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Deep Neural Networks Motivated by Partial Differential Equations
v1v2 (latest)

Deep Neural Networks Motivated by Partial Differential Equations

12 April 2018
Lars Ruthotto
E. Haber
    AI4CE
ArXiv (abs)PDFHTML

Papers citing "Deep Neural Networks Motivated by Partial Differential Equations"

50 / 244 papers shown
Unraveled Multilevel Transformation Networks for Predicting
  Sparsely-Observed Spatiotemporal Dynamics
Unraveled Multilevel Transformation Networks for Predicting Sparsely-Observed Spatiotemporal Dynamics
Priyabrata Saha
Saibal Mukhopadhyay
112
1
0
16 Mar 2022
Learning Deep Implicit Fourier Neural Operators (IFNOs) with
  Applications to Heterogeneous Material Modeling
Learning Deep Implicit Fourier Neural Operators (IFNOs) with Applications to Heterogeneous Material ModelingComputer Methods in Applied Mechanics and Engineering (CMAME), 2022
Huaiqian You
Quinn Zhang
Colton J. Ross
Chung-Hao Lee
Yue Yu
AI4CE
268
134
0
15 Mar 2022
NINNs: Nudging Induced Neural Networks
NINNs: Nudging Induced Neural Networks
Harbir Antil
R. Löhner
Randy Price
AI4CE
85
2
0
15 Mar 2022
FinNet: Solving Time-Independent Differential Equations with Finite
  Difference Neural Network
FinNet: Solving Time-Independent Differential Equations with Finite Difference Neural Network
Son N. T. Tu
Thu Nguyen
AI4CE
119
0
0
18 Feb 2022
Learning continuous models for continuous physics
Learning continuous models for continuous physicsCommunications Physics (Commun. Phys.), 2022
Aditi S. Krishnapriyan
A. Queiruga
N. Benjamin Erichson
Michael W. Mahoney
AI4CE
363
39
0
17 Feb 2022
Bounded nonlinear forecasts of partially observed geophysical systems
  with physics-constrained deep learning
Bounded nonlinear forecasts of partially observed geophysical systems with physics-constrained deep learning
Said Ouala
Steven L. Brunton
A. Pascual
Bertrand Chapron
F. Collard
L. Gaultier
Ronan Fablet
PINNAI4TSAI4CE
330
13
0
11 Feb 2022
LyaNet: A Lyapunov Framework for Training Neural ODEs
LyaNet: A Lyapunov Framework for Training Neural ODEsInternational Conference on Machine Learning (ICML), 2022
I. D. Rodriguez
Aaron D. Ames
Yisong Yue
230
72
0
05 Feb 2022
Machine Learning in Heterogeneous Porous Materials
Machine Learning in Heterogeneous Porous Materials
Martha DÉli
H. Deng
Cedric G. Fraces
K. Garikipati
L. Graham‐Brady
...
