SSPDEBench/Reuglar_and_Singular_SPDEBench

Regular_and_Singular_SPDEBench is a benchmark dataset for evaluating machine learning-based approaches to solving stochastic partial differential equations (SPDEs). In the SPDEBench, we generate two classes of the datasets: the nonsingular SPDE datasets and a novel singular SPDE dataset.

The nonsingular SPDE contains:

• Stochastic Ginzburg-Landau equation(Phi41):
• Stochastic Korteweg–De Vries equation(KdV);
• Stochastic wave equation;
• Stochastic Navier-Stokes equation(NS).

The novel singular SPDE contains:

• The dynamical Phi42 model(Phi42).

Each equation's dataset contains 1200 samples, where 70%(840) samples for training, 15%(180) samples for validation and 15%(180) for testing. Each sample includes data of initial condition, driving noise and the spacial grid and the time grid.

For each SPDE, we provide data for different truncation degree (denoted by eps) of driving noise and different type of initial condition (non-fixed initial condition is denoted by u0). For the dynamical Phi42 model, we provide data generated by two different method: with implementing renormalization (denoted by reno) and without implementing renormalization (denoted by expl). For the stochastic Ginzburg-Landau equation, we provide data of different value of additive diffusive term sigma (sigma = 0.1 or sigma = 1). For the KdV equation, we provide data of two different type of diving noise: cylindrical Wiener process (denoted by cyl) and Q-Wiener process (denoted by Q).

The code is available at Github.