Microcosmos avoids quadratic-scaling operations by design — local fluid updates and grid-based steric repulsion instead of pairwise checks — to reach GPU-scale populations

gpu-simulationcomputational-scalingartificial-lifejaxdifferentiable-physics

The organizing constraint behind Microcosmos (arXiv:2607.02954) is that every component avoids operations that scale quadratically with the number of interacting elements, because quadratic cost is what caps population size on a GPU. Two design choices carry this: the Lattice Boltzmann fluid solver uses only local updates (no all-pairs force computation), and self-avoidance is handled by grid-based steric repulsion rather than pairwise collision detection. The whole engine is implemented in JAX, giving automatic differentiation over the physics for free (claim-microcosmos-elastic-filaments-differentiable-gpu-fluid).

Promotion wording (2026-07-09), kept as history: The capture records the paper's performance claim — runtime scaling linearly with particle count, tested to ~500k particles on a single NVIDIA L40S GPU — but that specific figure is held under [unverified-quant]. The capture author explicitly noted that "exact benchmark numbers/methodology beyond this summary should be checked against the paper's own figures before reuse," so the number is recorded, not treated as settled. Under the vault's sourcing floor a specific benchmark figure is a Tier 1–2 quantitative claim that should be confirmed against the primary source's own plots before going load-bearing; the verification is routed to question-verify-microcosmos-benchmarks-and-experiments and the note stays seedling.

Flag discharged (audit 2026-07-09; re-read 2026-08-20; text-located 2026-09-11). The figures are in the paper's running text, not only in its plot. Scalability section: "we measure wall clock time as we increase the number of particles at a fixed grid resolution (256 × 256), running 1000 steps with up to 500k particles," footnoted "Ran with 1 NVIDIA L40S GPU, JAX version 0.8.1"; and "Microcosmos scales linearly, unlike simulators that rely on pairwise interactions such as Particle Life (Mohr, 2023), which scale as O(n²)." Figure 5's caption: "Wall clock time scales linearly with the number of particles in Microcosmos, in contrast to the O(n²) scaling of simulators that compute pairwise particle interactions." The routed question is answered (50-questions/_answered/). What the paper does not supply is a data table behind Figure 5 — the 2026-08-20 recheck's ~1.4–1.6 ms/step at 500k particles is a visual read of the plot and remains so.

The durable content here is the design principle — trade pairwise exactness for local/grid approximations to buy linear scaling — not the exact particle count. This "kill the quadratic term to hit hardware scale" pattern is a recurring theme in GPU-era ML systems work, adjacent to the throughput-oriented engineering in claim-gift-2026-gradient-anisotropy-isotropic-transform.