ARXIV:2603.19058 · DATA ASSIMILATION · SUBMITTED 31 MAR · 20:30 UTC · FRESHNESS STALE

VerifiedSource: PDF linkedVerifiedPaperPack: citation fields availablePartialProof: unverified proof status

Adaptive Nonlinear Data Assimilation through P-Spline Triangular Measure Transport

Berent Å. S. Lunde · Maximilian Ramgraber · arXiv

An adaptive algorithm for nonlinear data assimilation that automatically balances model complexity using P-splines and an information criterion.

Ship in 2-4 weeks›Score4.0Evidence unverified

Opportunity summary

Pain An adaptive algorithm for nonlinear data assimilation that automatically balances model complexity using P-splines and an information criterion.

Evidence 0 refs | 0 sources | 33% coverage

Blocker Evidence unverified

Open Build Read PDF Signal Canvas Track

PROBLEM

An adaptive algorithm for nonlinear data assimilation that automatically balances model complexity using P-splines and an information criterion. Linear methods oversimplify the problem, yet fully nonlinear methods are often too expensive to use in…

METHOD

Non-Gaussian statistics are a challenge for data assimilation. Linear methods oversimplify the problem, yet fully nonlinear methods are often too expensive to use in practice.

Full abstract

Non-Gaussian statistics are a challenge for data assimilation. Linear methods oversimplify the problem, yet fully nonlinear methods are often too expensive to use in practice. The best solution usually lies between these extremes. Triangular measure transport offers a flexible framework for nonlinear data assimilation. Its success, however, depends on how the map is parametrized. Too much flexibility leads to overfitting; too little misses important structure. To address this balance, we develop an adaptation algorithm that selects a parsimonious parametrization automatically. Our method uses P-spline basis functions and an information criterion as a continuous measure of model complexity. This formulation enables gradient descent and allows efficient, fine-scale adaptation in high-dimensional settings. The resulting algorithm requires no hyperparameter tuning. It adjusts the transport map to the appropriate level of complexity based on the system statistics and ensemble size. We demonstrate its performance in nonlinear, non-Gaussian problems, including a high-dimensional distributed groundwater model.

RESULT

ScienceToStartup currently rates this 4.0/10 on the public viability pass. This formulation enables gradient descent and allows efficient, fine-scale adaptation in high-dimensional settings. Code availability is flagged in the production record; the public repository…

WHY NOW

Data Assimilation moved forward this cycle; last verified April 2026. Public score 4.0/10. Production flags indicate code availability.

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

Opportunity summary

Score4.0

PainAn adaptive algorithm for nonlinear data assimilation that automatically balances model complexity using P-splines and an information criterion.

Evidence0 refs | 0 sources | 33% coverage

Blockerno shell-level blocker reported

Analysis summary

An adaptive algorithm for nonlinear data assimilation that automatically balances model complexity using P-splines and an information criterion.

VerifiedSource: PDF linkedVerifiedPaperPack: citation fields availablePartialProof: unverified proof status

ARXIV:2603.19058 · DATA ASSIMILATION · SUBMITTED 31 MAR · 20:30 UTC · FRESHNESS STALE

VerifiedSource: PDF linkedVerifiedPaperPack: citation fields availablePartialProof: unverified proof status

Adaptive Nonlinear Data Assimilation through P-Spline Triangular Measure Transport

Berent Å. S. Lunde · Maximilian Ramgraber · arXiv

An adaptive algorithm for nonlinear data assimilation that automatically balances model complexity using P-splines and an information criterion.

Ship in 2-4 weeks›Score4.0Evidence unverified

Opportunity summary

Pain An adaptive algorithm for nonlinear data assimilation that automatically balances model complexity using P-splines and an information criterion.

Evidence 0 refs | 0 sources | 33% coverage

Blocker Evidence unverified

Open Build Read PDF Signal Canvas Track

PROBLEM

METHOD

Non-Gaussian statistics are a challenge for data assimilation. Linear methods oversimplify the problem, yet fully nonlinear methods are often too expensive to use in practice.

Full abstract

RESULT

WHY NOW

Data Assimilation moved forward this cycle; last verified April 2026. Public score 4.0/10. Production flags indicate code availability.

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

Opportunity summary

Score4.0

PainAn adaptive algorithm for nonlinear data assimilation that automatically balances model complexity using P-splines and an information criterion.

Evidence0 refs | 0 sources | 33% coverage

Blockerno shell-level blocker reported

Analysis summary

An adaptive algorithm for nonlinear data assimilation that automatically balances model complexity using P-splines and an information criterion.

