NeuralPDE.jl is a solver package which consists of neural network solvers for partial differential equations using scientific machine learning (SciML) techniques such as physics-informed neural networks (PINNs) and deep BSDE solvers. This package utilizes deep neural networks and neural stochastic differential equations to solve high-dimensional PDEs at a greatly reduced cost and greatly increased generality compared with classical methods.

References in zbMATH (referenced in 33 articles )

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  1. Antoñana, Mikel; Chartier, Philippe; Murua, Ander: Majorant series for the (N)-body problem (2022)
  2. Zhang, Hong; Constantinescu, Emil M.; Smith, Barry F.: \textttPETScTSAdjoint: a discrete adjoint ODE solver for first-order and second-order sensitivity analysis (2022)
  3. Alvestad, Daniel; Larsen, Rasmus; Rothkopf, Alexander: Stable solvers for real-time complex Langevin (2021)
  4. Browning, Alexander P.; Maclaren, Oliver J.; Buenzli, Pascal R.; Lanaro, Matthew; Allenby, Mark C.; Woodruff, Maria A.; Simpson, Matthew J.: Model-based data analysis of tissue growth in thin 3D printed scaffolds (2021)
  5. Cancès, Eric; Fermanian Kammerer, Clotilde; Levitt, Antoine; Siraj-Dine, Sami: Coherent electronic transport in periodic crystals (2021)
  6. Han Veiga, Maria; Öffner, Philipp; Torlo, Davide: DeC and ADER: similarities, differences and a unified framework (2021)
  7. Hegedűs, Ferenc: Program package MPGOS: challenges and solutions during the integration of a large number of independent ODE systems using GPUs (2021)
  8. Kulyabov, D. S.; Korol’kova, A. V.: Computer algebra in Julia (2021)
  9. Lindner, Michael; Lincoln, Lucas; Drauschke, Fenja; Koulen, Julia M.; Würfel, Hans; Plietzsch, Anton; Hellmann, Frank: NetworkDynamics.jl -- composing and simulating complex networks in Julia (2021)
  10. López, Oscar; Oleaga, Gerardo; Sánchez, Alejandra: Markov-modulated jump-diffusion models for the short rate: pricing of zero coupon bonds and convexity adjustment (2021)
  11. Ranocha, Hendrik; de Luna, Manuel Quezada; Ketcheson, David I.: On the rate of error growth in time for numerical solutions of nonlinear dispersive wave equations (2021)
  12. Ranocha, Hendrik; Mitsotakis, Dimitrios; Ketcheson, David I.: A broad class of conservative numerical methods for dispersive wave equations (2021)
  13. Roesch, Elisabeth; Rackauckas, Christopher; Stumpf, Michael P. H.: Collocation based training of neural ordinary differential equations (2021)
  14. Sinha, Nirvik; Heckman, C. J.; Yang, Yuan: Slowly activating outward membrane currents generate input-output sub-harmonic cross frequency coupling in neurons (2021)
  15. Snyder, Jordan; Callaham, Jared L.; Brunton, Steven L.; Kutz, J. Nathan: Data-driven stochastic modeling of coarse-grained dynamics with finite-size effects using Langevin regression (2021)
  16. Week, Bob; Nuismer, Scott L.; Harmon, Luke J.; Krone, Stephen M.: A white noise approach to evolutionary ecology (2021)
  17. Wei Peng, Jun Zhang, Weien Zhou, Xiaoyu Zhao, Wen Yao, Xiaoqian Chen: IDRLnet: A Physics-Informed Neural Network Library (2021) arXiv
  18. Antoñana, Mikel; Chartier, Philippe; Makazaga, Joseba; Murua, Ander: Global time-renormalization of the gravitational (N)-body problem (2020)
  19. Bakir, Toufik; Bonnard, Bernard; Bourdin, Loïc; Rouot, Jérémy: Pontryagin-type conditions for optimal muscular force response to functional electrical stimulations (2020)
  20. Haller, George; Karrasch, Daniel; Kogelbauer, Florian: Barriers to the transport of diffusive scalars in compressible flows (2020)

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