Allex Kan, Ji Zhang, Hao Yin, Hao Li, Owen Fu, Xunxing Chen, Lin Huang, Zion Wang 等 13 位作者
Molecular dynamics predicts molecular motion from atomic forces and trajectory integration. Density functional theory (DFT) provides first-principles forces, but its $O(N^3)$ cost limits simulations to thousands of atoms; empirical force fields scale to millions but miss bond breaking and charge transfer. Equivariant message-passing Transformers learn the ab initio potential at linear cost. Stacked layers propagate information beyond a single cutoff, giving four layers a receptive field up to 23Å. At this frontier, scale is limited by communication: layers exchange boundary features across devices, force backpropagation repeats the exchange, and moving atoms change neighbor graphs and tensor shapes. We present Tessera, a distributed runtime that fixes workload shapes between rebuilds. It sorts atoms along a space-filling curve into equal-count shards, ensuring identical atom counts and tensor shapes per rank. Peer sets scale as $K^{0.5}$, not $K$. A conservative neighbor skin preserves topology across updates, enabling each rebuild interval to replay as one CUDA Graph. Fused kernels, three-level neighbor search, and overlapped All-to-All complete it. On 512 GPUs, Tessera sustains 30.7M atoms at 89.7% weak-scaling efficiency (77--90% across three per-GPU loads); per-step time rises 1.11--1.29x as machine and problem grow 16x. Graph reuse cuts full-step time $1.87\times$. Across an $8\times$ device increase, neighbor-search cost grows $1.7\times$, versus $3.0\times$ for Morton order. In a live $10.24$M-atom salt solution, NVE energy drift is $0.42\,μ$eV/atom/ps over $10$ ps, and structure matches a serial reference. A 10.06M-atom Norovirus capsid sustains 100 ps of NVT at $\approx 8$ ps/day on 256 A100 GPUs. Over 200,000 steps, it has no broken bonds or anomalously close pairs and uses three compiled variants, with no graph breaks or eager fallbacks.
Foraging recruitment is modeled as a contagion: an agent that finds a resource triggers a linear-threshold cascade on the group's communication network. Because activation is degree-normalized, crowding shuts the cascade off, so the swarm aggregates on a resource and then disperses to explore again. Acting on the cascade moves agents in space, and that motion rewires the network, so recruitment and exploration are one coupled process; removing this coupling alone abolishes the self-limitation. Recruitment spreads only within a connectivity window, bounded below by percolation onset and above by degree-blocking. The swarm self-organizes to the near-critical edge of this window -- self-organized quasi-criticality: recruitment sits near but below the critical point without settling onto a clean, size-invariant critical state, and the activity spectrum has a finite correlation time (Lorentzian-like, not 1/f), consistent with local rather than global criticality. Recruitment raises harvest up to 2.7x over solitary search on sparse, clustered resource fields and loses (down to 0.37x) on abundant or uniform ones; because resources generically aggregate, the favourable regime is the common one. The empirically motivated Levy search and the resource field it exploits are both least-committal: the search a maximum-caliber walk, and the field a maximum-entropy point process whose generic, aggregation-set sign is clustered (attractive). The search exponent that maximizes harvest tracks the field's fractal dimension (a heavier-tailed, more ballistic search for more strongly clustered fields). These are one coupled mechanism: heavy-tailed Levy exploration crosses the field's sparse voids while recruitment cascades exploit its clusters, so one maximum-entropy geometry binds exploration and recruitment into a single self-organizing cycle.
The spring-loaded inverted pendulum (SLIP) describes the center-of-mass (COM) motion of runners but has no trunk. In trunk models, the hip torque couples posture and COM motion and destroys the central-force structure on which SLIP analysis relies. As a result, trunk models have been studied almost only numerically. We show that this structure can be restored. The central pivot point (CPP), a hip-torque law that directs the ground reaction force through the COM, decouples pitch exactly and reduces stance to a planar central-force problem. At upright posture, time-reversal symmetry produces one-parameter families of periodic gaits. A stance-phase pitch law and a stride-level regulator stabilize all computed gaits, also with bounded hip torque and friction. Under CPP, any radial force law in virtual-leg coordinates can be embedded independently of posture. For a linear radial template, the stance radius and the constant-momentum sweep have exact closed forms. With a new gravity correction, the resulting analytic return map, to our knowledge the first for a trunk model, predicts liftoff velocity and apex position with mean errors of 1.6% and 0.9%. The natural gaits of the embedded runner are symmetric and need no force step at touchdown. A near-reversibility argument explains their unit multiplier, and a scalar equation predicts them within 0.8%. A deadbeat stride controller based on the analytic map tracks changes of speed, height and posture. CPP thus makes trunk models accessible to the analytic tools developed for SLIP.