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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
Riemannian Residual Neural Networks
Riemannian Residual Neural Networks
Isay Katsman
Eric Chen
Sidhanth Holalkere
Anna Asch
Aaron Lou
Ser-Nam Lim
Christopher De Sa
251
21
0
16 Oct 2023
Physics-aware Machine Learning Revolutionizes Scientific Paradigm for
  Machine Learning and Process-based Hydrology
Physics-aware Machine Learning Revolutionizes Scientific Paradigm for Machine Learning and Process-based Hydrology
Qingsong Xu
Yilei Shi
Jonathan Bamber
Ye Tuo
Ralf Ludwig
Xiao Xiang Zhu
AI4CE
870
19
0
08 Oct 2023
A Spectral Approach for Learning Spatiotemporal Neural Differential
  Equations
A Spectral Approach for Learning Spatiotemporal Neural Differential Equations
Mingtao Xia
Xiangting Li
Qijing Shen
Tom Chou
158
0
0
28 Sep 2023
Deep Learning in Deterministic Computational Mechanics
Deep Learning in Deterministic Computational Mechanics
L. Herrmann
Stefan Kollmannsberger
AI4CEPINN
313
1
0
27 Sep 2023
OS-net: Orbitally Stable Neural Networks
OS-net: Orbitally Stable Neural Networks
M. Ngom
Carlo Graziani
132
0
0
26 Sep 2023
Anisotropic Diffusion Stencils: From Simple Derivations over Stability
  Estimates to ResNet Implementations
Anisotropic Diffusion Stencils: From Simple Derivations over Stability Estimates to ResNet Implementations
Karl Schrader
Joachim Weickert
Michael Krause
DiffM
185
0
0
11 Sep 2023
Separable Hamiltonian Neural Networks
Separable Hamiltonian Neural Networks
Zi-Yu Khoo
Dawen Wu
Jonathan Sze Choong Low
Stéphane Bressan
322
2
0
03 Sep 2023
A Novel Convolutional Neural Network Architecture with a Continuous
  Symmetry
A Novel Convolutional Neural Network Architecture with a Continuous SymmetryCAAI International Conference on Artificial Intelligence (ICCAI), 2023
Y. Liu
Han-Juan Shao
Bing Bai
AI4CE
337
3
0
03 Aug 2023
Feature Transportation Improves Graph Neural Networks
Feature Transportation Improves Graph Neural NetworksAAAI Conference on Artificial Intelligence (AAAI), 2023
Moshe Eliasof
E. Haber
Eran Treister
GNN
277
21
0
29 Jul 2023
PottsMGNet: A Mathematical Explanation of Encoder-Decoder Based Neural
  Networks
PottsMGNet: A Mathematical Explanation of Encoder-Decoder Based Neural NetworksSIAM Journal of Imaging Sciences (JSIS), 2023
X. Tai
Hao Liu
Raymond H. F. Chan
378
19
0
18 Jul 2023
Inverse Evolution Layers: Physics-informed Regularizers for Deep Neural
  Networks
Inverse Evolution Layers: Physics-informed Regularizers for Deep Neural Networks
Chao Liu
Zhonghua Qiao
Chong Li
Carola-Bibiane Schönlieb
224
0
0
14 Jul 2023
Multigrid-Augmented Deep Learning Preconditioners for the Helmholtz
  Equation using Compact Implicit Layers
Multigrid-Augmented Deep Learning Preconditioners for the Helmholtz Equation using Compact Implicit LayersSIAM Journal on Scientific Computing (SISC), 2023
Bar Lerer
Ido Ben-Yair
Eran Treister
AI4CE
338
7
0
30 Jun 2023
Designing Stable Neural Networks using Convex Analysis and ODEs
Designing Stable Neural Networks using Convex Analysis and ODEs
Ferdia Sherry
E. Celledoni
Matthias Joachim Ehrhardt
Davide Murari
B. Owren
Carola-Bibiane Schönlieb
307
16
0
29 Jun 2023
Time Regularization in Optimal Time Variable Learning