H. Tchelepi
B. Važić
Hari S. Viswanathan
H. Yoon
P. Zarzycki
AI4CE
193
11
0
04 Feb 2022
Imbedding Deep Neural Networks
Imbedding Deep Neural NetworksInternational Conference on Learning Representations (ICLR), 2022
A. Corbett
D. Kangin
AI4TS
238
2
0
31 Jan 2022
Convergence of Invariant Graph Networks
Convergence of Invariant Graph NetworksInternational Conference on Machine Learning (ICML), 2022
Chen Cai
Yusu Wang
402
8
0
25 Jan 2022
Nonlocal Kernel Network (NKN): a Stable and Resolution-Independent Deep
  Neural Network
Nonlocal Kernel Network (NKN): a Stable and Resolution-Independent Deep Neural Network
Huaiqian You
Yue Yu
M. DÉlia
T. Gao
Stewart Silling
222
82
0
06 Jan 2022
Neural Piecewise-Constant Delay Differential Equations
Neural Piecewise-Constant Delay Differential EquationsAAAI Conference on Artificial Intelligence (AAAI), 2022
Qunxi Zhu
Yifei Shen
Dongsheng Li
Wei-Jer Lin
PINN
231
8
0
04 Jan 2022
Latent Time Neural Ordinary Differential Equations
Latent Time Neural Ordinary Differential EquationsAAAI Conference on Artificial Intelligence (AAAI), 2021
Srinivas Anumasa
P. K. Srijith
BDL
129
8
0
23 Dec 2021
Neural Born Iteration Method For Solving Inverse Scattering Problems: 2D
  Cases
Neural Born Iteration Method For Solving Inverse Scattering Problems: 2D CasesIEEE Transactions on Antennas and Propagation (IEEE Trans. Antennas Propag.), 2021
Tao Shan
Zhichao Lin
Xiaoqian Song
Maokun Li
Fan Yang
Zhensheng Xu
194
30
0
18 Dec 2021
Learning High-Dimensional Parametric Maps via Reduced Basis Adaptive
  Residual Networks
Learning High-Dimensional Parametric Maps via Reduced Basis Adaptive Residual Networks
Thomas O'Leary-Roseberry
Xiaosong Du
A. Chaudhuri
J. Martins
Karen E. Willcox
Omar Ghattas
289
30
0
14 Dec 2021
Nonparametric inference of stochastic differential equations based on
  the relative entropy rate
Nonparametric inference of stochastic differential equations based on the relative entropy rate
Min Dai
Jinqiao Duan
Jianyu Hu
Xiangjun Wang
126
3
0
09 Dec 2021
Characteristic Neural Ordinary Differential Equations
Characteristic Neural Ordinary Differential EquationsInternational Conference on Learning Representations (ICLR), 2021
Xingzi Xu
Ali Hasan
Khalil Elkhalil
Jie Ding
Vahid Tarokh
BDL
388
3
0
25 Nov 2021
Constructing Neural Network-Based Models for Simulating Dynamical
  Systems
Constructing Neural Network-Based Models for Simulating Dynamical SystemsACM Computing Surveys (CSUR), 2021
Christian Møldrup Legaard
Thomas Schranz
G. Schweiger
Ján Drgovna
Basak Falay
Ana Cavalcanti
Alexandros Iosifidis
M. Abkar
Peter Gorm Larsen
PINNAI4CE
266
126
0
02 Nov 2021
Sinkformers: Transformers with Doubly Stochastic Attention
Sinkformers: Transformers with Doubly Stochastic AttentionInternational Conference on Artificial Intelligence and Statistics (AISTATS), 2021
Michael E. Sander
Pierre Ablin
Mathieu Blondel
Gabriel Peyré
255
118
0
22 Oct 2021
GCCN: Global Context Convolutional Network
GCCN: Global Context Convolutional Network
Ali Hamdi
Flora D. Salim
D. Kim
161
2
0
22 Oct 2021
Signature-Graph Networks
Signature-Graph Networks
Ali Hamdi
Flora D. Salim
D. Kim
Xiaojun Chang
157
2
0
22 Oct 2021
Solving Image PDEs with a Shallow Network
Solving Image PDEs with a Shallow Network
Pascal Getreuer
P. Milanfar
Xiyang Luo
173
1
0
15 Oct 2021
Differential Motion Evolution for Fine-Grained Motion Deformation in
  Unsupervised Image Animation
Differential Motion Evolution for Fine-Grained Motion Deformation in Unsupervised Image Animation
Peirong Liu
Rui Wang
Xuefei Cao
Yipin Zhou
Ashish Shah
Ser-Nam Lim
DiffM
480
3
0