VerifiedSource: PDF linkedVerifiedPaperPack: citation fields availablePartialProof: unverified proof status

Paper Pack

10.48550/arXiv.2603.19058

Adaptive Nonlinear Data Assimilation through P-Spline Triangular Measure Transport

An adaptive algorithm for nonlinear data assimilation that automatically balances model complexity using P-splines and an information criterion.

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; 33% coverage.

What was readable

linkedon filenot materializedderived fallback26 indexednot indexed

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

Viability

4.0

Time to MVP

MVP estimate missing

Commercial

code

Export

Preparing verified analysis

lens / founder

PROBLEM

METHOD

Non-Gaussian statistics are a challenge for data assimilation. Linear methods oversimplify the problem, yet fully nonlinear methods are often too expensive to use in practice.

RESULT

WHY NOW

Data Assimilation moved forward this cycle; last verified April 2026. Public score 4.0/10. Production flags indicate code availability.

Claim map

Abstract-backed public claims while anchored extraction refreshes.

Strong 0Mixed 0Weak 4

Evidencepartial
An adaptive algorithm for nonlinear data assimilation that automatically balances model complexity using P-splines and an information criterion. Linear methods oversimplify the problem, yet fully nonlinear methods are often too expensive to use in practice.
Implicationpartial
Abstract-backed fallback claim; anchored extraction has not materialized a public claim row yet.
Verificationpartial
partial
Evidencepartial
Non-Gaussian statistics are a challenge for data assimilation. Linear methods oversimplify the problem, yet fully nonlinear methods are often too expensive to use in practice.
Implicationpartial
Abstract-backed fallback claim; anchored extraction has not materialized a public claim row yet.
Verificationpartial
partial
Evidencepartial
ScienceToStartup currently rates this 4.0/10 on the public viability pass. This formulation enables gradient descent and allows efficient, fine-scale adaptation in high-dimensional settings. Code availability is flagged in the production record; the public repository link still needs proof alignment.
Implicationpartial
Abstract-backed fallback claim; anchored extraction has not materialized a public claim row yet.
Verificationpartial
partial
Evidencepartial
Data Assimilation moved forward this cycle; last verified April 2026. Public score 4.0/10. Production flags indicate code availability.
Implicationpartial
Abstract-backed fallback claim; anchored extraction has not materialized a public claim row yet.
Verificationpartial
partial

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Concepts

not indexed

Methods

Non-Gaussian statistics are a challenge for data assimilation. Linear methods oversimplify the problem, yet fully nonlinear methods are often too expensive to use in practice.

Materials

PDF linked

Markets

Data Assimilation

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Competitive landscape

An adaptive algorithm for nonlinear data assimilation that automatically balances model complexity using P-splines and an information criterion.

Segment

Data Assimilation

Adoption evidence

No public code link in the paper record yet

Commercial read

4.0/10 public viability

Direct

not classified

Adjacent

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Substitute

not classified

Unknown

not classified

Buzz

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References(26)

A friendly introduction to triangular transport

2025M. Ramgraber, Daniel Sharp et al.

An Ensemble Information Filter: Retrieving Markov-information from the SPDE discretisation

2025Berent AAnund Stromnes Lunde

Ensemble transport smoothing. Part II: Nonlinear updates

2022M. Ramgraber, R. Baptista et al.

Practical Smoothing: The Joys of P‐splinesPaul H. C.Eilers and Brian D.MarxCambridge University Press, 2021, xii + 199 pages, $59.99, hardcover ISBN: 978‐1‐1084‐8295‐0

2022K. Podgórski

Scalable Bayesian Transport Maps for High-Dimensional Non-Gaussian Spatial Fields

2021M. Katzfuss, Florian Schäfer

On the Representation and Learning of Monotone Triangular Transport Maps

2020R. Baptista, Y. Marzouk et al.

Sparse Cholesky factorization by Kullback-Leibler minimization

2020Florian Schäfer, M. Katzfuss et al.

Inference and computation with generalized additive models and their extensions

2020S. Wood

Coupling Techniques for Nonlinear Ensemble Filtering

2019Alessio Spantini, R. Baptista et al.

A model-independent iterative ensemble smoother for efficient history-matching and uncertainty quantification in very high dimensions

2018J. White

Data assimilation in the geosciences: An overview of methods, issues, and perspectives

2017A. Carrassi, M. Bocquet et al.

Inference via Low-Dimensional Couplings

2017Alessio Spantini, Daniele Bigoni et al.

An introduction to sampling via measure transport

2016Y. Marzouk, T. Moselhy et al.

