Fetching the paper…
Reading the bibliography…
Simulating physical systems is a core component of scientific computing, encompassing a wide range of physical domains and applications.
Hamiltonian graph networks with ODE integrators
A. Sanchez-Gonzalez, V. Bapst, K. Cranmer, and P. Battaglia · 1909
Earlier work this paper cites.
Geometry from a time series
N. H. Packard, J. P. Crutchfield, J. D. Farmer, and R. S. Shaw · 1980
Earlier work this paper cites.
On the scalar rational interpolation problem
A. C. Antoulas and B. D. O. Anderson · 1986
Earlier work this paper cites.
Equations of motion from a data series
J. P. Crutchfield and B. S. Mcnamara · 1987
Earlier work this paper cites.
Learning with Kernels
B. Schölkopf and A. J. Smola · 1998
Earlier work this paper cites.
Rational approximation of frequency domain responses by vector fitting
B. Gustavsen and A. Semlyen · 1999
Earlier work this paper cites.
An Introduction to Numerical Analysis , chapter Initial Value Problems for ODEs, pages 349–353
E. Süli and D. F. Mayers · 2003
Earlier work this paper cites.
Discovering symbolic models from deep learning with inductive biases
M. Cranmer, A. Sanchez-Gonzalez, P. Battaglia, R. Xu, K. Cranmer, D. Spergel, and S. Ho · 2006
Earlier work this paper cites.
Matplotlib: A 2D graphics environment
J. D. Hunter · 2007
Earlier work this paper cites.
Random features for large-scale kernel machines
A. Rahimi and B. Recht · 2007
Earlier work this paper cites.
Dynamic mode decomposition of numerical and experimental data
P. Schmid and S. J · 2008
Earlier work this paper cites.
Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems
E. Hairer and G. Wanner · 2009
Earlier work this paper cites.
Solving Ordinary Differential Equations I: Nonstiff Problems
E. Hairer, S. P. Nørsett, and G. Wanner · 2009
Earlier work this paper cites.
Learning mesh-based simulation with graph networks
T. Pfaff, M. Fortunato, A. Sanchez-Gonzalez, and P. W. Battaglia · 2010
Earlier work this paper cites.
Dynamic mode decomposition of numerical and experimental data
P. Schmid · 2010
Earlier work this paper cites.
Scikit-learn: Machine learning in Python
F. Pedregosa, G. Varoquaux, A. Gramfort, V. Michel, B. Thirion, O. Grisel, M. Blondel, P. Prettenhofer, R. Weiss, V. Dubourg, J. Vanderplas, A. Passos, D. Cournapeau, M. Brucher, M. Perrot, and E. Duchesnay · 2011
Earlier work this paper cites.
Adam: A method for stochastic optimization
D. P. Kingma and J. Ba · 2014
Earlier work this paper cites.
On dynamic mode decomposition: Theory and applications
J. H. Tu, C. W. Rowley, D. M. Luchtenburg, S. L. Brunton, and J. N. Kutz · 2014
Earlier work this paper cites.
Numba: A LLVM-based Python JIT compiler
S. K. Lam, A. Pitrou, and S. Seibert · 2015
Earlier work this paper cites.
Discovering governing equations from data by sparse identification of nonlinear dynamical systems
S. L. Brunton, J. L. Proctor, and J. N. Kutz · 2016
Cited alongside, same era.
Big data need big theory too
P. V. Coveney, E. R. Dougherty, and R. R. Highfield · 2016
Cited alongside, same era.
Symplectic model reduction of hamiltonian systems
L. Peng and K. Mohseni · 2016
Cited alongside, same era.
Singularity: Scientific containers for mobility of compute
G. M. Kurtzer, V. Sochat, and M. W. Bauer · 2017
Cited alongside, same era.
A deep learning approach to estimate stress distribution: a fast and accurate surrogate of finite-element analysis
L. Liang, M. Liu, C. Martin, and W. Sun · 2017
Cited alongside, same era.
Deep fluids: A generative network for parameterized fluid simulations
B. Kim, V. C. Azevedo, N. Thuerey, T. Kim, M. Gross, and B. Solenthaler · 2019
Later among the works it cites.
Image-based reconstruction for the impact problems by using DPNNs
Y. Li, H. Wang, W. Shuai, H. Zhang, and Y. Peng · 2019
Later among the works it cites.
DeepXDE: A deep learning library for solving differential equations
L. Lu, X. Meng, Z. Mao, and G. E. Karniadakis · 2019
Later among the works it cites.
