ARXIV:2602.22059 · NEURAL OPERATORS · SUBMITTED 02 APR · 02:30 UTC · FRESHNESS STALE

VerifiedSource: PDF linkedPartialPaperPack: 3 of 4 citation fields filledMissingMissing fields: authorsPartialProof: unverified proof status

NESTOR: A Nested MOE-based Neural Operator for Large-Scale PDE Pre-Training

arXiv

A specialized nested MoE neural operator for efficient large-scale PDE pre-training and transfer learning.

Blocked on Code›Score5.0Evidence unverified

Opportunity summary

Pain A specialized nested MoE neural operator for efficient large-scale PDE pre-training and transfer learning.

Evidence 0 refs | 0 sources | 17% coverage

Blocker Evidence unverified

Open Build Read PDF Signal Canvas Track

PROBLEM

A specialized nested MoE neural operator for efficient large-scale PDE pre-training and transfer learning. However, due to the diversity and complexity of PDE systems, existing neural operators typically rely on a single network architecture,…

METHOD

Full abstract

Neural operators have emerged as an efficient paradigm for solving PDEs, overcoming the limitations of traditional numerical methods and significantly improving computational efficiency. However, due to the diversity and complexity of PDE systems, existing neural operators typically rely on a single network architecture, which limits their capacity to fully capture heterogeneous features and complex system dependencies. This constraint poses a bottleneck for large-scale PDE pre-training based on neural operators. To address these challenges, we propose a large-scale PDE pre-trained neural operator based on a nested Mixture-of-Experts (MoE) framework. In particular, the image-level MoE is designed to capture global dependencies, while the token-level Sub-MoE focuses on local dependencies. Our model can selectively activate the most suitable expert networks for a given input, thereby enhancing generalization and transferability. We conduct large-scale pre-training on twelve PDE datasets from diverse sources and successfully transfer the model to downstream tasks. Extensive experiments demonstrate the effectiveness of our approach.

RESULT

ScienceToStartup currently rates this 5.0/10 on the public viability pass. Extensive experiments demonstrate the effectiveness of our approach.

WHY NOW

Neural Operators moved forward this cycle; last verified April 2026. Public score 5.0/10.

Continue into Read for claims, analysis, references, and neighboring papers.

Opportunity summary

Score5.0

PainA specialized nested MoE neural operator for efficient large-scale PDE pre-training and transfer learning.

Evidence0 refs | 0 sources | 17% coverage

Blockermissing authors

Analysis summary

A specialized nested MoE neural operator for efficient large-scale PDE pre-training and transfer learning.

VerifiedSource: PDF linkedPartialPaperPack: 3 of 4 citation fields filledMissingMissing fields: authorsPartialProof: unverified proof status

ARXIV:2602.22059 · NEURAL OPERATORS · SUBMITTED 02 APR · 02:30 UTC · FRESHNESS STALE

VerifiedSource: PDF linkedPartialPaperPack: 3 of 4 citation fields filledMissingMissing fields: authorsPartialProof: unverified proof status

NESTOR: A Nested MOE-based Neural Operator for Large-Scale PDE Pre-Training

arXiv

A specialized nested MoE neural operator for efficient large-scale PDE pre-training and transfer learning.

Blocked on Code›Score5.0Evidence unverified

Opportunity summary

Pain A specialized nested MoE neural operator for efficient large-scale PDE pre-training and transfer learning.

Evidence 0 refs | 0 sources | 17% coverage

Blocker Evidence unverified

Open Build Read PDF Signal Canvas Track

PROBLEM

METHOD

Full abstract

RESULT

ScienceToStartup currently rates this 5.0/10 on the public viability pass. Extensive experiments demonstrate the effectiveness of our approach.

WHY NOW

Neural Operators moved forward this cycle; last verified April 2026. Public score 5.0/10.

Continue into Read for claims, analysis, references, and neighboring papers.

Opportunity summary

Score5.0

PainA specialized nested MoE neural operator for efficient large-scale PDE pre-training and transfer learning.

Evidence0 refs | 0 sources | 17% coverage

Blockermissing authors

Analysis summary

A specialized nested MoE neural operator for efficient large-scale PDE pre-training and transfer learning.

