{"paper":{"title":"Dynamic models with $p$ parameters are identified by $2p+1$ random features","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.PR","nlin.CD","physics.data-an"],"primary_cat":"stat.ME","authors_text":"Cosma Rohilla Shalizi, Michael Wieck-Sosa","submitted_at":"2026-07-17T15:08:20Z","abstract_excerpt":"A foundational principle in nonlinear dynamics is that the structure of a dynamical system can be recovered from a small number of generic measurements or coordinates. We develop an analogous principle for the identification of dynamic models for time series {\\em with noise}, which builds on previous identification results for noiseless dynamical systems. The noise is allowed to be non-iid, non-Gaussian, and dependent on the state. Our results cover noisily observed differential equations and discrete-time dynamical systems, as well as stochastic models with process noise. We illustrate the ut"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.16035","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.16035/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}