Fetching the paper…
Reading the bibliography…
We present a novel class of approximations for variational losses, being applicable for the training of physics-informed neural nets (PINNs).
The Stone-Weierstrass Theorem
De Branges, L · 1959
Earlier work this paper cites.
Approximate calculation of multiple integrals: Prentice-Hall series in automatic computation
Stroud, A · 1971
Earlier work this paper cites.
Introductory Quantum Mechanics
Liboff, R. L · 1980
Earlier work this paper cites.
Spectral methods
Bernardi, C. and Maday, Y · 1997
Earlier work this paper cites.
Partial Differential Equations
Jost, J · 2002
Earlier work this paper cites.
Sobolev spaces , volume 140
Adams, R. A. and Fournier, J. J · 2003
Earlier work this paper cites.
Theory and practice of finite elements , volume 159
Ern, A. and Guermond, J.-L · 2004
Earlier work this paper cites.
Spectral methods: fundamentals in single domains
Canuto, C., Hussaini, M. Y., Quarteroni, A., and Zang, T. A · 2007
Earlier work this paper cites.
Finite difference methods for ordinary and partial differential equations: steady-state and time-dependent problems
LeVeque, R. J · 2007
Earlier work this paper cites.
Meshfree particle methods
Li, S. and Liu, W. K · 2007
Earlier work this paper cites.
Neural network learning: Theoretical foundations
Anthony, M. and Bartlett, P. L · 2009
Earlier work this paper cites.
Functional analysis, Sobolev spaces and partial differential equations , volume 2
Brezis, H · 2011
Cited alongside, same era.
Secrest. d.(1966). Gaussian quadrature formulas, 2011
Stroud, A · 2011
Cited alongside, same era.
Adam: A method for stochastic optimization
Kingma, D. P. and Ba, J · 2014
Cited alongside, same era.
Deep learning
Goodfellow, I., Bengio, Y., and Courville, A · 2016
Cited alongside, same era.
Wasserstein generative adversarial networks
Arjovsky, M., Chintala, S., and Bottou, L · 2017
Cited alongside, same era.
A quadratic-time algorithm for general multivariate polynomial interpolation
Hecht, M., Cheeseman, B. L., Hoffmann, K. B., and Sbalzarini, I. F · 2017
Dgm: A deep learning algorithm for solving partial differential equations
Sirignano, J. A. and Spiliopoulos, K · 2018
Later among the works it cites.
Variational physics-informed neural networks for solving partial differential equations
Kharazmi, E., Zhang, Z., and Karniadakis, G. E · 2019
Later among the works it cites.
Approximation theory and approximation practice , volume 164
Trefethen, L. N · 2019
Later among the works it cites.
Multivariate interpolation in unisolvent nodes–lifting the curse of dimensionality
Hecht, M., Gonciarz, K., Michelfeit, J., Sivkin, V., and Sbalzarini, I. F · 2020
Later among the works it cites.
hp-vpinns: Variational physics-informed neural networks with domain decomposition
Kharazmi, E., Zhang, Z., and Karniadakis, G. E · 2020
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Cited alongside, same era.
Introduction to quantum mechanics
Griffiths, D. J. and Schroeter, D. F · 2018
Cited alongside, same era.
Fast interpolation and Fourier transform in high-dimensional spaces
Hecht, M. and Sbalzarini, I. F · 2018
Cited alongside, same era.
Multivariate Newton interpolation
Hecht, M., Hoffmann, K. B., Cheeseman, B. L., and Sbalzarini, I. F · 2018
Cited alongside, same era.
Pde-net: Learning pdes from data
Long, Z., Lu, Y., Ma, X., and Dong, B · 2018
Cited alongside, same era.
Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
Raissi, M., Perdikaris, P., and Karniadakis, G · 2018
Cited alongside, same era.
Automatic differentiation in machine learning: a survey
Baydin, A. G., Pearlmutter, B. A., Radul, A. A., and Siskind, J. M
Cited in the paper.
Later among the works it cites.
Physics-informed generative adversarial networks for stochastic differential equations
Yang, L., Zhang, D., and Karniadakis, G. E · 2020
Later among the works it cites.
minterpy
Hernandez Acosta, U., Krishnan Thekke Veettil, S., Wicaksono, D., and Hecht, M · 2021
Later among the works it cites.
Inverse dirichlet weighting enables reliable training of physics informed neural networks
Maddu, S., Sturm, D., Müller, C. L., and Sbalzarini, I. F · 2021
Later among the works it cites.
Understanding and mitigating gradient flow pathologies in physics-informed neural networks
Wang, S., Teng, Y., and Perdikaris, P · 2021
Later among the works it cites.
Sobolev cubature based PDE-learning
Suraz Cardona, J. E · 2022
Closest in time.