VerifiedSource: PDF linkedPartialPaperPack: 3 of 4 citation fields filledMissingMissing fields: authorsPartialProof: unverified proof status

Paper Pack

10.48550/arXiv.2602.22059

NESTOR: A Nested MOE-based Neural Operator for Large-Scale PDE Pre-Training

A specialized nested MoE neural operator for efficient large-scale PDE pre-training and transfer learning.

Abstract

Source availability

PDF linked

The paper record includes a public PDF URL.

Extraction status

Derived fallback

Read summaries are estimated from adjacent metadata, not verified extraction rows.

Proof status

unverified

0 refs; 0 sources; 17% coverage.

What was readable

linkedon filenot materializedderived fallback32 indexednot indexed

Derived fallback: Estimated from adjacent evidence; not verified from source.

Viability

5.0

Time to MVP

MVP estimate missing

Commercial

No commercial flags on file

Export

Preparing verified analysis

lens / founder

PROBLEM

METHOD

RESULT

ScienceToStartup currently rates this 5.0/10 on the public viability pass. Extensive experiments demonstrate the effectiveness of our approach.

WHY NOW

Neural Operators moved forward this cycle; last verified April 2026. Public score 5.0/10.

Claim map

Abstract-backed public claims while anchored extraction refreshes.

Strong 0Mixed 0Weak 4

Evidencepartial
A specialized nested MoE neural operator for efficient large-scale PDE pre-training and transfer learning. However, due to the diversity and complexity of PDE systems, existing neural operators typically rely on a single network architecture, which limits their capacity to fully capture heterogeneous features and complex system dependencies.
Implicationpartial
Abstract-backed fallback claim; anchored extraction has not materialized a public claim row yet.
Verificationpartial
partial
Evidencepartial
Neural operators have emerged as an efficient paradigm for solving PDEs, overcoming the limitations of traditional numerical methods and significantly improving computational efficiency. However, due to the diversity and complexity of PDE systems, existing neural operators typically rely on a single network architecture, which limits their capacity to fully capture heterogeneous features and complex system dependencies.
Implicationpartial
Abstract-backed fallback claim; anchored extraction has not materialized a public claim row yet.
Verificationpartial
partial
Evidencepartial
ScienceToStartup currently rates this 5.0/10 on the public viability pass. Extensive experiments demonstrate the effectiveness of our approach.
Implicationpartial
Abstract-backed fallback claim; anchored extraction has not materialized a public claim row yet.
Verificationpartial
partial
Evidencepartial
Neural Operators moved forward this cycle; last verified April 2026. Public score 5.0/10.
Implicationpartial
Abstract-backed fallback claim; anchored extraction has not materialized a public claim row yet.
Verificationpartial
partial

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Methods

Materials

PDF linked

Markets

Neural Operators

Competitors

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Competitive landscape

A specialized nested MoE neural operator for efficient large-scale PDE pre-training and transfer learning.

Segment

Neural Operators

Adoption evidence

No public code link in the paper record yet

Commercial read

5.0/10 public viability

Direct

not classified

Adjacent

not classified

Substitute

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Unknown

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Buzz

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References(32)

Mixture-of-Experts Operator Transformer for Large-Scale PDE Pre-Training

2025Hong Wang, Haiyang Xin et al.

HMoE: Heterogeneous Mixture of Experts for Language Modeling

2024An Wang, Xingwu Sun et al.

Poseidon: Efficient Foundation Models for PDEs

2024Maximilian Herde, Bogdan Raoni'c et al.

Unisolver: PDE-Conditional Transformers Towards Universal Neural PDE Solvers

2024Hang Zhou, Yuezhou Ma et al.

DPOT: Auto-Regressive Denoising Operator Transformer for Large-Scale PDE Pre-Training

2024Zhongkai Hao, Chang Su et al.

Multiple Physics Pretraining for Physical Surrogate Models

2023Michael McCabe, Bruno Régaldo-Saint Blancard et al.

