Spline-PINN: Approaching PDEs without Data Using Fast, Physics-Informed Hermite-Spline CNNs
Authors: Nils Wandel, Michael Weinmann, Michael Neidlin, Reinhard Klein8529-8538
AAAI 2022 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We demonstrate the potential of our method at the examples of the incompressible Navier-Stokes equation and the damped wave equation. Our quantitative assessment and an interactive real-time demo show that we are narrowing the gap in accuracy of unsupervised ML based methods to industrial solvers for computational fluid dynamics (CFD) while being orders of magnitude faster. |
| Researcher Affiliation | Academia | 1 University of Bonn 2 Delft University of Technology 3 RWTH Aachen University |
| Pseudocode | No | The paper does not contain any pseudocode or clearly labeled algorithm blocks. |
| Open Source Code | Yes | To ensure full reproducibility, our code is publicly available on github: https://github.com/aschethor/SplinePINN. |
| Open Datasets | Yes | To assess the accuracy of our method, we compute drag and lift coefficients on a CFD benchmark domain [Sch afer and Turek 1996] and compare the results with official benchmark values. Sch afer, M.; and Turek, S. 1996. Benchmark Computations of Laminar Flow Around a Cylinder (The CFD Benchmarking Project). http://www.mathematik.tu-dortmund.de/featflow/en/benchmarks/cfdbenchmarking.html. (accessed at 08-Sep-2021). |
| Dataset Splits | No | The paper describes a training procedure with a 'training pool' but does not specify traditional train/validation/test dataset splits. It trains with 'little to no ground truth data' and generates data on the fly. |
| Hardware Specification | Yes | Training took 1-2 days on a NVidia Ge Force RTX 2080 Ti. |
| Software Dependencies | No | The paper mentions using the Adam optimizer but does not specify versions for other key software components or libraries (e.g., Python, PyTorch, CUDA). |
| Experiment Setup | Yes | To this end, we use the Adam optimizer (learning rate = 0.0001). Finally, we update the training pool with the just predicted spline coefficients in order to fill the pool with more and more realistic training data over the course of training. Here, we set hyperparameters α = 10 and β = 20. For the wave equation, we set the hyperparameters α = 1, β = 0.1, γ = 10. |