09 Oct 2021
Kinematically consistent recurrent neural networks for learning inverse
  problems in wave propagation
Kinematically consistent recurrent neural networks for learning inverse problems in wave propagation
Wrik Mallik
R. Jaiman
J. Jelovica
AI4CE
155
3
0
08 Oct 2021
Redesigning the Transformer Architecture with Insights from
  Multi-particle Dynamical Systems
Redesigning the Transformer Architecture with Insights from Multi-particle Dynamical Systems
Subhabrata Dutta
Tanya Gautam
Soumen Chakrabarti
Tanmoy Chakraborty
315
25
0
30 Sep 2021
slimTrain -- A Stochastic Approximation Method for Training Separable
  Deep Neural Networks
slimTrain -- A Stochastic Approximation Method for Training Separable Deep Neural Networks
Elizabeth Newman
Julianne Chung
Matthias Chung
Lars Ruthotto
216
8
0
28 Sep 2021
Short-term traffic prediction using physics-aware neural networks
Short-term traffic prediction using physics-aware neural networks
M. Pereira
Annika Lang
Balázs Kulcsár
159
31
0
21 Sep 2021
Quantized Convolutional Neural Networks Through the Lens of Partial
  Differential Equations
Quantized Convolutional Neural Networks Through the Lens of Partial Differential EquationsResearch in the Mathematical Sciences (Res. Math. Sci.), 2021
Ido Ben-Yair
Gil Ben Shalom
Moshe Eliasof
Eran Treister
MQ
274
5
0
31 Aug 2021
Designing Rotationally Invariant Neural Networks from PDEs and
  Variational Methods
Designing Rotationally Invariant Neural Networks from PDEs and Variational MethodsResearch in the Mathematical Sciences (Res. Math. Sci.), 2021
Tobias Alt
Karl Schrader
Joachim Weickert
Pascal Peter
M. Augustin
282
4
0
31 Aug 2021
m-RevNet: Deep Reversible Neural Networks with Momentum
Duo Li
Shangqi Gao
232
5
0
12 Aug 2021
Deep Microlocal Reconstruction for Limited-Angle Tomography
Deep Microlocal Reconstruction for Limited-Angle TomographyApplied and Computational Harmonic Analysis (ACHA), 2021
Héctor Andrade-Loarca
Gitta Kutyniok
Ozan Oktem
P. Petersen
146
9
0
12 Aug 2021
Deep Neural Networks and PIDE discretizations
Deep Neural Networks and PIDE discretizationsSIAM Journal on Mathematics of Data Science (SIMODS), 2021
B. Bohn
M. Griebel
D. Kannan
189
1
0
05 Aug 2021
PDE-GCN: Novel Architectures for Graph Neural Networks Motivated by
  Partial Differential Equations
PDE-GCN: Novel Architectures for Graph Neural Networks Motivated by Partial Differential EquationsNeural Information Processing Systems (NeurIPS), 2021
Moshe Eliasof
E. Haber
Eran Treister
GNNAI4CE
311
149
0
04 Aug 2021
Connections between Numerical Algorithms for PDEs and Neural Networks
Connections between Numerical Algorithms for PDEs and Neural NetworksJournal of Mathematical Imaging and Vision (JMIV), 2021
Tobias Alt
Karl Schrader
M. Augustin
Pascal Peter
Joachim Weickert
PINN
264
27
0
30 Jul 2021
Bridging the Gap between Spatial and Spectral Domains: A Unified
  Framework for Graph Neural Networks
Bridging the Gap between Spatial and Spectral Domains: A Unified Framework for Graph Neural NetworksACM Computing Surveys (CSUR), 2021
Zhiqian Chen
Fanglan Chen
Lei Zhang
Taoran Ji
Kaiqun Fu
Bo Pan
Feng Chen
Lingfei Wu
Charu C. Aggarwal
Chang-Tien Lu
670
35
0
21 Jul 2021
Inverse Problem of Nonlinear Schrödinger Equation as Learning of
  Convolutional Neural Network
Inverse Problem of Nonlinear Schrödinger Equation as Learning of Convolutional Neural Network
Yiran Wang
Zhen Li
107
3
0
19 Jul 2021
Data-driven reduced order modeling of environmental hydrodynamics using
  deep autoencoders and neural ODEs
Data-driven reduced order modeling of environmental hydrodynamics using deep autoencoders and neural ODEs
