VortexNet: Learning Complex Dynamic Systems with Physics-Embedded Networks
Bibliographic record
Abstract
In this paper, we present a novel physics-rooted network structure that dramatically facilitates the learning of complex dynamic systems. Our method is inspired by the Vortex Method in fluid dynamics, whose key idea lies in that, given the observed flow field, instead of describing it with a function of space and time, one can equivalently understand the observation as being caused by a number of Lagrangian particles ----- vortices, flowing with the field. Since the number of such vortices are much smaller than that of the Eulerian, grid discretization, this Lagrangian discretization in essence encodes the system dynamics on a compact physics-based latent space. Our method enforces such Lagrangian discretization with a Encoder---Dynamics---Decode network structure, and trains it with a novel three-stage curriculum learning algorithm. With data generated from the high precision Eulerian DNS method, our alorithm takes advantage of the simplifying power of the Lagrangian method while persisting the physical integrity. This method fundamentally differs from the current approaches in the field of physics-informed learning, and provides superior results for being more versatile, yielding more physical-correctness with less data sample, and faster to compute at high precision. Beyond providing a viable way of simulating complex fluid at high-precision, our method opens up a brand new horizon for embedding knowledge prior via constructing physically-valid latent spaces, which can be applied to further research areas beyond physical simulation.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".