Shape constrained additive models

2015N. Pya, S. Wood

Ensemble smoother with multiple data assimilation

2013A. Emerick, A. Reynolds

Asymptotic properties of penalized spline estimators

2009G. Claeskens, T. Krivobokova et al.

Model selection and multimodel inference : a practical information-theoretic approach

2003K. Burnham, David R. Anderson

The Ensemble Kalman Filter: theoretical formulation and practical implementation

2003G. Evensen

An ensemble Kalman smoother for nonlinear dynamics

2000G. Evensen, P. Leeuwen

Evaluating derivatives - principles and techniques of algorithmic differentiation, Second Edition

2000A. Griewank, A. Walther

Showing 20 of 26 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

Prior WorkAdaptive Diffusion Posterior Sampling for Data and Model Fusion of Complex Nonlinear Dynamical Systems

4.0

Prior WorkData-Driven Integration Kernels for Interpretable Nonlocal Operator Learning

4.0

Extension

Builds On ThisLearning Where the Physics Is: Probabilistic Adaptive Sampling for Stiff PDEs

1.0

Builds On ThisAmortized Energy-Based Bayesian Inference

2.0

Builds On ThisPreconditioned One-Step Generative Modeling for Bayesian Inverse Problems in Function Spaces

2.0

Commercially relevant

Higher ViabilityPhysics-informed diffusion models in spectral space

6.0

Higher ViabilityActive Timepoint Selection for Learning Measure-Valued Trajectories

7.0

Higher ViabilityParametric Prior Mapping Framework for Non-stationary Probabilistic Time Series Forecasting

5.0

Higher ViabilityProbabilistic Geometric Alignment via Bayesian Latent Transport for Domain-Adaptive Foundation Models

5.0

Conflicting

Competing ApproachRethinking Forward Processes for Score-Based Data Assimilation in High Dimensions

4.0

Related Resources

What is the role of data assimilation in improving weather simulation models?(question)

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Agent drawer

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Run context

Paper: 2603.19058
Route: /paper/adaptive-nonlinear-data-assimilation-through-p-spline-triangular-measure-transport
Active tab: read
Artifact: adaptive-nonlinear-data-assimilation-through-p-spline-triangular-measure-transport

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API/MCP endpoints

REST paper pack API/api/v1/paper/adaptive-nonlinear-data-assimilation-through-p-spline-triangular-measure-transport/paper-pack
REST build passport API/api/v1/paper/adaptive-nonlinear-data-assimilation-through-p-spline-triangular-measure-transport/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/adaptive-nonlinear-data-assimilation-through-p-spline-triangular-measure-transport

stale

Proof freshness: stale
Proof status: unverified
Display score: 4/10
Last proof check: 2026-03-31
Score updated: 2026-04-02
Score fresh until: 2026-05-02
References: 0
Source count: 0
Coverage: 33%

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

Adaptive Nonlinear Data Assimilation through P-Spline Triangular Measure Transport

Canonical ID adaptive-nonlinear-data-assimilation-through-p-spline-triangular-measure-transport | Route /paper/adaptive-nonlinear-data-assimilation-through-p-spline-triangular-measure-transport

REST example

curl https://sciencetostartup.com/api/v1/agent-handoff/paper/adaptive-nonlinear-data-assimilation-through-p-spline-triangular-measure-transport

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

Not build-ready: Adaptive Nonlinear Data Assimilation through P-Spline Triangular Measure Transport

/buildability/adaptive-nonlinear-data-assimilation-through-p-spline-triangular-measure-transport

Ignoreblocked

Subject: Adaptive Nonlinear Data Assimilation through P-Spline Triangular Measure Transport

Verdict

Ignore

Verdict is Ignore because current viability and proof state do not clear the buildability gate.

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/adaptive-nonlinear-data-assimilation-through-p-spline-triangular-measure-transport

Paper ref

adaptive-nonlinear-data-assimilation-through-p-spline-triangular-measure-transport

arXiv id

2603.19058

Freshness

Generated at

2026-03-31T20:30:20.275Z

Evidence freshness

stale

Last verification

2026-03-31T20:30:20.275Z

Sources

References

Coverage

33%

Hash state

Lineage hash

82c052a382886ddaf5774728d271d9346a584ada81831beff25863ef6efc715e

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: distribution_readiness_scores
Missing: paper_extraction_scorecards
Unknown: distribution readiness has not been computed 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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Adaptive Nonlinear Data Assimilation through P-Spline Triangular Measure Transport

Adaptive Nonlinear Data Assimilation through P-Spline Triangular Measure Transport

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