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.

---

Table of Contents

• 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

ForcedDiffusion2D_1

ForcedDiffusion2D_2

ForcedDiffusion2D_3

---

---

2D Kolmogorov Flow

We now consider the 2D Navier-Stokes equations in vorticity form for a viscous incompressible fluid.

We first consider the case where all the data samples correspond to the same Reynolds number Re = 20, but with different initial states

Kolmogorov_Re20_Ex1

Kolmogorov_Re20_Ex2

Next, we consider the same dataset but only use the first half of the low-resolution simulationas input of the branch network.

Kolmogorov_Re20_Partial_Ex1

Kolmogorov_Re20_Partial_Ex2

Finally, we consider the case where each data samples corresponds to a different Reynolds number in [200,500] with a different initial state

Kolmogorov_MixedRe_Ex1

Kolmogorov_MixedRe_Ex2

Kolmogorov_MixedRe_Ex3