aiqbench analysis
COSMOS introduces a soft mechanism-mixture neural operator that continuously blends multiple physics-based specialists rather than relying on discrete routing, addressing the compositional nature of real-world physical systems. While initial evaluations suggested accuracy gains over standard solvers, an expanded audit revealed instability in specific regimes and highlighted that learned gating mechanisms may not strictly align with intended physical processes. This work underscores the importance of robust benchmarking and caution when interpreting performance claims from small-seed rollouts in complex PDE forecasting tasks.
COSMOS: Soft Mechanism Mixtures with Verifiable Routing for Long-Horizon PDE Forecasting
arXiv:2610.04427v1 Announce Type: cross Abstract: Neural operators offer an efficient alternative to classical PDE solvers, but most learn a monolithic map per equation family and discretization. Real systems are compositional: transport, diffusion, wave, and reaction processes can act simultaneously. Existing mixture-of-experts operators typically use sparse top-$K$ routing, although concurrent physics is naturally a blend rather than a discrete choice. We propose COSMOS (Cooperative Operator Specialists with Mechanism-level Operator Soft-routing), a soft mechanism-mixture neural operator. Four process-biased specialists remain active at every step and are continuously mixed by a learned gate, with their features fused by a small network. Specialists share a coarse latent grid, while a zero-initialized full-resolution residual restores detail lost through the bottleneck. We also introduce an operator-splitting compositional benchmark with known mixture weights $w^\star$ per trajectory. Against family-tuned FNO under 20-step rollouts, an initial 3-seed evaluation suggested gains on diffusion--reaction, parity on Navier--Stokes, and weaker shallow-water performance. An 11-seed audit showed that the diffusion--reaction gain was unstable, motivating caution in small-seed rollout comparisons and precluding a reliable accuracy-win claim on these families. Ablations show that uniform routing or removing the specialist mixture substantially degrades stable-regime rollouts. On the labeled benchmark, dense soft routing yields $2.2\times$ lower error than hard top-1 routing at identical fusion; using generator weights $w^\star$ at inference further lowers rollout error to $0.034$, diagnosing limitations of the learned gate. However, routing labels do not align with the specialists' intended mechanisms: COSMOS supports compositional accuracy, not mechanism identity.
Abstract:Neural operators offer an efficient alternative to classical PDE solvers, but most learn a monolithic map per equation family and discretization. Real systems are compositional: transport, diffusion, wave, and reaction processes can act simultaneously. Existing mixture-of-experts operators typically use sparse top-$K$ routing, although concurrent physics is naturally a blend rather than a discrete choice. We propose COSMOS (Cooperative Operator Specialists with Mechanism-level Operator Soft-routing), a soft mechanism-mixture neural operator. Four process-biased specialists remain active at every step and are continuously mixed by a learned gate, with their features fused by a small network. Specialists share a coarse latent grid, while a zero-initialized full-resolution residual restores detail lost through the bottleneck. We also introduce an operator-splitting compositional benchmark with known mixture weights $w^\star$ per trajectory. Against family-tuned FNO under 20-step rollouts, an initial 3-seed evaluation suggested gains on diffusion--reaction, parity on Navier--Stokes, and weaker shallow-water performance. An 11-seed audit showed that the diffusion--reaction gain was unstable, motivating caution in small-seed rollout comparisons and precluding a reliable accuracy-win claim on these families. Ablations show that uniform routing or removing the specialist mixture substantially degrades stable-regime rollouts. On the labeled benchmark, dense soft routing yields $2.2\times$ lower error than hard top-1 routing at identical fusion; using generator weights $w^\star$ at inference further lowers rollout error to $0.034$, diagnosing limitations of the learned gate. However, routing labels do not align with the specialists' intended mechanisms: COSMOS supports compositional accuracy, not mechanism identity.
Machine Learning (cs.LG); Artificial Intelligence (cs.AI)
arXiv:2610.04427 [cs.LG]
(or arXiv:2610.04427v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2610.04427 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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