Michael Doane — Independent Researcher, Cary, NC
This repository compares physical solvers with neural forecasts when the available equations are correct, their coefficients are biased, or a mechanism is missing. It asks which forecasting option has the lowest held-out error, how validation data can guide that choice, and how much computation each option requires. A related set of experiments tests the use of imperfect physics to generate additional neural training examples.
The neural candidates are a standard transformer, a transformer that applies a shared block three times, and a compact Fourier neural operator (FNO). They predict observed physical states. A separate latent world-model architecture was outside the implemented study.
Calibration learned three shared coefficient multipliers from observed training trajectories. Validation forecasts selected the multipliers before the new test evaluation. In all 14 biased-coefficient settings, calibrated physics had lower error than the validation-selected neural model. Physics also had lower error in all 14 correct-coefficient settings. Neural forecasts had lower error in both settings with a missing equation term. This pattern held at 64 and 96 forecast steps, for both ordinary test coefficients and coefficients outside the training range.
A validation-based choice among unchanged physics, calibrated physics, and the archived neural candidates selected physics in the 28 settings with complete equations and a neural model in both missing-term settings. The FNO was the best neural validation choice in every seed-specific comparison. These counts include repeated stages and spatial grids across eight physical families.
The complete calibration extension ran on CPU in about 85 seconds, with 30/30 settings completed, 28/28 regenerated datasets matching the archived hashes, and no neural retraining. Median calibration time was about 0.72 seconds per setting. Matched CPU forward-step medians were about 0.45 ms for calibrated physics, 0.67 ms for the FNO, and 1.2 ms for each transformer architecture. Fresh neural timing measurements used initialized copies of the archived architectures; accuracy came from the saved trained-model evaluations.
The experiments use noiseless, fully observed, one-dimensional periodic synthetic systems. The coefficient bias can be represented exactly by the fitted multipliers, and the physical solver shares the generating equation family. The calibration extension is exploratory because earlier test results informed its design. These conditions limit claims about general physical model selection.
- Revised manuscript and review files
- Calibrated-physics results
- Complete calibration tables
- Study design, interpretation, and limitations
- Direct audit of the original forecasts
- Reproduction instructions
- GitHub and Zenodo update instructions
- Release changes
Saved results can be inspected without fitting any model. The dependency-free integrity checker verifies the release inventory, original experiments, the calibration source and output hashes, and the frozen validation decisions:
python scripts/verify_release.py
The check establishes file consistency with this release. The saved scientific intervals and diagnostics describe the evidence. No minimum effect size or required number of successful systems is imposed for the calibration extension.
| Path | Contents |
|---|---|
experiments/development/ |
Original source for 864 neural fits across six equations |
experiments/confirmation/ |
Original source for 720 resolution and augmentation-selector fits |
experiments/calibration/ |
Frozen calibration source, compact archived neural scores, source metadata, and tests |
results/development/ |
Original development records and evaluation arrays |
results/confirmation/ |
Original follow-up records, frozen choices, and evaluation arrays |
results/calibration/ |
All 30 fitted settings, frozen choices, test errors, timings, and audit records |
analysis/model_choice_audit/ |
Direct error and cost audit of the 1,584 archived neural fits |
manuscript/ |
Revised manuscript, section review documents, figures, tables, and source |
provenance/v1.0.0/ |
Original release metadata and documentation |
scripts/ |
Integrity and report replay tools |
manifest.json |
SHA-256 inventory for this release |
The original experimental source and results remain byte-for-byte intact. The archived neural experiments contain 1,584 fits across eight equations. Calibration adds 30 settings and reuses the saved neural scores. Generated raw trajectory caches are omitted from the release because they can be regenerated; their metadata and hashes are included. Trained neural checkpoints were absent from the original archives.
The earlier guarded augmentation selector and the new validation-based forecasting choice answer different questions. Their outputs remain in their respective result directories. Historical reports retain their original language and status rules for reproducibility; the revised manuscript explains the current interpretation.
This is the prepared v1.1.0 release. The published v1.0.0 archive is DOI 10.5281/zenodo.22728288. That DOI identifies the earlier evidence package. A DOI for this updated version has yet to be assigned. Cite the new version DOI when it is published; preserve the earlier DOI when referring specifically to the original release.
Repository: MRDOANE/physics-guided-learning. Citation metadata is in CITATION.cff. The software retains its MIT License. The included manuscript is a research draft prepared for the Journal of Computational Science.