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This study delivers a rigorous negative result demonstrating that learned surrogates fail to accelerate stiff coupled simulations due to structural barriers like Amdahl's law limits and closed-loop drift, rather than model deficiencies. The authors prove that even with perfect out-of-distribution gating, the system slows down because visited states lie far outside the training manifold, causing near-total deferral of cells. For practitioners in scientific computing, this highlights the critical need to account for runtime share and state distribution before deploying AI surrogates in production physics engines.
When a neural surrogate cannot accelerate a solver: runtime share, closed-loop drift, and the economics of uncertainty gating in a stiff coupled simulation
arXiv:2608.23075v1 Announce Type: cross Abstract: Learned surrogates for expensive inner solver blocks are a widely pursued route to faster multiphysics simulation. We report a controlled, end-to-end negative result and identify three structural barriers, none of them a deficiency of the network we trained. The testbed is the implicit Newton solve coupling energy-dependent neutrino radiation to matter in a general-relativistic radiation-hydrodynamics code, its most expensive physics routine per call. First, per-call cost and share of runtime are different quantities, and only the second bounds acceleration. An exclusive self-time profile puts the target block at 16.9% of critical-rank wall clock, capping any surrogate at ~1.2x by Amdahl's law. A surrogate 5.8x cheaper per call merely ties the solver, and the configuration stable enough to run without fallback reaches only parity. Second, offline accuracy cannot rank surrogates for deployment: across fourteen networks the pooled Spearman error-versus-survival correlation (rho = +0.73) is a between-family confound that vanishes under control (rho = -0.04). Third, a correct out-of-distribution gate cannot accelerate a loop that leaves its training distribution. We give the break-even deferral fraction in closed form: because the visited states sit 73x off the data manifold, the gate defers 96.8 to 99.7% of cells, almost invariant to surrogate quality. Including its own cost, the gated loop is a 0.94 to 0.96x slowdown. We further separate stability from fidelity: a never-crashing gated run accumulates a linear -19.9% density bias over 6000 steps. The error is a directed, ballistically accumulating bias, not the variance-driven divergence the autoregressive literature targets.
Abstract:Learned surrogates for expensive inner solver blocks are a widely pursued route to faster multiphysics simulation. We report a controlled, end-to-end negative result and identify three structural barriers, none of them a deficiency of the network we trained. The testbed is the implicit Newton solve coupling energy-dependent neutrino radiation to matter in a general-relativistic radiation-hydrodynamics code, its most expensive physics routine per call. First, per-call cost and share of runtime are different quantities, and only the second bounds acceleration. An exclusive self-time profile puts the target block at 16.9% of critical-rank wall clock, capping any surrogate at ~1.2x by Amdahl's law. A surrogate 5.8x cheaper per call merely ties the solver, and the configuration stable enough to run without fallback reaches only parity. Second, offline accuracy cannot rank surrogates for deployment: across fourteen networks the pooled Spearman error-versus-survival correlation (rho = +0.73) is a between-family confound that vanishes under control (rho = -0.04). Third, a correct out-of-distribution gate cannot accelerate a loop that leaves its training distribution. We give the break-even deferral fraction in closed form: because the visited states sit 73x off the data manifold, the gate defers 96.8 to 99.7% of cells, almost invariant to surrogate quality. Including its own cost, the gated loop is a 0.94 to 0.96x slowdown. We further separate stability from fidelity: a never-crashing gated run accumulates a linear -19.9% density bias over 6000 steps. The error is a directed, ballistically accumulating bias, not the variance-driven divergence the autoregressive literature targets.
Instrumentation and Methods for Astrophysics (astro-ph.IM); High Energy Astrophysical Phenomena (astro-ph.HE); Machine Learning (cs.LG); Computational Physics (physics.comp-ph)
arXiv:2608.23075 [astro-ph.IM]
(or arXiv:2608.23075v1 [astro-ph.IM] for this version)
https://doi.org/10.48550/arXiv.2608.23075 arXiv-issued DOI via DataCite (pending registration)
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