Time Regularization in Optimal Time Variable LearningPamm (PAMM), 2023
Evelyn Herberg
Roland A. Herzog
Frederik Köhne
AI4TSAI4CE
92
1
0
28 Jun 2023
Learning Latent Dynamics via Invariant Decomposition and
  (Spatio-)Temporal Transformers
Learning Latent Dynamics via Invariant Decomposition and (Spatio-)Temporal Transformers
Kai Lagemann
C. Lagemann
Swarnava Mukherjee
271
2
0
21 Jun 2023
A Note on Dimensionality Reduction in Deep Neural Networks using
  Empirical Interpolation Method
A Note on Dimensionality Reduction in Deep Neural Networks using Empirical Interpolation Method
Harbir Antil
Madhu Gupta
Randy Price
119
2
0
16 May 2023
Analysis of Numerical Integration in RNN-Based Residuals for Fault
  Diagnosis of Dynamic Systems
Analysis of Numerical Integration in RNN-Based Residuals for Fault Diagnosis of Dynamic SystemsIFAC-PapersOnLine (IFAC-PapersOnLine), 2023
Arman Mohammadi
Theodor Westny
Daniel E. Jung
Mattias Krysander
182
9
0
08 May 2023
Predictions Based on Pixel Data: Insights from PDEs and Finite
  Differences
Predictions Based on Pixel Data: Insights from PDEs and Finite DifferencesJournal of Computational Physics (JCP), 2023
E. Celledoni
James Jackaman
Davide Murari
B. Owren
324
2
0
01 May 2023
Pseudo-Hamiltonian neural networks for learning partial differential
  equations
Pseudo-Hamiltonian neural networks for learning partial differential equationsJournal of Computational Physics (JCP), 2023
Sølve Eidnes
K. Lye
368
13
0
27 Apr 2023
Neural Delay Differential Equations: System Reconstruction and Image
  Classification
Neural Delay Differential Equations: System Reconstruction and Image ClassificationInternational Conference on Learning Representations (ICLR), 2021
Qunxi Zhu
Yao Guo
Wei Lin
174
39
0
11 Apr 2023
DRIP: Deep Regularizers for Inverse Problems
DRIP: Deep Regularizers for Inverse ProblemsInverse Problems (IP), 2023
Moshe Eliasof
E. Haber
Eran Treister
345
9
0
30 Mar 2023
GNN-based physics solver for time-independent PDEs
GNN-based physics solver for time-independent PDEs
R. J. Gladstone
H. Rahmani
V. Suryakumar
Hadi Meidani
M. DÉlia
A. Zareei
AI4CE
147
17
0
28 Mar 2023
Multilevel Diffusion: Infinite Dimensional Score-Based Diffusion Models
  for Image Generation
Multilevel Diffusion: Infinite Dimensional Score-Based Diffusion Models for Image Generation
Paul Hagemann
Sophie Mildenberger
Lars Ruthotto
Gabriele Steidl
Ni Yang
DiffM
440
32
0
08 Mar 2023
Learning Hamiltonian Systems with Mono-Implicit Runge-Kutta Methods
Learning Hamiltonian Systems with Mono-Implicit Runge-Kutta MethodsInternational Conference on Geometric Science of Information (GSI), 2023
Haakon Noren
192
3
0
07 Mar 2023
Efficiency 360: Efficient Vision Transformers
Efficiency 360: Efficient Vision Transformers
Badri N. Patro
Vijay Srinivas Agneeswaran
406
7
0
16 Feb 2023
CQnet: convex-geometric interpretation and constraining neural-network
  trajectories
CQnet: convex-geometric interpretation and constraining neural-network trajectories
Bas Peters
251
0
0
09 Feb 2023
Learning PDE Solution Operator for Continuous Modeling of Time-Series
Learning PDE Solution Operator for Continuous Modeling of Time-Series
Yesom Park
Jaemoo Choi
Changyeon Yoon
