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Copy file name to clipboardExpand all lines: README.rst
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@@ -8,14 +8,16 @@ You can use TorchPhysics e.g. to
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- solve ordinary and partial differential equations
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- train a neural network to approximate solutions for different parameters
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- solve inverse problems and interpolate external data
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- learn function operators mapping functional parameters to solutions
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The following approaches are implemented using high-level concepts to make their usage as easy
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as possible:
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- physics-informed neural networks (PINN) [1]_
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- QRes [2]_
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- the Deep Ritz method [3]_
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- DeepONets [4]_ and Physics-Informed DeepONets [5]_
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- Physics-informed neural networks (PINN) [1]_
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- The Deep Ritz method [2]_
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- DeepONets [3]_ and physics-informed DeepONets [4]_
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- Fourier Neural Operators (FNO) [6]_ and physics-informed FNO
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- Model order reduction networks (PCANN) [7]_
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We aim to also include further implementations in the future.
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@@ -50,7 +52,7 @@ Some built-in features are:
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- pre implemented fully connected neural network and easy implementation
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of additional model structures
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- sequentially or parallel evaluation/training of different neural networks
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- normalization layers and adaptive weights [6]_ to speed up the training process
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- normalization layers and adaptive weights [5]_ to speed up the training process
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- powerful and versatile training thanks to `PyTorch Lightning`_
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- many options for optimizers and learning rate control
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Bibliography
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============
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.. [1] Raissi, Perdikaris und Karniadakis, “Physics-informed neuralnetworks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations”, 2019.
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.. [2] Bu and Karpatne, “Quadratic Residual Networks: A New Class of Neural Networks for Solving Forward and Inverse Problems in Physics Involving PDEs”, 2021
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.. [3] E and Yu, "The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problems", 2017
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.. [4] Lu, Jin and Karniadakis, “DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators”, 2020
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.. [5] Wang, Wang and Perdikaris, “Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets”, 2021
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.. [6] McClenny und Braga-Neto, “Self-Adaptive Physics-Informed NeuralNetworks using a Soft Attention Mechanism”, 2020
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.. [2] E and Yu, "The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problems", 2017
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.. [3] Lu, Jin and Karniadakis, “DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators”, 2020
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.. [4] Wang, Wang and Perdikaris, “Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets”, 2021
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.. [5] McClenny und Braga-Neto, “Self-Adaptive Physics-Informed NeuralNetworks using a Soft Attention Mechanism”, 2020
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.. [6] Zong-Yi Li et al., "Fourier Neural Operator for Parametric Partial Differential Equations", 2020
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.. [7] Kaushik Bhattacharya et al., "Model Reduction And Neural Networks For Parametric PDEs", 2021
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