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FiniteNet: A Fully Convolutional LSTM Network Architecture for Time-Dependent Partial Differential Equations
In this work, we present a machine learning approach for reducing the er...
02/07/2020 ∙ by Ben Stevens, et al. ∙
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Reduced operator inference for nonlinear partial differential equations
We present a new scientific machine learning method that learns from dat...
01/29/2021 ∙ by Elizabeth Qian, et al. ∙
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Learning emergent PDEs in a learned emergent space
We extract data-driven, intrinsic spatial coordinates from observations ...
12/23/2020 ∙ by Felix P. Kemeth, et al. ∙
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PDE-Net: Learning PDEs from Data
In this paper, we present an initial attempt to learn evolution PDEs fro...
10/26/2017 ∙ by Zichao Long, et al. ∙
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Data-driven discovery of PDEs in complex datasets
Many processes in science and engineering can be described by partial di...
08/31/2018 ∙ by Jens Berg, et al. ∙
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Anomaly detection and classification for streaming data using PDEs
Nondominated sorting, also called Pareto Depth Analysis (PDA), is widely...
08/15/2016 ∙ by Bilal Abbasi, et al. ∙
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Computing Derivatives for PETSc Adjoint Solvers using Algorithmic Differentiation
Most nonlinear partial differential equation (PDE) solvers require the J...
09/06/2019 ∙ by J. G. Wallwork, et al. ∙
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Neural Time-Dependent Partial Differential Equation
09/08/2020 ∙ by Yihao Hu, et al. ∙
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Partial differential equations (PDEs) play a crucial role in studying a vast number of problems in science and engineering. Numerically solving nonlinear and/or high-dimensional PDEs is often a challenging task. Inspired by the traditional finite difference and finite elements methods and emerging advancements in machine learning, we propose a sequence deep learning framework called Neural-PDE, which allows to automatically learn governing rules of any time-dependent PDE system from existing data by using a bidirectional LSTM encoder, and predict the next n time steps data. One critical feature of our proposed framework is that the Neural-PDE is able to simultaneously learn and simulate the multiscale variables.We test the Neural-PDE by a range of examples from one-dimensional PDEs to a high-dimensional and nonlinear complex fluids model. The results show that the Neural-PDE is capable of learning the initial conditions, boundary conditions and differential operators without the knowledge of the specific form of a PDE system.In our experiments the Neural-PDE can efficiently extract the dynamics within 20 epochs training, and produces accurate predictions. Furthermore, unlike the traditional machine learning approaches in learning PDE such as CNN and MLP which require vast parameters for model precision, Neural-PDE shares parameters across all time steps, thus considerably reduces the computational complexity and leads to a fast learning algorithm.
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