Changhoon Song
Myung-joo Kang
AI4TSAI4CE
189
3
0
02 Feb 2023
Modelling Long Range Dependencies in $N$D: From Task-Specific to a
  General Purpose CNN
Modelling Long Range Dependencies in NNND: From Task-Specific to a General Purpose CNNInternational Conference on Learning Representations (ICLR), 2023
David M. Knigge
David W. Romero
Albert Gu
E. Gavves
Erik J. Bekkers
Jakub M. Tomczak
Mark Hoogendoorn
Jan-Jakob Sonke
3DV
214
28
0
25 Jan 2023
Improved generalization with deep neural operators for engineering
  systems: Path towards digital twin
Improved generalization with deep neural operators for engineering systems: Path towards digital twinEngineering applications of artificial intelligence (Eng. Appl. Artif. Intell.), 2023
Kazuma Kobayashi
James Daniell
S. B. Alam
AI4CE
252
41
0
17 Jan 2023
Continuous Depth Recurrent Neural Differential Equations
Continuous Depth Recurrent Neural Differential Equations
Srinivas Anumasa
Geetakrishnasai Gunapati
P. K. Srijith
AI4TS
146
1
0
28 Dec 2022
Deep Learning Methods for Partial Differential Equations and Related
  Parameter Identification Problems
Deep Learning Methods for Partial Differential Equations and Related Parameter Identification ProblemsInverse Problems (IP), 2022
Derick Nganyu Tanyu
Jianfeng Ning
Tom Freudenberg
Nick Heilenkötter
A. Rademacher
U. Iben
Peter Maass
AI4CE
276
57
0
06 Dec 2022
Moving Frame Net: SE(3)-Equivariant Network for Volumes
Moving Frame Net: SE(3)-Equivariant Network for Volumes
Mateus Sangalli
S. Blusseau
Santiago Velasco-Forero
Jesús Angulo
228
8
0
07 Nov 2022
FO-PINNs: A First-Order formulation for Physics Informed Neural Networks
FO-PINNs: A First-Order formulation for Physics Informed Neural Networks
R. J. Gladstone
M. A. Nabian
N. Sukumar
Ankit Srivastava
Hadi Meidani
PINNAI4CE
148
0
0
25 Oct 2022
PDEBENCH: An Extensive Benchmark for Scientific Machine Learning
PDEBENCH: An Extensive Benchmark for Scientific Machine LearningNeural Information Processing Systems (NeurIPS), 2022
M. Takamoto
T. Praditia
Raphael Leiteritz
Dan MacKinlay
Francesco Alesiani
Dirk Pflüger
Mathias Niepert
AI4CE
615
333
0
13 Oct 2022
Dynamical systems' based neural networks
Dynamical systems' based neural networks
E. Celledoni
Davide Murari
B. Owren
Carola-Bibiane Schönlieb
Ferdia Sherry
OOD
336
13
0
05 Oct 2022
Neural Generalized Ordinary Differential Equations with Layer-varying
  Parameters
Neural Generalized Ordinary Differential Equations with Layer-varying ParametersJournal of Data Science (JDS), 2022
Duo Yu
Hongyu Miao
Hulin Wu
175
5
0
21 Sep 2022
STDEN: Towards Physics-Guided Neural Networks for Traffic Flow
  Prediction
STDEN: Towards Physics-Guided Neural Networks for Traffic Flow PredictionAAAI Conference on Artificial Intelligence (AAAI), 2022
Jiahao Ji
Jingyuan Wang
Zhe Jiang
Jiawei Jiang
Hu Zhang
DiffMPINNOODAI4CE
292
99
0
01 Sep 2022
Estimating a potential without the agony of the partition function
Estimating a potential without the agony of the partition functionSIAM Journal on Mathematics of Data Science (SIMODS), 2022
E. Haber
Moshe Eliasof
L. Tenorio
272
2
0
19 Aug 2022
Physics-Informed Deep Neural Operator Networks
Physics-Informed Deep Neural Operator Networks
S. Goswami
Aniruddha Bora
Yue Yu
