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We introduce Poseidon, a foundation model for learning the solution operators of PDEs.
A study of singularity formation in a vortex sheet with a point vortex approximation
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A second-order projection method for the incompressible Navier-Stokes equations
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Convergence of spectral methods for nonlinear conservation laws
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Universal approximation to nonlinear operators by neural networks with arbitrary activation functions and its application to dynamical systems
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Vorticity and Incompressible Flow
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Burgers’ Equation with Vanishing Hyper-Viscosity
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Partial differential equations
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Automated solution of differential equations by the finite element method: The FEniCS book
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Multi-level Monte Carlo finite volume methods for nonlinear systems of conservation laws in multi-dimensions
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Adam: A method for stochastic optimization
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Well-balanced schemes for the euler equations with gravitation
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Reduced basis methods for partial differential equations: an introduction
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Layer normalization, 2016
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Construction of approximate entropy measure valued solutions for hyperbolic systems of conservation laws
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Geometric comparison of aerofoil shape parameterization methods
D. A. Masters, N. J. Taylor, T. Rendall, C. B. Allen, and D. J. Poole · 2017
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Film: Visual reasoning with a general conditioning layer
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Numerical methods for conservation laws: From analysis to algorithms
J. S. Hesthaven · 2018
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Bayesian deep convolutional encoder–decoder networks for surrogate modeling and uncertainty quantification
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Decoupled weight decay regularization, 2019
I. Loshchilov and F. Hutter · 2019
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Language models are few-shot learners, 2020
T. B. Brown, B. Mann, N. Ryder, M. Subbiah, J. Kaplan, P. Dhariwal, A. Neelakantan, P. Shyam, G. Sastry, A. Askell, S. Agarwal, A. Herbert-Voss, G. Krueger, T. Henighan, R. Child, A. Ramesh, D. M. Ziegler, J. Wu, C. Winter, C. Hesse, M. Chen, E. Sigler, M. Litwin, S. Gray, B. Chess, J. Clark, C. Berner, S. McCandlish, A. Radford, I. Sutskever, and D. Amodei · 2020
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On the convergence of the spectral viscosity method for the two-dimensional incompressible euler equations with rough initial data
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Multipole graph neural operator for parametric partial differential equations
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Architecture and performance of devito, a system for automated stencil computation
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Computation of statistical solutions of hyperbolic systems of conservation laws
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Rt-2: Vision-language-action models transfer web knowledge to robotic control, 2023
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Gaussian error linear units (gelus), 2023
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Transformer for partial differential equations’ operator learning, 2023
Z. Li, K. Meidani, and A. B. Farimani · 2023
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Deep learning observables in computational fluid dynamics
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Learning to Simulate Complex Physics with Graph Networks
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Transformers: State-of-the-Art Natural Language Processing
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Choose a transformer: Fourier or galerkin
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Physics informed machine learning
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Neural operator: Learning maps between function spaces
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Statistical solutions of the incompressible euler equations
S. Lanthaler, S. Mishra, and C. Parés-Pulido · 2021
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Multiple Physics Pretraining for Physical Surrogate Models, Oct. 2023
M. McCabe, B. R.-S. Blancard, L. H. Parker, R. Ohana, M. Cranmer, A. Bietti, M. Eickenberg, S. Golkar, G. Krawezik, F. Lanusse, M. Pettee, T. Tesileanu, K. Cho, and S. Ho · 2023
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4M: Massively Multimodal Masked Modeling, Dec. 2023
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Neural inverse operators for solving pde inverse problems, 2023
R. Molinaro, Y. Yang, B. Engquist, and S. Mishra · 2023
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Climax: A foundation model for weather and climate, 2023
T. Nguyen, J. Brandstetter, A. Kapoor, J. K. Gupta, and A. Grover · 2023
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Convolutional Neural Operators for robust and accurate learning of PDEs, Dec. 2023
B. Raonić, R. Molinaro, T. De Ryck, T. Rohner, F. Bartolucci, R. Alaifari, S. Mishra, and E. de Bézenac · 2023
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Universal cell embeddings: A foundation model for cell biology
Y. Rosen, Y. Roohani, A. Agarwal, L. Samotorcan, S. R. Quake, and J. Leskovec · 2023
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PDEBENCH: An Extensive Benchmark for Scientific Machine Learning, Mar. 2023
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Llama: Open and efficient foundation language models, 2023
H. Touvron, T. Lavril, G. Izacard, X. Martinet, M.-A. Lachaux, T. Lacroix, B. Rozière, N. Goyal, E. Hambro, F. Azhar, A. Rodriguez, A. Joulin, E. Grave, and G. Lample · 2023
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In-context operator learning with data prompts for differential equation problems
L. Yang, S. Liu, T. Meng, and S. J. Osher · 2023
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Universal physics transformers: A framework for efficiently scaling neural operators, 2024
B. Alkin, A. Fürst, S. Schmid, L. Gruber, M. Holzleitner, and J. Brandstetter · 2024
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