Mellow Baixuan Chen | Search arXiv

arXiv2026

Machine-learned spectral PDE solvers for fluids and plasmas

Sparse regression methods for discovering governing partial differential equations (PDEs) from data are sensitive to observation noise and are not constrained to reproduce the data under forward integration. We address both limitations by performing weak-form discovery in the spatial discretization in which the PDE is solved, learned by differentiating through multistep rollouts anchored at the observed states. The new method, Weak-form Anchored Rollout for PDEs (WARP), produces a machine-learned PDE solver. In this work, we focus on systems amenable to a spectral Galerkin solver. Across eight benchmark fluid and plasma systems, including high-dimensional turbulent simulations, WARP produces numerically stable rollouts from new random initial conditions and substantially improves coefficient recovery, rollout accuracy, and statistical measures compared with a single-step weak-form SINDy baseline.

physics.comp-ph↗

arXiv2026

When Does Overlap Help? OSU-Mem and a Cell-Conditional Analysis of Trajectory Memory for LLM Agents

Long-horizon large language model (LLM) agents accumulate interaction trajectories that quickly exceed any practical prompt budget, and existing memory methods either truncate aggressively and lose non-local evidence or retain boilerplate that degrades decision quality. We ask a mechanism question rather than claiming a better general-purpose memory system: when does organizing trajectory memory into overlapping semantic units (OSUs) -- groups of related steps in which one step may belong to several units -- help retrieval over flat or disjoint alternatives? We instantiate this in OSU-Mem, which retrieves from an overlapping OSU pool via budgeted coarse-to-fine expansion, and show its benefit is conditional: overlapping memory helps when the evidence steps a query needs share tool calls or entities, but hurts when those steps are fully heterogeneous and share neither. On a synthetic benchmark where evidence carries such shared structure by construction, OSU-Mem improves over the strongest baseline as the theory predicts; yet on a concatenated, constructed unaugmented $τ$-bench setting its aggregate advantage over flat retrieval vanishes. Splitting queries by whether their evidence shares tools and entities shows this near-tie to be an artifact of mixing query types rather than a property of either method, and ToolBench, a controlled probe built to carry shared structure by design, corroborates the same mechanism via an overlap-vs.-disjoint construction contrast (under a coverage-guided variant), isolating the construction principle rather than validating the full default system. Because the relevant sharing is cheaply estimable from metadata, the analysis yields a metadata-based heuristic for predicting when overlap is likely to improve retrieval. We deliberately isolate the retrieval layer, assessed by retrieval quality and an LLM-mediated evidence-selection stage.

cs.IR↗