CFDBench: A Large-Scale Benchmark for Machine Learning Methods in Fluid Dynamics

2023Yining Luo, Yingfa Chen et al.

ViTO: Vision Transformer-Operator

2023O. Ovadia, Adar Kahana et al.

GNOT: A General Neural Operator Transformer for Operator Learning

2023Zhongkai Hao, Chengyang Ying et al.

PDEBENCH: An Extensive Benchmark for Scientific Machine Learning

2022M. Takamoto, T. Praditia et al.

Towards Multi-spatiotemporal-scale Generalized PDE Modeling

2022Jayesh K. Gupta, Johannes Brandstetter

FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awareness

2022Tri Dao, Daniel Y. Fu et al.

FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operators

2022Jaideep Pathak, Shashank Subramanian et al.

Adaptive Fourier Neural Operators: Efficient Token Mixers for Transformers

2021John Guibas, M. Mardani et al.

Neural Operator: Learning Maps Between Function Spaces

2021Nikola B. Kovachki, Zong-Yi Li et al.

Scaling Vision with Sparse Mixture of Experts

2021C. Riquelme, J. Puigcerver et al.

Choose a Transformer: Fourier or Galerkin

2021Shuhao Cao

Physics-informed machine learning

2021G. Karniadakis, I. Kevrekidis et al.

Learning Transferable Visual Models From Natural Language Supervision

2021Alec Radford, Jong Wook Kim et al.

Switch Transformers: Scaling to Trillion Parameter Models with Simple and Efficient Sparsity

2021W. Fedus, Barret Zoph et al.

Showing 20 of 32 references

CITED BY

No citing papers are indexed in the public S2S graph yet. This is an explicit zero-signal state, not a hidden lookup.

Foundation

none indexed

Extension

Builds On ThisSCNO: Spiking Compositional Neural Operator -- Towards a Neuromorphic Foundation Model for Nuclear PDE Solving

3.0

Builds On ThisLatentMoE: Toward Optimal Accuracy per FLOP and Parameter in Mixture of Experts

3.0

Builds On ThisPiper: Efficient Large-Scale MoE Training via Resource Modeling and Pipelined Hybrid Parallelism

3.0

Builds On ThisEradicating Negative Transfer in Multi-Physics Foundation Models via Sparse Mixture-of-Experts Routing

3.0

Builds On ThisMoEless: Efficient MoE LLM Serving via Serverless Computing

3.0

Builds On ThisNeuro-Symbolic Multitasking: A Unified Framework for Discovering Generalizable Solutions to PDE Families

4.0

Commercially relevant

Higher ViabilityDynaMoE: Dynamic Token-Level Expert Activation with Layer-Wise Adaptive Capacity for Mixture-of-Experts Neural Networks

6.0

Higher ViabilityMoE Lens -- An Expert Is All You Need

7.0

Higher ViabilityLinear-Nonlinear Fusion Neural Operator for Partial Differential Equations

7.0

Higher ViabilityOmniMoE: An Efficient MoE by Orchestrating Atomic Experts at Scale

7.0

Conflicting

none indexed

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Agent drawer

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Developer contracts, payload previews, evidence maps, and run controls stay here instead of the Read, Build, and Track workspace.

Run context

Paper: 2602.22059
Route: /paper/nestor-a-nested-moe-based-neural-operator-for-large-scale-pde-pre-training
Active tab: read
Artifact: nestor-a-nested-moe-based-neural-operator-for-large-scale-pde-pre-training

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API/MCP endpoints

REST paper pack API/api/v1/paper/nestor-a-nested-moe-based-neural-operator-for-large-scale-pde-pre-training/paper-pack
REST build passport API/api/v1/paper/nestor-a-nested-moe-based-neural-operator-for-large-scale-pde-pre-training/build-passport
REST OpenAPI/api/openapi.json
MCP descriptor/api/mcp
MCP resourcesciencetostartup://surfaces/paper-workspace

Tool contracts

paper_packbuild_passportopportunity_kernelforesightsource_proofevidence_state

Payload preview

Inspect payload

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Schema validation

paper-r2 contract: present
JSON-LD twin: SSR emitted
OpenAPI path parity: /api/openapi.json
MCP resource parity: paper-workspace

Job trace

queued: drawer opened by user action
running: inspect or copy payload
succeeded: payload available in SSR
failed: route errors appear in evidence cards

Evidence map

sources used: page freshness, source proof anchors, JSON-LD
missing sources: exposed by PaperPack and EvidenceState chips
derived fallbacks: marked unverified before handoff

Page Freshness

Canonical route, proof status, last verified, refs, sources, and coverage.