PyTorch: An imperative style, high-performance deep learning library
A. Paszke, S. Gross, F. Massa, A. Lerer, J. Bradbury, G. Chanan, T. Killeen, Z. Lin, N. Gimelshein, L. Antiga, A. Desmaison, A. Kopf, E. Yang, Z. DeVito, M. Raison, A. Tejani, S. Chilamkurthy, B. Steiner, L. Fang, J. Bai, and S. Chintala · 2019
Later among the works it cites.
Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
M. Raissi, P. Perdikaris, and G. E. Karniadakis · 2017
Cited alongside, same era.
Falkon: An optimal large scale kernel method
A. Rudi, L. Carratino, and L. Rosasco · 2017
Cited alongside, same era.
Learning partial differential equations via data discovery and sparse optimization
H. Schaeffer · 2017
Cited alongside, same era.
Neural relational inference for interacting systems
T. Kipf, E. Fetaya, K.-C. Wang, M. Welling, and R. Zemel · 2018
Cited alongside, same era.
Reconstruction of simulation-based physical field by reconstruction neural network method
Y. Li, H. Wang, K. Mo, and T. Zeng · 2018
Cited alongside, same era.
The AAA algorithm for rational approximation
Y. Nakatsukasa, O. Sète, and L. N. Trefethen · 2018
Cited alongside, same era.
Graph networks as learnable physics engines for inference and control
A. Sanchez-Gonzalez, N. Heess, J. T. Springenberg, J. Merel, M. Riedmiller, R. Hadsell, and P. Battaglia · 2018
Cited alongside, same era.
M. Raissi, P. Perdikaris, and G. E. Karniadakis · 2019
Later among the works it cites.
Interpolatory Methods for Model Reduction
A. C. Antoulas, C. Beattie, and S. Gugercin · 2020
Later among the works it cites.
Symplectic recurrent neural networks
Z. Chen, J. Zhang, M. Arjovsky, and L. Bottou · 2020
Later among the works it cites.
A deep learning framework for solution and discovery in solid mechanics, 2020
E. Haghighat, M. Raissi, A. Moure, H. Gomez, and R. Juanes · 2020
Later among the works it cites.
Array programming with NumPy
C. R. Harris, K. J. Millman, S. J. van der Walt, R. Gommers, P. Virtanen, D. Cournapeau, E. Wieser, J. Taylor, S. Berg, N. J. Smith, R. Kern, M. Picus, S. Hoyer, M. H. van Kerkwijk, M. Brett, A. Haldane, J. F. del R’ıo, M. Wiebe, P. Peterson, P. G’erard-Marchant, K. Sheppard, T. Reddy, W. Weckesser, H. Abbasi, C. Gohlke, and T. E. Oliphant · 2020
Later among the works it cites.
Machine learning in cardiovascular flows modeling: Predicting arterial blood pressure from non-invasive 4D flow MRI data using physics-informed neural networks
G. Kissas, Y. Yang, E. Hwuang, W. R. Witschey, J. A. Detre, and P. Perdikaris · 2020
Later among the works it cites.
A feasibility study of deep learning for predicting hemodynamics of human thoracic aorta
L. Liang, W. Mao, and W. Sun · 2020
Later among the works it cites.
Deep learning over reduced intrinsic domains for efficient mechanics of the left ventricle
G. D. Maso Talou, T. P. Babarenda Gamage, M. Sagar, and M. P. Nash · 2020
Later among the works it cites.
Stress field prediction in cantilevered structures using convolutional neural networks
Z. Nie, H. Jiang, and L. B. Kara · 2020
Later among the works it cites.
Lift & learn: Physics-informed machine learning for large-scale nonlinear dynamical systems
E. Qian, B. Kramer, B. Peherstorfer, and K. Willcox · 2020
Later among the works it cites.
DeepCFD: Efficient steady-state laminar flow approximation with deep convolutional neural networks
M. D. Ribeiro, A. Rehman, S. Ahmed, and A. Dengel · 2020
Later among the works it cites.
Deep learning methods for reynolds-averaged navier–stokes simulations of airfoil flows
N. Thuerey, K. Weißenow, L. Prantl, and X. Hu · 2020
Later among the works it cites.
SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python
P. Virtanen, R. Gommers, T. E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S. J. van der Walt, M. Brett, J. Wilson, K. J. Millman, N. Mayorov, A. R. J. Nelson, E. Jones, R. Kern, E. Larson, C. J. Carey, İ. Polat, Y. Feng, E. W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E. A. Quintero, C. R. Harris, A. M. Archibald, A. H. Ribeiro, F. Pedregosa, P. van Mulbregt, and SciPy 1.0 Contributors · 2020
Later among the works it cites.
The imperative of physics-based modeling and inverse theory in computational science
K. E. Willcox, O. Ghattas, and P. Heimbach · 2021
Closest in time.