---
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.