[ICML Paper] To-Do List
ICML Paper
ICML deadline : [2023-01-26 jeu.]
Use Case and Models
We need to show Melissa is working for a decent number of use cases and models. We do not have to propose completely novel equations to be solved or models to do so. There are already quite a few articles presenting models to solve specific equations. We are looking for data-driven training and multi-parametric equations.
- PDEBench Compare UNet, FNO and PINNs on multiple equations (1D, 2D, time independent and dependent). Code is available but confused. Data generation relies on JAX and GPU parallelisation PDEBENCH: An Extensive Benchmark for Scientific Machine Learning
- Benchmark with few equations (Springs to Navier Stokes) and simple models (CNN) An Extensible Benchmark Suite for Learning to Simulate Physical Systems
- Stokes with few models Towards Multi-spatiotemporal-scale Generalized PDE Modeling
- AirfRANS High Fidelity Computational Fluid Dynamics Dataset generated with solvers.
Models of interet commonly found in the literature:
- CNN/FCN simple straightforward models
- Fourier Neural Operator for Parametric Partial Differential Equations only works with periodic boundary conditions but SOTA
- Message Passing Neural PDE Solvers GNN approach to solve PDEs. It is an autoregressive model that requires different time steps not only subsequent ones, which may complicates the implementation of the data storage.
- Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations works with data but mostly with the equation directly (i.e. not data-driven)
The MP-PDE Solvers and PINNs may be more complex to use. The first one because it requires a more fine grained management of the data. The latter because it is not really data-driven.
Compare Performance of Models on Use Cases given the Amount of Available Data
The assumption is more data yields to better performance. The performance is measured on test trajectories whose parameters are selected beforehand. The training set should be representative of the same parameters selected for the test set.
Compare Performance with Online Training of Melissa
If more data means better training, can we still reach the same performance with online training?
Active Learning with Melissa
To explore all the parameter space is not feasible due to the curse of the dimensionality, even with the possibilites offered by HPC and Melissa. Hence, we must explore the most informative trajectories.
To-Do List
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Study the different benchmarks to identify which equations and which models can be suitable for our need; - Check that data can be generated online on different clients (CPU, online);
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Check the performance of training depending on the number of training data available; -
Put the data generation and models in Melissa:
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FNO (c.f. https://gitlab.inria.fr/melissa/melissa-combined/-/issues/7) -
UNet (c.f. https://gitlab.inria.fr/melissa/melissa-combined/-/issues/7) -
MP-PDE Solver