{"paper":{"title":"Highly Efficient Rank-Adaptive Sweep-based SI-DSA for the Radiative Transfer Equation via Mild Space Augmentation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"A mild-augmentation approach lets rank-adaptive SI-DSA match full-rank accuracy for the radiative transfer equation while cutting memory and time.","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Wei Guo, Zhichao Peng","submitted_at":"2026-03-26T09:34:18Z","abstract_excerpt":"Low-rank methods have emerged as a promising strategy for reducing the memory footprint and computational cost of discrete-ordinates discretizations of the radiative transfer equation (RTE). However, most existing rank-adaptive approaches rely on rank-proportional space augmentation, which can negate efficiency gains when the effective solution rank becomes moderately large. To overcome this limitation, we develop a rank-adaptive sweep-based source iteration with diffusion synthetic acceleration (SI-DSA) for the first-order steady-state RTE. The core of our method is a sweep-based low-rank SI "},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Numerical experiments show that the proposed solver achieves accuracy and iteration counts comparable to those of full-rank SI-DSA while substantially reducing memory usage and runtime, even for challenging multiscale problems in which the effective rank reaches 30-45% of the full rank.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the residual-based greedy angular subsampling combined with mild augmentation will preserve stability and convergence rate across all problem classes without problem-specific tuning or hidden post-hoc adjustments.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A sweep-based SI-DSA solver for the RTE uses mild space augmentation and residual-driven subsampling to match full-rank accuracy while cutting memory and runtime even when the effective rank reaches 30-45 percent of full rank.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A mild-augmentation approach lets rank-adaptive SI-DSA match full-rank accuracy for the radiative transfer equation while cutting memory and time.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"b3828cf49c022330120c74e6751d352fdd1c8b56ae3d3bcfe48ee1970a8dfa3b"},"source":{"id":"2603.25233","kind":"arxiv","version":3},"verdict":{"id":"3035510e-621e-46c0-91c8-b81069e49749","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T00:40:06.996261Z","strongest_claim":"Numerical experiments show that the proposed solver achieves accuracy and iteration counts comparable to those of full-rank SI-DSA while substantially reducing memory usage and runtime, even for challenging multiscale problems in which the effective rank reaches 30-45% of the full rank.","one_line_summary":"A sweep-based SI-DSA solver for the RTE uses mild space augmentation and residual-driven subsampling to match full-rank accuracy while cutting memory and runtime even when the effective rank reaches 30-45 percent of full rank.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the residual-based greedy angular subsampling combined with mild augmentation will preserve stability and convergence rate across all problem classes without problem-specific tuning or hidden post-hoc adjustments.","pith_extraction_headline":"A mild-augmentation approach lets rank-adaptive SI-DSA match full-rank accuracy for the radiative transfer equation while cutting memory and time."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2603.25233/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"}