Solving hyperbolic conservation laws with characteristic based neural network
Keywords: neural network, hyperbolic conservation laws, characteristics
TL;DR: A new way to solve the hyperbolic conservation laws by characteristic lines
Abstract: Neural network PDE solvers have recently gained popularity.However, it faces difficulty to deal with sharp discontinuity like shock waves in hyperbolic conservation laws.In this paper we propose a characteristic-based neural network to solve one dimension hyperbolic laws.The smooth solution can be derived by equation of characteristic lines ,and shock waves are decided by simple ODE solver.This method achieves a high accuracy with high efficiency. In the future it is hopeful to apply this method to higher dimension problems.
Primary Area: applications to physical sciences (physics, chemistry, biology, etc.)
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Submission Number: 8488
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