Editing Fluid Flows with Divergence-Free Biharmonic Vector Field Interpolation
Bibliographic record
Abstract
Achieving satisfying fluid animation through numerical simulation can be time-consuming because such simulations are computationally expensive to perform and there are few practical post-processing tools for editing of completed simulations – often, the user must modify their scene setup and launch it again from scratch. To address this challenge, we present a divergence-free biharmonic vector field interpolation and extrapolation method for reusing and/or stitching together spatial regions of existing flows. Given velocities and velocity gradients on the boundary of a domain at each timestep, which may be either user-defined or drawn from existing simulations, we fill in the given domain by constructing an optimally smooth, divergence-free, boundary-satisfying vector field. We measure smoothness using the Laplacian energy to allow smooth boundary behavior and enforce divergence constraints through explicit Lagrange multipliers. The prior methods for this \nproblem suffer from non-zero divergence and associated visible compression artifacts, or cannot smoothly match the desired slopes at the domain boundaries. Moreover, we introduce a new extrapolation scheme that can handle unprescribed boundaries by smoothly extending the vector field through the unspecified boundary. In this case, we measure the smoothness using the Hessian energy which provides well-behaved solutions for “free” or natural boundary conditions. We demonstrate that our new interpolation and extrapolation procedures always produce smooth and incompressible flows, as well as enabling a \nrange of natural simulation editing capabilities including hole-filling, copy-pasting, extrapolation, and scene stretching.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
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 teacher head, 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".