{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:7JTTVU5COTYGXBUUXMHHYSOEDK","short_pith_number":"pith:7JTTVU5C","schema_version":"1.0","canonical_sha256":"fa673ad3a274f06b8694bb0e7c49c41aa275814a6c2919a219ce7b470a3bff59","source":{"kind":"arxiv","id":"2405.11907","version":5},"attestation_state":"computed","paper":{"title":"Ensemble and Mixture-of-Experts DeepONets For Operator Learning","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Ramansh Sharma, Varun Shankar","submitted_at":"2024-05-20T09:42:44Z","abstract_excerpt":"We present a novel deep operator network (DeepONet) architecture for operator learning, the ensemble DeepONet, that allows for enriching the trunk network of a single DeepONet with multiple distinct trunk networks. This trunk enrichment allows for greater expressivity and generalization capabilities over a range of operator learning problems. We also present a spatial mixture-of-experts (MoE) DeepONet trunk network architecture that utilizes a partition-of-unity (PoU) approximation to promote spatial locality and model sparsity in the operator learning problem. We first prove that both the ens"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2405.11907","kind":"arxiv","version":5},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.LG","submitted_at":"2024-05-20T09:42:44Z","cross_cats_sorted":[],"title_canon_sha256":"17eec165b27796abb4a1e76128772a3eb78fb4f1a6a6874dffeef098134575ea","abstract_canon_sha256":"23bb0d9e79d5de94a92fabf51cbb0750e860b8330395fda88d7e071fe4a64c4a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:31:43.418802Z","signature_b64":"KIM4Nxyr77KJmzaXRswOrXJWb1HGfFcs42E0wnul3sfLWNPTkcp1Bdvu+wugKxASuL4V4uXwujS/M5TBn60kCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fa673ad3a274f06b8694bb0e7c49c41aa275814a6c2919a219ce7b470a3bff59","last_reissued_at":"2026-07-05T10:31:43.418292Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:31:43.418292Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Ensemble and Mixture-of-Experts DeepONets For Operator Learning","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Ramansh Sharma, Varun Shankar","submitted_at":"2024-05-20T09:42:44Z","abstract_excerpt":"We present a novel deep operator network (DeepONet) architecture for operator learning, the ensemble DeepONet, that allows for enriching the trunk network of a single DeepONet with multiple distinct trunk networks. This trunk enrichment allows for greater expressivity and generalization capabilities over a range of operator learning problems. We also present a spatial mixture-of-experts (MoE) DeepONet trunk network architecture that utilizes a partition-of-unity (PoU) approximation to promote spatial locality and model sparsity in the operator learning problem. We first prove that both the ens"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.11907","kind":"arxiv","version":5},"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/2405.11907/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2405.11907","created_at":"2026-07-05T10:31:43.418360+00:00"},{"alias_kind":"arxiv_version","alias_value":"2405.11907v5","created_at":"2026-07-05T10:31:43.418360+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.11907","created_at":"2026-07-05T10:31:43.418360+00:00"},{"alias_kind":"pith_short_12","alias_value":"7JTTVU5COTYG","created_at":"2026-07-05T10:31:43.418360+00:00"},{"alias_kind":"pith_short_16","alias_value":"7JTTVU5COTYGXBUU","created_at":"2026-07-05T10:31:43.418360+00:00"},{"alias_kind":"pith_short_8","alias_value":"7JTTVU5C","created_at":"2026-07-05T10:31:43.418360+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":4,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.25820","citing_title":"Operator Learning on the Data-Driven Multiscale Space for Nonlinear Flow in Random Heterogeneous Porous Media","ref_index":24,"is_internal_anchor":false},{"citing_arxiv_id":"2606.28519","citing_title":"A Trainable-by-Parts Operator Learning Framework: Bridging DeepONet and Karhunen-Loeve Expansions for Large-Scale Applications","ref_index":13,"is_internal_anchor":false},{"citing_arxiv_id":"2510.12999","citing_title":"AMORE: Adaptive Multi-Output Operator Network for Stiff Chemical Kinetics","ref_index":36,"is_internal_anchor":false},{"citing_arxiv_id":"2604.07421","citing_title":"SPAMoE: Spectrum-Aware Hybrid Operator Framework for Full-Waveform Inversion","ref_index":16,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/7JTTVU5COTYGXBUUXMHHYSOEDK","json":"https://pith.science/pith/7JTTVU5COTYGXBUUXMHHYSOEDK.json","graph_json":"https://pith.science/api/pith-number/7JTTVU5COTYGXBUUXMHHYSOEDK/graph.json","events_json":"https://pith.science/api/pith-number/7JTTVU5COTYGXBUUXMHHYSOEDK/events.json","paper":"https://pith.science/paper/7JTTVU5C"},"agent_actions":{"view_html":"https://pith.science/pith/7JTTVU5COTYGXBUUXMHHYSOEDK","download_json":"https://pith.science/pith/7JTTVU5COTYGXBUUXMHHYSOEDK.json","view_paper":"https://pith.science/paper/7JTTVU5C","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2405.11907&json=true","fetch_graph":"https://pith.science/api/pith-number/7JTTVU5COTYGXBUUXMHHYSOEDK/graph.json","fetch_events":"https://pith.science/api/pith-number/7JTTVU5COTYGXBUUXMHHYSOEDK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7JTTVU5COTYGXBUUXMHHYSOEDK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7JTTVU5COTYGXBUUXMHHYSOEDK/action/storage_attestation","attest_author":"https://pith.science/pith/7JTTVU5COTYGXBUUXMHHYSOEDK/action/author_attestation","sign_citation":"https://pith.science/pith/7JTTVU5COTYGXBUUXMHHYSOEDK/action/citation_signature","submit_replication":"https://pith.science/pith/7JTTVU5COTYGXBUUXMHHYSOEDK/action/replication_record"}},"created_at":"2026-07-05T10:31:43.418360+00:00","updated_at":"2026-07-05T10:31:43.418360+00:00"}