ...  These measurements are often generated by approximately linear time-invariant (LTI) dynamical interactions with the hidden system and may therefore be described as a convolution of hidden state-variables  ...  These approaches suffer, however, in terms of scalability and data quantity.  ... 
doi:10.1101/2020.03.20.000661 fatcat:i4mb35raaraotevchq6wlsoxjq

A Physics-Driven Neural Networks-Based Simulation System (PhyNNeSS) for Multimodal Interactive Virtual Environments Involving Nonlinear Deformable Objects

Suvranu De, Dhannanjay Deo, Ganesh Sankaranarayanan, Venkata S. Arikatla
2011 Presence - Teleoperators and Virtual Environments  
Background-While an update rate of 30 Hz is considered adequate for real time graphics, a much higher update rate of about 1 kHz is necessary for haptics.  ...  We show, through careful error analysis, that the scheme is scalable, with the accuracy being controlled by the number of neurons used in the simulation.  ...  Acknowledgments The authors gratefully acknowledge the support of this work by NIH/NIBIB through grant # R01 EB005807.  ... 
doi:10.1162/pres_a_00054 pmid:22629108 pmcid:PMC3357955 fatcat:ewe4u64m3fc6rax36ywe7ukwfq

Exploiting Spatio-Temporal Structure with Recurrent Winner-Take-All Networks [article]

Eder Santana, Matthew Emigh, Pablo Zegers, Jose C Principe
2017 arXiv   pre-print
of the previously proposed Winner-Take-All Autoencoders to sequences in time, and a new technique for initializing and regularizing convolutional-recurrent neural networks.  ...  proposed by Chalasani and Principe.Our contributions can be summarized as a scalable reinterpretation of the Deep Predictive Coding Networks trained end-to-end with backpropagation through time, an extension  ...  This forces a balance between the stateless encoder and the recurrent neural network. Hence the system will look for solution that consider spatial and temporal invariances.  ... 
arXiv:1611.00050v2 fatcat:osouttaz4vgrpft7s3lea6qgli

CaSPR: Learning Canonical Spatiotemporal Point Cloud Representations [article]

Davis Rempe, Tolga Birdal, Yongheng Zhao, Zan Gojcic, Srinath Sridhar, Leonidas J. Guibas
2020 arXiv   pre-print
We then leverage this canonicalization to learn a spatiotemporal latent representation using neural ordinary differential equations and a generative model of dynamically evolving shapes using continuous  ...  Our goal is to enable information aggregation over time and the interrogation of object state at any spatiotemporal neighborhood in the past, observed or not.  ...  Toyota Research Institute ("TRI") provided funds to assist the authors with their research but this article solely reflects the opinions and conclusions of its authors and not TRI or any other Toyota entity  ... 
arXiv:2008.02792v2 fatcat:xxn7tf5r3vf35exzpajhqzeazi

Deep ℒ^1 Stochastic Optimal Control Policies for Planetary Soft-landing [article]

Marcus A. Pereira, Camilo A. Duarte, Ioannis Exarchos, Evangelos A. Theodorou
2021 arXiv   pre-print
This is achieved by building off of recent work on deep Forward-Backward Stochastic Differential Equations (FBSDEs) and differentiable non-convex optimization neural-network layers based on stochastic  ...  Our algorithm solves the PDG problem by framing it as an ℒ^1 SOC problem for minimum fuel consumption.  ...  These so called deep FBSDE controllers are scalable solutions to solve high-dimensional parabolic partial differential equations such as the Hamilton-Jacobi-Bellman (HJB) PDE that one encounters in continuous-time  ... 
arXiv:2109.00183v1 fatcat:3wrtmixvnzbjhbbilh2bh3ucd4

FPGA-Based Multimodal Embedded Sensor System Integrating Low- and Mid-Level Vision

Guillermo Botella, José Antonio Martín H., Matilde Santos, Uwe Meyer-Baese
2011 Sensors  
The bioinspired sensor has been designed for Very Large Scale Integration (VLSI) using properties of the mammalian cortical motion pathway.  ...  The results are described trough experiments showing the validity of the proposed system and an analysis of the computational resources and performance of the applied algorithms.  ...  Dale, from the Vision Group at University College London, for their great help and support for some of the previous works mentioned here.  ... 
doi:10.3390/s110808164 pmid:22164069 pmcid:PMC3231703 fatcat:iqyo4qu3cvevlmsygvfaciwo4e

PhyGeoNet: Physics-Informed Geometry-Adaptive Convolutional Neural Networks for Solving Parameterized Steady-State PDEs on Irregular Domain [article]

Han Gao, Luning Sun, Jian-Xun Wang
2020 arXiv   pre-print
Recently, the advent of deep learning has spurred interest in the development of physics-informed neural networks (PINN) for efficiently solving partial differential equations (PDEs), particularly in a  ...  The proposed method has been assessed by solving a number of PDEs on irregular domains, including heat equations and steady Navier-Stokes equations with parameterized boundary conditions and varying geometries  ...  Acknowledgment The authors would like to acknowledge the funds from National Science Foundation (NSF contract CMMI-1934300) and startup funds from the College of Engineering at University of Notre Dame  ... 
arXiv:2004.13145v2 fatcat:yopnmvhjsvdflmmv7ycggbhx5m
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