SROpNet - An Operator Learning Framework for Spatiotemporal Super-Resolution of Scientific Simulations

Authors: Valentin Duruisseaux and Amit Chakraborty

This repository provides animated versions of the results presented in our paper

An Operator Learning Framework for Spatiotemporal Super-Resolution of Scientific Simulations.
Valentin Duruisseaux and Amit Chakraborty, 2023.

1D Diffusion with Parametric Forcing
1D Diffusion with Forcing and Varied Initial Conditions
1D Diffusion with Parametric Forcing and Varied Sensor and Prediction Locations
2D Diffusion with Fixed Diffusion Constant
2D Diffusion with Varied Diffusion Constant
2D Forced Diffusion
2D Kolmogorov Flow

1D Diffusion with Parametric Forcing

Here, each data sample corresponds to a solution to a Forced 1D Diffusion equation with a different forcing term.

1D_Diffusion_Varied_Forcing/Diff1D_Exp1.png

1D Diffusion with Forcing and Varied Initial Conditions

Here, each data sample corresponds to a solution to a Forced 1D Diffusion equation with a different initial state. We learn the dynamics with different SROpNets, using different existing super-resolution approaches as part of architecture.

1D Diffusion with Parametric Forcing and Varied Sensor and Prediction Locations

We now consider a dataset where each data sample corresponds to a solution to the Forced 1D Diffusion equation with a different forcing term. In addition, we sample randomly the locations of the low-resolution sensor locations and high-resolution prediction locations, as shown in the example below

We compare our results with those obtained using cubic interpolation

2D Diffusion with Fixed Diffusion Constant

Here, every data sample corresponds to a solution to the 2D Diffusion equation with the same diffusion constant, but with different initial states

Diffusion2D_Exp1_1

Diffusion2D_Exp1_2

Diffusion2D_Exp1_3

Here is one more example with the low-resolution numerical solution counterpart

Diffusion2D_Exp1_4_LR

Diffusion2D_Exp1_4

2D Diffusion with Varied Diffusion Constant

Here, each data sample corresponds to a solution to the 2D Diffusion equation with a different diffusion constant and a different initial state

Diffusion2D_Speeds_1

Diffusion2D_Speeds_2

Diffusion2D_Speeds_3

We also tested our approach on diffusion dynamics with larger diffusion constants outside the interval of diffusion constants experienced during training. We compare our results against a similar operator learning architecture which only takes the high-resolution initial state and the prediction locations as inputs.

Diffusion2D_Speeds_Compare_1

Diffusion2D_Speeds_Compare_2

Diffusion2D_Speeds_Compare_3

2D Forced Diffusion

Here, each data sample corresponds to a solution to the 2D Forced Diffusion equation with a different diffusion forcing term and a different initial state