| --- |
| tags: |
| - partial-differential-equations |
| - scientific-machine-learning |
| - self-supervised-learning |
| - jepa |
| - sparse-observations |
| --- |
| |
| # SCOPE: trained checkpoints |
|
|
| Final checkpoints of the SCOPE experiments on **observation-conditioned PDE field recovery**: recovering |
| a full physical field pair from a sparse set of observed grid points. SCOPE combines a mask-aware spatial |
| Transformer encoder, a latent predictor, a nonlinear field decoder and an EMA full-field target encoder. |
| Each PDE is trained independently. |
|
|
| ## What is here |
|
|
| 61 checkpoints, 28.7 GB, one file per completed run: the last checkpoint the run wrote, not one selected |
| on validation or test error. |
|
|
| | Group | Case ids | PDEs | Epochs | Files | |
| |---|---|---|---:|---:| |
| | Field-only baseline (`fo`) | `fo-<pde>` | Poisson, Darcy, Helmholtz, NS without obstacle | 500 | 4 | |
| | Field + grounding (`fg`) | `fg-<pde>` | all five | 500 | 5 | |
| | Field + JEPA + variance (`fjv`) | `fjv-<pde>` | all five | 500 | 5 | |
| | Decoder probes, fully visible pair | `dp{5m,10m,15m}-{fjv,full}-<pde>` | all five | 100 | 30 | |
| | Decoder probes, sparse condition | `sp{5m,10m,15m}-full-<pde>`, `sp15m-fjv-{darcy,helmholtz}` | all five | 100 | 17 | |
|
|
| The five PDEs are `poisson`, `darcy`, `helmholtz`, `ns-nonbounded` (Navier–Stokes without an obstacle) |
| and `ns-bounded` (Navier–Stokes with an internal cylinder). |
|
|
| ``` |
| models/<case_id>/epoch-<N>.000.pt the run's final checkpoint (N = 500 for training runs, 100 for probes) |
| manifest.*.json inventory: case id, kind, PDE, epoch, byte size and SHA-256 of every file |
| ``` |
|
|
| ## The runs |
|
|
| **Objective variants.** All variants share one model, dataset, optimizer (AdamW, batch 32), seed 20260913, |
| schedule and evaluation contract, and differ only in the objective. `fjv` trains the field loss with the |
| JEPA and variance terms after a 10-epoch teacher-pretraining stage, without grounding. `fg` trains the |
| field loss with grounding only; its EMA teacher is frozen after pretraining and never read in main |
| training. `fo` trains the field loss alone for 500 epochs from random initialization, with no teacher and |
| no pretraining stage; it is not a single-term ablation. The reference `full` and `fjvg` training runs |
| are not in this repository. |
|
|
| **Decoder probes.** A probe measures how much field information a frozen latent carries. The encoder, |
| predictor, observation condition and EMA teacher of a completed run are loaded and frozen (78,027,776 |
| parameters, none trained), and the decoder is replaced by a fresh probe decoder of about 5M, 10M or 15M |
| parameters, the only module trained, for 100 epochs with 5 warmup epochs. `dp` probes decode the encoder |
| latent of the fully visible pair; `sp` probes decode the predictor latent on the sparse condition of 500 |
| uniformly placed visible points. The second part of the case id names the base run (`fjv` or `full`). |
|
|
| ## Using the files |
|
|
| The files are PyTorch checkpoints written by the SCOPE trainer; load them with |
| `torch.load(path, map_location="cpu", weights_only=False)` and the SCOPE model code. Verify a download |
| against its SHA-256 in `manifest.*.json` first. |
|
|
| | PDE | Train / test records | Field pair | |
| |---|---:|---| |
| | `poisson` | 50,000 / 1,024 | source `a`, solution `u` | |
| | `darcy` | 50,000 / 10,000 | coefficient `a`, solution `u` | |
| | `helmholtz` | 50,000 / 10,000 | input `a`, response `u` | |
| | `ns-nonbounded` | 50,000 / 1,000 | earlier / later vorticity snapshots | |
| | `ns-bounded` | 14,000 / 1,000 | earlier / later speed snapshots | |
|
|
| No licence has been declared for these checkpoints yet. |
|
|
| ## Citation |
|
|
| Please cite the SCOPE paper (arXiv preprint). A BibTeX entry will be added here once the arXiv |
| identifier is assigned. |
|
|
