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Approximation of Solution Operators for High-dimensional PDEs
Using the computational technique of neural ordinary differential equation, we learn the control over the parameter space such that from any initial starting point, the controlled trajectories closely approximate the solutions to the PDE.
Neural Control of Parametric Solutions for High-dimensional Evolution PDEs
Numerical experiments on different high-dimensional evolution PDEs with various initial conditions demonstrate the promising results of the proposed method.
Lyapunov-Net: A Deep Neural Network Architecture for Lyapunov Function Approximation
We develop a versatile deep neural network architecture, called Lyapunov-Net, to approximate Lyapunov functions of dynamical systems in high dimensions.
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