{"paper":{"title":"Randomized Atomic Feature Models for Physics-Informed Identification of Dynamic Systems","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Impulse responses are recovered as random superpositions of damped exponentials from poles sampled inside a disk using convex optimization with physical constraints.","cross_cats":["cs.LG","cs.SY"],"primary_cat":"eess.SY","authors_text":"Lennart Ljung, Mario Sznaier, Rajiv Singh","submitted_at":"2026-05-14T04:25:07Z","abstract_excerpt":"We present a physics-informed framework for system identification based on randomized stable atomic features. Impulse responses are represented as random superpositions of stable atoms, namely damped complex exponentials associated with poles sampled inside a prescribed disk. Identification is then cast as a convex regularized least-squares problem with optional linear, second-order-cone, and KYP constraints. The approach generalizes random Fourier and random Laplace features to the damped, nonstationary regime relevant to engineering systems while retaining modal interpretability and scalable"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"The main analytic point is an operator-theoretic Disk-Bochner viewpoint: positive measures over stable poles generate positive-definite kernels with a radius-dependent shift defect, while a converse scalar disk moment representation for an arbitrary kernel is characterized by subnormality of the canonical shift.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That random sampling of poles inside a prescribed disk produces a sufficiently rich and stable atomic dictionary whose finite realizations satisfy the restricted-eigenvalue properties needed for the stated sparse-recovery guarantees.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Impulse responses are cast as random atomic superpositions of stable poles inside a disk and recovered through constrained convex optimization that encodes engineering priors.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Impulse responses are recovered as random superpositions of damped exponentials from poles sampled inside a disk using convex optimization with physical constraints.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"22c3cc4fec720c7020645435291371e83364af770db7af22140f65cc0bc46d6a"},"source":{"id":"2605.14351","kind":"arxiv","version":1},"verdict":{"id":"a545946b-8e93-4aa2-9dd5-eb79093e7a23","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T02:38:40.486298Z","strongest_claim":"The main analytic point is an operator-theoretic Disk-Bochner viewpoint: positive measures over stable poles generate positive-definite kernels with a radius-dependent shift defect, while a converse scalar disk moment representation for an arbitrary kernel is characterized by subnormality of the canonical shift.","one_line_summary":"Impulse responses are cast as random atomic superpositions of stable poles inside a disk and recovered through constrained convex optimization that encodes engineering priors.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That random sampling of poles inside a prescribed disk produces a sufficiently rich and stable atomic dictionary whose finite realizations satisfy the restricted-eigenvalue properties needed for the stated sparse-recovery guarantees.","pith_extraction_headline":"Impulse responses are recovered as random superpositions of damped exponentials from poles sampled inside a disk using convex optimization with physical constraints."},"references":{"count":47,"sample":[{"doi":"","year":null,"title":"SIAM Journal on Matrix Analysis and Applications , year =","work_id":"839af712-a026-492c-9f5a-a5ef9f0be8a4","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2013,"title":"IEEE Transactions on Information Theory , volume =","work_id":"783026d1-ed8e-4d1f-af63-42f5109eedb5","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Yang, Jiyan and Sindhwani, Vikas and Fan, Quanfu and Avron, Haim and Mahoney, Michael W. , title =. 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