Apprentissage et calcul scientifique

B. Després, Numerical methods for Eulerian and Lagrangian conservation laws, (2017) Birkhäuser;

B. Haasdonk and M. Ohlberger, Reduced basis method for finite volume approximations of parametrized linear evolution equations, (2008) ESAIM M2AN 2008;

Kevin Carlberg, Matthew Barone and Harbir Antil, Galerkin v. least-squares Petrov–Galerkin projection in nonlinear model reduction, (2017) Journal of Computational Physics;

S. Chaturantabut, D. C. Sorensen, Nonlinear model reduction via discrete empirical interpolation, (2010) SIAM J. SCI. COMPUT.;

D.B Szyld, The many proofs of an identity on the norm of oblique projections, (2006) Numerical Algorithms.;

N. Kovackhi, Z. Li, B. Liu, K. Azizzadenesheli, K. Bhattacharya, A. Stuart, A. Anandkumar, Neural operator: Learning maps between function spaces, (2021) Arxiv.;

B. Ghojogh, A. Ghodsi, F. Karray, M. Crowley, Locally Linear Embedding and its Variants: Tutorial and Survey, (2020) Arxiv.;

J. Wang, Geometric Structure of High-Dimensional Data and Dimensionality Reduction, (20??) ??;

Shady E. Ahmed, S. Pawar, O. San, Adil Rasheed, T. Iliescu, Bernd R. Noack,, On closures for reduced order models { A spectrum of  rst-principle to machine-learned avenues, (2021) Phys. Fluids 33, 091301 (2021);

W. Snyder, C. Mou, H. Liu, O. San, R. De Vita, and T. Iliescu, Reduced Order Model Closures: A Brief Tutorial, (2022) Preprint Arxiv;

M. M. Bronstein, J. Bruna, T. Cohen, P. Velickovic, Geometric deep learning, Grids, Groups, Graph, Geodesic and Gauges, (2021) Arxiv;

S. Mallat, Understanding deepconvolutional networks, (2022) Philosophical transactions A;

K. Lee, K. T.Carlberg, Model reduction of dynamical systems on nonlinear manifolds using deep convolutional autoencoders, (2019) Journal of computational physics;

Y. Kim, Y. Choisy, D. Widemannz, T. Zohdi , A fast and accurate physic informed neural network reduced order model with shallow masked auto-encoder, (2022) Journal of Computational Physics;

L. Cicci, S. Fresca , A. Manzoni, Deep-HyROMnet: A deep learning-based operator approximation for hyper-reduction of nonlinear parametrized PDEs, (2022) Journal of Scientific Computing;

R. T. Q. Chen*, Y. Rubanova, J. Bettencourt, D. Duvenaud, Neural Ordinary Differential Equations, (2018) NeurIPS 2018;

A. Zang, Z. C. Lipton, M. Li, A. Smola, Dive into Deep Learning, (2020) Livre en ligne;

D. Bahdanau, K. Cho, Y. Bengio, Neural machine translation by jointly learning to align and translate, (2015) ICLR 2015;

G. Allaire et A. Ern, Optimisation et contrôle, (2022) Ecole Polytechnique;

Y. Bengio, J. F. Paiement, P. Vincent, O. Delalleau, N. Le Roux and M. Ouimet, Out-of-Sample Extensions for LLE, Isomap, MDS, Eigenmaps, and Spectral Clustering, (2003) NIPS 2003;

Ameya D. Jagtapa, G. E. Karniadakisa, Adaptive activation functions accelerate convergence in deep and physics-informed neural networks, (2020) Arxiv;

A. Krishnapriyan , A. Gholami, S. Zhe, R. M. Kirby, M. W. Mahoney, Characterizing possible failure modes in physics-informed neural networks, (2021) Arxiv;

S. Wang, S. SanKaran, P. Perdikaris, CRESPECTING CAUSALITY IS ALL YOU NEED FOR TRAINING PHYSICS-INFORMED NEURAL NETWORKS, (2021) Arxiv;

Peter J. Baddoo, Benjamin Herrmann, Beverley J. McKeon, J. Nathan Kutz, Steven L. Brunton, Physics-informed dynamic mode decomposition (piDMD), (2021) Arxiv;

M. H. Saadat, B. Gjorgiev, L. Das and G. Sansavini, Neural tangent kernel analysis of PINN for advection-diffusion equation, (2022) Arxiv;

Sean P. Carney, Arnav Gangal, Luis Kim, Physics informed neural networks for elliptic equations with oscillatory differential operators, (2022) Arxiv;

Sifan Wanga, Xinling Yua, Paris Perdikaris, When and why PINNs fail to train: A neural tangent kernel perspective, (2022) JCP;

S Fresca, A Manzoni, POD-DL-ROM: enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition, (2022) Computer Methods in Applied Mechanics and Engineering;

Kathleen Champion, Bethany Luschb, J. Nathan Kutza, and Steven L. Brunton, Data-driven discovery of coordinates andgoverning equations, (2019) PNAS;

Ehsan Kharazmi, Zhongqiang Zhang, George Em Karniadakis, hp-VPINNs: Variational Physics-Informed Neural Networks With Domain Decomposition, (2021) ....;

Gengxiang Chen, Xu Liu, Yingguang Li, Qinglu Meng, Lu Chen, Laplace neural operator for complex geometries, (2023) Arxiv;

J. H Seidman, G. Kissas, P.Perdikaris, G. J. Passas, NOMAD: Nonlinear Manifold Decoders for Operator Learning, (2022) Arxiv;

Kaushik Bhattacharya, Bamdad Hosseini, Nikola B. Kovachki, Andrew M. Stuart, Model Reduction And Neural Networks For Parametric PDEs, (2021) SMAI Journal of computational mathematics;

Lu Lu, Pengzhan Jin, Guofei Pang, Zhongqiang Zhang and George Em Karniadakis, Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators, (2021) Nature machine intelligence;

R. Sutton, A. G Barto, Reinforcement Learning: An introduction, (2018) MIT press;

H. V. Hasselt, Double Q learning, (2010) NIPS;