Boosting Generalization in Parametric PDE Neural Solvers through Adaptive Conditioning
Authors: Armand Kassaï Koupaï, Jorge Mifsut Benet, Yuan Yin, Jean-Noël Vittaut, Patrick Gallinari
NeurIPS 2024 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We demonstrate the versatility of our approach for both fully datadriven and for physics-aware neural solvers. Validation performed on a whole range of spatio-temporal forecasting problems demonstrates excellent performance for generalizing to unseen conditions including initial conditions, PDE coefficients, forcing terms and solution domain. Project page: https://geps-project.github.io/ |
| Researcher Affiliation | Collaboration | 1 Sorbonne Université, CNRS, ISIR, 75005 Paris, France 2 Valeo.ai, Paris, France 3 Sorbonne Université, CNRS, LIP6, 75005 Paris, France 4 Criteo AI Lab, Paris, France |
| Pseudocode | Yes | Algorithm 1: Training and adaptation for our method |
| Open Source Code | Yes | Project page: https://geps-project.github.io/ Question: Does the paper provide open access to the data and code, with sufficient instructions to faithfully reproduce the main experimental results, as described in supplemental material? Answer: [Yes] Justification: We provided open access to our code and access to the code used to generate our data. |
| Open Datasets | No | The paper describes how the data for the experiments (e.g., 2D Gray-Scott, 1D Burgers equations, Pendulum, Kolmogorov flow, Combined equation) was generated through simulations, specifying parameters, solvers, and resolutions in Appendix B. While the authors claim to provide access to the code used to generate the data in the NeurIPS checklist, the datasets themselves are not provided with a direct URL, DOI, repository, or citation as publicly available or open datasets. |
| Dataset Splits | Yes | We define Etr as the set of environments used to train our model. In each training environment, Ntr trajectories are available De tr = {ui(x, t)}Ntr i=1. For the in-distribution evaluation, the model has already learned conditioning context parameters (described later in section 4.1) for each training environment and is simply tested on new trajectories from the same environments using the appropriate context. For out-of-distribution, the model is evaluated on trajectories from new environments from an evaluation set Eev and is adapted. We then assume access to Nad trajectories De ev = {ui(x, t)}Nad i=1 from the new environments to adapt the network. In our experiments we consider a scarce data, few-shot scenario where Nad = 1. After adaptation, we test our model on new unseen trajectories from these evaluation environments Eev. This setting is illustrated in Figure 1. |
| Hardware Specification | Yes | All experiments were conducted on a single GPU:NVIDIA RTX A5000 (25 Go). |
| Software Dependencies | No | The code has been written in Pytorch (Paszke et al., 2019). The paper mentions "Pytorch" but does not specify a version number or other key software components with their versions. |
| Experiment Setup | Yes | We used a standard MLP for the Pendulum equation, a Conv Net for GS and Burgers equations and FNO for the vorticity equation. All activation functions are Swish functions. We use an Adam optimizer over all datasets. |