Fetching the paper…
Reading the bibliography…
Stochastic partial differential equations (SPDEs) are the mathematical tool of choice for modelling spatiotemporal PDE-dynamics under the influence of randomness.
Vi. on the general theory integration
William Henry Young · 1905
Earlier work this paper cites.
An algorithm for the machine calculation of complex fourier series
James W Cooley and John W Tukey · 1965
Earlier work this paper cites.
Multiple fourier series and fourier integrals
Sh A Alimov, RR Ashurov, and AK Pulatov · 1992
Earlier work this paper cites.
The DFT: an owner’s manual for the discrete Fourier transform
William L Briggs and Van Emden Henson · 1995
Earlier work this paper cites.
Universal approximation to nonlinear operators by neural networks with arbitrary activation functions and its application to dynamical systems
Tianping Chen and Hong Chen · 1995
Earlier work this paper cites.
Stochastic partial differential equations
Helge Holden, Bernt Øksendal, Jan Ubøe, and Tusheng Zhang · 1996
Earlier work this paper cites.
Wong-zakai approximations for stochastic differential equations
Krystyna Twardowska · 1996
Earlier work this paper cites.
Differential equations driven by rough signals
Terry J Lyons · 1998
Earlier work this paper cites.
Neural operator: Graph kernel network for partial differential equations
Zongyi Li, Nikola Kovachki, Kamyar Azizzadenesheli, Burigede Liu, Kaushik Bhattacharya, Andrew Stuart, and Anima Anandkumar · 2003
Earlier work this paper cites.
Controlling rough paths
Massimiliano Gubinelli · 2004
Earlier work this paper cites.
Stochastic navier–stokes equations for turbulent flows
Remigijus Mikulevicius and Boris L Rozovskii · 2004
Earlier work this paper cites.
An introduction to stochastic pdes
Martin Hairer · 2009
Cited alongside, same era.
Solitary waves theory
Abdul-Majid Wazwaz · 2009
Cited alongside, same era.
Infinite-dimensional dynamical systems in mechanics and physics , volume 68
Roger Temam · 2012
Cited alongside, same era.
Solving the kpz equation
Martin Hairer · 2013
Cited alongside, same era.
A theory of regularity structures
Martin Hairer · 2014
Cited alongside, same era.
An introduction to computational stochastic PDEs , volume 50
Gabriel J Lord, Catherine E Powell, and Tony Shardlow · 2014
Cited alongside, same era.
A course on rough paths
Peter K Friz and Martin Hairer · 2020
Later among the works it cites.
Neural controlled differential equations for irregular time series
Patrick Kidger, James Morrill, James Foster, and Terry Lyons · 2020
Later among the works it cites.
Policy analysis using synthetic controls in continuous-time
Alexis Bellot and Mihaela Van Der Schaar · 2021
Closest in time.
Feature engineering with regularity structures
Ilya Chevyrev, Andris Gerasimovics, and Hendrik Weber · 2021
Closest in time.
Neural operator: Learning maps between function spaces
Nikola Kovachki, Zongyi Li, Burigede Liu, Kamyar Azizzadenesheli, Kaushik Bhattacharya, Andrew Stuart, and Anima Anandkumar · 2021
Closest in time.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Martin Hairer and Étienne Pardoux · 2015
Cited alongside, same era.
A proposal on machine learning via dynamical systems
E Weinan · 2017
Cited alongside, same era.
Neural ordinary differential equations
Ricky TQ Chen, Yulia Rubanova, Jesse Bettencourt, and David Duvenaud · 2018
Cited alongside, same era.
Deep equilibrium models
Shaojie Bai, J Zico Kolter, and Vladlen Koltun · 2019
Cited alongside, same era.
Neural sde: Stabilizing neural ode networks with stochastic noise
Xuanqing Liu, Tesi Xiao, Si Si, Qin Cao, Sanjiv Kumar, and Cho-Jui Hsieh · 2019
Cited alongside, same era.
Efficient and accurate gradients for neural sdes
Patrick Kidger, James Foster, Xuechen Li, and Terry Lyons
Cited in the paper.
Learning nonlinear operators via deeponet based on the universal approximation theorem of operators
Lu Lu, Pengzhan Jin, Guofei Pang, Zhongqiang Zhang, and George Em Karniadakis · 2021
Closest in time.
Neural rough differential equations for long time series
James Morrill, Cristopher Salvi, Patrick Kidger, and James Foster · 2021
Closest in time.
The signature kernel is the solution of a goursat pde
Cristopher Salvi, Thomas Cass, James Foster, Terry Lyons, and Weixin Yang · 2021
Closest in time.
Neural operator with regularity structure for modeling dynamics driven by spdes
Peiyan Hu, Qi Meng, Bingguang Chen, Shiqi Gong, Yue Wang, Wei Chen, Rongchan Zhu, Zhi-Ming Ma, and Tie-Yan Liu · 2022
Closest in time.
On neural differential equations
Patrick Kidger · 2022
Closest in time.
A comprehensive and fair comparison of two neural operators (with practical extensions) based on fair data
Lu Lu, Xuhui Meng, Shengze Cai, Zhiping Mao, Somdatta Goswami, Zhongqiang Zhang, and George Em Karniadakis · 2022
Closest in time.