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.