George Karniadakis
PINNAI4CE
309
156
0
08 Jul 2022
Zero Stability Well Predicts Performance of Convolutional Neural
  Networks
Zero Stability Well Predicts Performance of Convolutional Neural NetworksAAAI Conference on Artificial Intelligence (AAAI), 2022
Liangming Chen
Long Jin
Mingsheng Shang
MLT
258
8
0
27 Jun 2022
Learning the parameters of a differential equation from its trajectory
  via the adjoint equation
Learning the parameters of a differential equation from its trajectory via the adjoint equationSocial Science Research Network (SSRN), 2022
I. Fekete
A. Molnár
P. Simon
55
0
0
17 Jun 2022
On the balance between the training time and interpretability of neural
  ODE for time series modelling
On the balance between the training time and interpretability of neural ODE for time series modelling
Yakov Golovanev
A. Hvatov
AI4TS
158
2
0
07 Jun 2022
A PDE-based Explanation of Extreme Numerical Sensitivities and Edge of
  Stability in Training Neural Networks
A PDE-based Explanation of Extreme Numerical Sensitivities and Edge of Stability in Training Neural NetworksJournal of machine learning research (JMLR), 2022
Yuxin Sun
Dong Lao
G. Sundaramoorthi
A. Yezzi
419
2
0
04 Jun 2022
A memory-efficient neural ODE framework based on high-level adjoint
  differentiation
A memory-efficient neural ODE framework based on high-level adjoint differentiationIEEE Transactions on Artificial Intelligence (IEEE TAI), 2022
Hong Zhang
Wenjun Zhao
238
6
0
02 Jun 2022
Bayesian Learning to Discover Mathematical Operations in Governing
  Equations of Dynamic Systems
Bayesian Learning to Discover Mathematical Operations in Governing Equations of Dynamic Systems
Hongpeng Zhou
W. Pan
149
6
0
01 Jun 2022
Do Residual Neural Networks discretize Neural Ordinary Differential
  Equations?
Do Residual Neural Networks discretize Neural Ordinary Differential Equations?Neural Information Processing Systems (NeurIPS), 2022
Michael E. Sander
Pierre Ablin
Gabriel Peyré
274
34
0
29 May 2022
Multi-resolution partial differential equations preserved learning
  framework for spatiotemporal dynamics
Multi-resolution partial differential equations preserved learning framework for spatiotemporal dynamicsCommunications Physics (Commun. Phys.), 2022
Xin-Yang Liu
Min Zhu
Lu Lu
Hao Sun
Jian-Xun Wang
PINNAI4CE
254
72
0
09 May 2022
An Optimal Time Variable Learning Framework for Deep Neural Networks
An Optimal Time Variable Learning Framework for Deep Neural NetworksAnnals of Mathematical Sciences and Applications (AMSA), 2022
Harbir Antil
Hugo Díaz
Evelyn Herberg
119
4
0
18 Apr 2022
Learning time-dependent PDE solver using Message Passing Graph Neural
  Networks
Learning time-dependent PDE solver using Message Passing Graph Neural Networks
Pourya Pilva
A. Zareei
AI4CE
145
11
0
15 Apr 2022
ODE Transformer: An Ordinary Differential Equation-Inspired Model for
  Sequence Generation
ODE Transformer: An Ordinary Differential Equation-Inspired Model for Sequence GenerationAnnual Meeting of the Association for Computational Linguistics (ACL), 2022
Bei Li
Quan Du
Tao Zhou
Yi Jing
Shuhan Zhou
Xin Zeng
Tong Xiao
JingBo Zhu
Xuebo Liu
Min Zhang
201
41
0
17 Mar 2022
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