Semi-supervised Learning of Partial Differential Operators and Dynamical
Flows
- URL: http://arxiv.org/abs/2207.14366v1
- Date: Thu, 28 Jul 2022 19:59:14 GMT
- Title: Semi-supervised Learning of Partial Differential Operators and Dynamical
Flows
- Authors: Michael Rotman, Amit Dekel, Ran Ilan Ber, Lior Wolf, Yaron Oz
- Abstract summary: We present a novel method that combines a hyper-network solver with a Fourier Neural Operator architecture.
We test our method on various time evolution PDEs, including nonlinear fluid flows in one, two, and three spatial dimensions.
The results show that the new method improves the learning accuracy at the time point of supervision point, and is able to interpolate and the solutions to any intermediate time.
- Score: 68.77595310155365
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: The evolution of dynamical systems is generically governed by nonlinear
partial differential equations (PDEs), whose solution, in a simulation
framework, requires vast amounts of computational resources. In this work, we
present a novel method that combines a hyper-network solver with a Fourier
Neural Operator architecture. Our method treats time and space separately. As a
result, it successfully propagates initial conditions in continuous time steps
by employing the general composition properties of the partial differential
operators. Following previous work, supervision is provided at a specific time
point. We test our method on various time evolution PDEs, including nonlinear
fluid flows in one, two, and three spatial dimensions. The results show that
the new method improves the learning accuracy at the time point of supervision
point, and is able to interpolate and the solutions to any intermediate time.
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