Page Freshness

Paper proof surface

Canonical route: /paper/nestor-a-nested-moe-based-neural-operator-for-large-scale-pde-pre-training

stale

Proof freshness: stale
Proof status: unverified
Display score: 5/10
Last proof check: 2026-04-02
Score updated: 2026-04-02
Score fresh until: 2026-05-02
References: 0
Source count: 0
Coverage: 17%

This page is showing the last landed evidence receipt and score bundle because the latest proof data is outside the freshness window.

OpenAlex: pending — this preprint is not yet indexed by OpenAlex.

Agent Handoff

Endpoint list, payload shape, route context, and copyable handoff data.

Agent Handoff

NESTOR: A Nested MOE-based Neural Operator for Large-Scale PDE Pre-Training

Canonical ID nestor-a-nested-moe-based-neural-operator-for-large-scale-pde-pre-training | Route /paper/nestor-a-nested-moe-based-neural-operator-for-large-scale-pde-pre-training

REST example

curl https://sciencetostartup.com/api/v1/agent-handoff/paper/nestor-a-nested-moe-based-neural-operator-for-large-scale-pde-pre-training

MCP example

{
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source_context

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Buildability Receipt

Verdict, compute envelope, blockers, signature state, and receipt links.

Paper proof page receipt window

Watch and verify: NESTOR: A Nested MOE-based Neural Operator for Large-Scale PDE Pre-Training

/buildability/nestor-a-nested-moe-based-neural-operator-for-large-scale-pde-pre-training

Watchwatch

Subject: NESTOR: A Nested MOE-based Neural Operator for Large-Scale PDE Pre-Training

Verdict

Watch

Verdict is Watch because viability or proof quality is intermediate and should be re-evaluated before execution.

Time to first demo

Insufficient data

No first-demo timestamp, owner estimate, or elapsed demo receipt is attached to this surface.

Compute envelope

Structured compute envelope

Insufficient data

No data, compute, hardware, memory, latency, dependency, or serving requirement receipt is attached.

Evidence ids

Receipt path

/buildability/nestor-a-nested-moe-based-neural-operator-for-large-scale-pde-pre-training

Paper ref

nestor-a-nested-moe-based-neural-operator-for-large-scale-pde-pre-training

arXiv id

2602.22059

Freshness

Generated at

2026-04-02T02:30:40.136Z

Evidence freshness

stale

Last verification

2026-04-02T02:30:40.136Z

Sources

References

Coverage

17%

Hash state

Lineage hash

6940c8aa13690dd7b83455b33caee4b74d247004d9a0a4215d19a70b293b42ca

Canonical opportunity-kernel lineage hash.

Signature state

External signature

unsigned_external

No founder, registry, pilot, or production-adoption signature is attached to this receipt.

Verification

not_verified

Verification is blocked until an external signature is provided.

Blockers

Missing: repo_url
Missing: references
Missing: proof_status
Missing: distribution_readiness_scores
Missing: paper_extraction_scorecards
Unknown: distribution readiness has not been computed yet
Unknown: proof verification has not been recorded yet

Verification pending / evidence receipt incomplete

repo_url

references

Missing proof, requirement, signature, approval, adoption, or telemetry fields are blockers and must not be inferred.

Open receipt API receipt Build Loop Signal Canvas Proof divergence Divergence API Brier outcomes API

Source Proof anchors

Visual citations from the paper document graph.

JSON-LD twin

The application/ld+json payload rendered for agents.

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NESTOR: A Nested MOE-based Neural Operator for Large-Scale PDE Pre-Training

NESTOR: A Nested MOE-based Neural Operator for Large-Scale PDE Pre-Training

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