Inpainting physics

Self‑supervised learning for context‑driven fluid simulation

Inlet & outlet stay fixed, the interior flow is inpainted.

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In a nutshell

Problem

Machine‑learning surrogates for fluid dynamics perform well on narrow tasks but they fail when faced with new geometries or boundary conditions.

1

Learn the fluid flow

We train a model on many velocity fields, with no boundary conditions, so it learns what plausible flow looks like.

2

Fix what is known, inpaint the rest

At inference we fix the known boundaries, such as inflow and outflow, or a region kept from a previous simulation, and the model inpaints the rest.

Result

One model, no retraining: it generalises to unseen geometries and flow speeds, and reuses unchanged context for local geometry edits.

Example application: Local geometry editing

When only a small region of a vessel changes (an aneurysm grown locally), most of an existing simulation stays valid: a forward surrogate must redo the whole field, the inpainting model only fills the edited region. Drag the divider on any artery to compare the two states (the divider moves on all of them together). Left: the original vessel with its ground-truth CFD field. Right: the same vessel with the aneurysm grown, showing the inpainting prediction. The edited region is in red.

Drag the white divider to wipe between ground truth (left) and the inpainting prediction on the deformed geometry (right).

Detailed overview

Three-stage overview: (1) tokenise velocity fields into local ball latent tokens; (2) self-supervised training with latent flow matching or a latent masked autoencoder; (3) context-driven inpainting that enforces boundary conditions and supports local geometry edits.
Inpainting physics. (1) We tokenise raw velocity fields into local ball-shaped latent representations. (2) We train a self-supervised model on these tokenised velocity fields using latent flow matching or a masked autoencoder. (3) At inference, boundary conditions are explicitly enforced by fixing known regions like inflow and outflow during inpainting, enabling generalisation to unseen geometries and flow conditions, preserving local flow structure.

Inpainting methods demo

We fix the boundaries at inlet and outlet and inpaint the rest based on the context. For the inference, we compare two different approaches: flow matching integrates the masked region from noise to flow, implicitly conditioned on the fixed inlet/outlet; masked auto-encoding predicts the masked region in a few steps, working inward from the fixed context. Drag to see the conceptual inpainting progress over time.

Flow matching

noise
t = 0 solution
t = 1
Integration time t = 0.00

Iterative masked auto-encoder

masked
step 0 solution
step 5
Step 0 of 5

Technical preprint

Inpainting physics: self-supervised learning for context-driven fluid simulation

Jonas Weidner1,2, Yeray Martin-Ruisanchez1, Daniel Rückert2,3,4,
Benedikt Wiestler1,2,∗, Julian Suk2,3,∗
1 AI for Image-Guided Diagnosis and Therapy, Technical University of Munich  ·  2 Munich Center for Machine Learning (MCML)  ·  3 AI in Healthcare and Medicine, Technical University of Munich  ·  4 Imperial College London  ·  * Shared senior authorship

Neural surrogate models for computational fluid dynamics (CFD) are typically trained as forward operators that map explicit problem specifications, such as geometry and boundary conditions, to solution fields. This ties the model to the conditioning variables seen during training and limits reuse under boundary-condition shifts or local geometry changes. We propose to reformulate steady CFD inference as an inpainting problem: instead of training on explicit boundary conditions, we learn a self-supervised prior over velocity fields and impose boundary constraints only during inference by fixing known regions such as inlet, outlet or unchanged regions from previous simulations. To scale this idea to large 3D meshes, we introduce a local neighbourhood tokeniser that represents high-resolution velocity fields as compact spatial latent tokens and train latent flow-matching and masked-autoencoder models on these tokens. On intracranial aneurysm hemodynamics, our method reconstructs full velocity fields from sparse boundary context, outperforms supervised neural surrogates under boundary-condition and dataset shift and enables local geometry editing by reusing unchanged simulation context. These results suggest that viewing CFD inference as context-conditioned inpainting can turn neural surrogates from task-specific predictors into reusable flow priors.

TL;DR

Train a self-supervised latent model on CFD velocity fields, impose boundary conditions at inference, predict the flow by inpainting, generalise more flexibly to unseen geometries and flow speeds.

Main contribution

Shift the modelling objective

We propose to view CFD emulation as context-conditioned inpainting rather than supervised neural-operator modelling.

Better generalisation

We show that this approach has significantly better generalisation properties with boundary conditions and geometric variations.

Local editing

We propose local editing as a preliminary downstream task tailored to generative models.

BibTeX

If you find this work useful, please consider citing it.

@article{weidner2026inpaintingphysics,
  title   = {Inpainting physics: self-supervised learning for context-driven fluid simulation},
  author  = {Weidner, Jonas and Martin-Ruisanchez, Yeray and R{\"u}ckert, Daniel
             and Wiestler, Benedikt and Suk, Julian},
  journal = {arXiv preprint arXiv:2605.08832},
  year    = {2026}
}