S. Dutta
Peter Rivera-Casillas
Orie M. Cecil
Matthew W. Farthing
E. Perracchione
M. Putti
AI4CE
154
9
0
06 Jul 2021
Cell-average based neural network method for hyperbolic and parabolic
  partial differential equations
Cell-average based neural network method for hyperbolic and parabolic partial differential equations
Changxin Qiu
Jue Yan
151
11
0
02 Jul 2021
Residual Networks as Flows of Velocity Fields for Diffeomorphic Time
  Series Alignment
Residual Networks as Flows of Velocity Fields for Diffeomorphic Time Series Alignment
Niraj Pudasaini
Boulbaba Ben Amor
Xichan Lin
Fan Zhu
Yi Fang
AI4TSMedIm
91
7
0
22 Jun 2021
Stateful ODE-Nets using Basis Function Expansions
Stateful ODE-Nets using Basis Function ExpansionsNeural Information Processing Systems (NeurIPS), 2021
A. Queiruga
N. Benjamin Erichson
Liam Hodgkinson
Michael W. Mahoney
258
18
0
21 Jun 2021
Steerable Partial Differential Operators for Equivariant Neural Networks
Steerable Partial Differential Operators for Equivariant Neural NetworksInternational Conference on Learning Representations (ICLR), 2021
Erik Jenner
Maurice Weiler
280
32
0
18 Jun 2021
Encoding physics to learn reaction-diffusion processes
Encoding physics to learn reaction-diffusion processesNature Machine Intelligence (Nat. Mach. Intell.), 2021
Chengping Rao
Pu Ren
Qi Wang
O. Buyukozturk
Haoqin Sun
Yang Liu
PINNAI4CEDiffM
270
143
0
09 Jun 2021
Hard Encoding of Physics for Learning Spatiotemporal Dynamics
Hard Encoding of Physics for Learning Spatiotemporal Dynamics
Chengping Rao
Hao Sun
Yang Liu
PINNAI4CE
218
16
0
02 May 2021
Neural Ordinary Differential Equations for Data-Driven Reduced Order
  Modeling of Environmental Hydrodynamics
Neural Ordinary Differential Equations for Data-Driven Reduced Order Modeling of Environmental Hydrodynamics
S. Dutta
Peter Rivera-Casillas
Matthew W. Farthing
AI4CE
155
14
0
22 Apr 2021
PDO-eS2CNNs: Partial Differential Operator Based Equivariant Spherical
  CNNs
PDO-eS2CNNs: Partial Differential Operator Based Equivariant Spherical CNNsAAAI Conference on Artificial Intelligence (AAAI), 2021
Zhengyang Shen
Tiancheng Shen
Zhouchen Lin
Jinwen Ma
173
23
0
08 Apr 2021
ODE Transformer: An Ordinary Differential Equation-Inspired Model for
  Neural Machine Translation
ODE Transformer: An Ordinary Differential Equation-Inspired Model for Neural Machine Translation
Bei Li
Quan Du
Tao Zhou
Shuhan Zhou
Xin Zeng
Tong Xiao
Jingbo Zhu
195
24
0
06 Apr 2021
Novel DNNs for Stiff ODEs with Applications to Chemically Reacting Flows
Novel DNNs for Stiff ODEs with Applications to Chemically Reacting Flows
Thomas S. Brown
Harbir Antil
R. Löhner
F. Togashi
Deepanshu Verma
AI4CE
99
18
0
01 Apr 2021
Translating Numerical Concepts for PDEs into Neural Architectures
Translating Numerical Concepts for PDEs into Neural ArchitecturesScale Space and Variational Methods in Computer Vision (SSVM), 2021
Tobias Alt
Pascal Peter
Joachim Weickert
Karl Schrader
146
7
0
29 Mar 2021
Rethinking ResNets: Improved Stacking Strategies With High Order Schemes
Rethinking ResNets: Improved Stacking Strategies With High Order SchemesComplex & Intelligent Systems (CIS), 2021
Zhengbo Luo
Zitang Sun
Weilian Zhou
Zizhang Wu
Sei-ichiro Kamata
198
19
0
28 Mar 2021
JFB: Jacobian-Free Backpropagation for Implicit Networks
JFB: Jacobian-Free Backpropagation for Implicit NetworksAAAI Conference on Artificial Intelligence (AAAI), 2021
Samy Wu Fung
Howard Heaton
Qiuwei Li
Daniel McKenzie
Stanley Osher
W. Yin
FedML
434
112
0
23 Mar 2021
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