# Transfer of a Multi-Fidelity Bayesian Uncertainty Quantification Framework to Large-Eddy Simulation for Systematic Error Propagation

## Metadata

- **SPORE ID**: SPR-2026-6BAF
- **Domaines**: Computational Physics and Python Applications x Fluid Dynamics and Turbulent Flows
- **Date de generation**: 2026-08-26
- **Panel consensus score**: 6.6/10
- **Novelty score**: 0.7/1.0
- **Panel verdict**: publish_brief

## Abstract

If the QUEENS multi-fidelity Bayesian UQ framework is applied to LES of turbulent flows, then the uncertainty in quantities of interest (e.g., Nusselt number) can be quantified with a computational cost reduced by at least an order of magnitude compared to brute-force Monte Carlo, because multi-fidelity surrogates exploit correlations between low- and high-fidelity LES runs.

The proposed mechanism involves 4 causal steps: (1) LES model inputs (SGS coefficients, grid resolution, inlet conditions) are treat -> (2) Multi-fidelity Gaussian process surrogates are trained on a set of LES runs at d -> (3) Bayesian inference or polynomial chaos expansion is used to propagate input unce -> (4) The resulting uncertainty estimates are compared to reference data (e.g., DNS or.

Literature grounding on 9 verified references yields a novelty score of 0.7 (novel). A 3-phase experimental protocol (budget: €20k-80k, timeline: 8-14 months) is proposed, starting with in silico validation. A panel of 5 expert reviewers reached a consensus score of 6.6/10.

## 1. Hypothese et mecanisme propose

### 1.1 Formulation formelle

If the QUEENS multi-fidelity Bayesian UQ framework is applied to LES of turbulent flows, then the uncertainty in quantities of interest (e.g., Nusselt number) can be quantified with a computational cost reduced by at least an order of magnitude compared to brute-force Monte Carlo, because multi-fidelity surrogates exploit correlations between low- and high-fidelity LES runs.

### 1.2 Variables

**Variables independantes :**

| Variable | Type | Plage | Unite |
|----------|------|-------|-------|
| SGS model coefficient (e.g., Smagorinsky constant Cs) | continuous | 0.1-0.25 | dimensionless |
| Grid resolution parameter (e.g., number of grid points N) | continuous | 1e6-1e8 | count |
| Inlet perturbation amplitude (e.g., turbulent intensity) | continuous | 0.01-0.1 | dimensionless |

**Variables dependantes :**

| Variable | Type | Direction attendue | Unite |
|----------|------|-------------------|-------|
| Nusselt number (Nu) | continuous | non-monotonic | dimensionless |
| Vortex shedding frequency (Strouhal number St) | continuous | non-monotonic | dimensionless |

### 1.3 Chaine causale

1. Step 1: LES model inputs (SGS coefficients, grid resolution, inlet conditions) are treated as uncertain parameters with specified probability distributions.
1. Step 2: Multi-fidelity Gaussian process surrogates are trained on a set of LES runs at different fidelities (e.g., coarse vs. fine grid) to approximate the mapping from inputs to QoIs.
1. Step 3: Bayesian inference or polynomial chaos expansion is used to propagate input uncertainties through the surrogate, yielding probability distributions of QoIs.
1. Step 4: The resulting uncertainty estimates are compared to reference data (e.g., DNS or experiments) to validate the UQ framework's accuracy.

**Hypotheses cles :**

- The LES model is a deterministic function of the uncertain inputs, and the input distributions are known or can be estimated.
- Multi-fidelity surrogates can accurately capture the input-output relationship with a limited number of high-fidelity runs.
- The QoIs are smooth functions of the inputs within the specified ranges.

**Inconnues identifiees :**

- The optimal choice of multi-fidelity surrogate (e.g., deep GP vs. linear autoregressive) for LES is unknown.
- The impact of correlated input uncertainties on the UQ results is not fully understood.

### 1.4 Conditions aux limites

- **Reynolds number based on characteristic length must be in the range 10^4 to 10^6** — Within this range, LES is applicable and wall-modeled LES is commonly used; outside, DNS or RANS may be more appropriate.
- **The flow must be incompressible or weakly compressible (Mach number < 0.3)** — The QUEENS framework and LES solvers used are typically validated for incompressible flows; compressibility effects may introduce additional uncertainties not captured.
- **The computational domain must be large enough to capture large-scale turbulent structures (e.g., at least 10 boundary layer thicknesses in streamwise direction)** — Insufficient domain size can lead to spurious confinement effects, violating the assumption of a statistically stationary turbulent flow.

### 1.5 Cadre theorique

Bayesian uncertainty quantification and multi-fidelity surrogate modeling

## 2. Etat de l'art et positionnement

### 2.1 Travaux les plus proches

- **[2018] Systematic study of accuracy of wall-modeled large eddy simulation using uncertainty quantification techniques** — [10.1016/j.compfluid.2019.03.025](https://doi.org/10.1016/j.compfluid.2019.03.025)
  - Similarite: related
  - Difference cle: This paper applies UQ to wall-modeled LES but focuses on accuracy assessment, not on transferring a general UQ framework like QUEENS to LES for systematic error propagation.
- **[2023] Sensitivity analysis of wall-modeled large-eddy simulation for separated turbulent flow** — [10.1016/j.jcp.2024.112948](https://doi.org/10.1016/j.jcp.2024.112948)
  - Similarite: related
  - Difference cle: This paper performs sensitivity analysis of LES to numerical choices, but does not propose a formal UQ framework transfer from computational physics.
- **[2018] Effect of grid resolution on large eddy simulation of wall-bounded turbulence** — [10.1063/1.5025131](https://doi.org/10.1063/1.5025131)
  - Similarite: related
  - Difference cle: This paper studies grid resolution effects but does not employ a formal UQ framework.

### 2.2 Base de preuves

- **[2018] Systematic study of accuracy of wall-modeled large eddy simulation using uncertainty quantification techniques** — [10.1016/j.compfluid.2019.03.025](https://doi.org/10.1016/j.compfluid.2019.03.025)
  - Type: direct | Citations: 41
  - Directly applies UQ techniques to LES, demonstrating the feasibility of systematic error quantification.
- **[2023] Sensitivity analysis of wall-modeled large-eddy simulation for separated turbulent flow** — [10.1016/j.jcp.2024.112948](https://doi.org/10.1016/j.jcp.2024.112948)
  - Type: direct | Citations: 26
  - Shows sensitivity of LES to SGS models, mesh resolution, and boundary conditions, highlighting the need for systematic UQ.
- **[2018] Effect of grid resolution on large eddy simulation of wall-bounded turbulence** — [10.1063/1.5025131](https://doi.org/10.1063/1.5025131)
  - Type: indirect | Citations: 58
  - Demonstrates grid resolution sensitivity in LES, a key source of numerical error that UQ could quantify.
- **[2019] MULTI-FIDELITY MODELING OF PROBABILISTIC AERODYNAMIC DATABASES FOR USE IN AEROSPACE ENGINEERING** — [10.1615/int.j.uncertaintyquantification.2020032841](https://doi.org/10.1615/int.j.uncertaintyquantification.2020032841)
  - Type: indirect | Citations: 27
  - Shows multi-fidelity UQ methods applied to aerodynamic simulations, analogous to LES, supporting the feasibility of cost-effective UQ.
- **[2023] Enhanced multi-fidelity modelling for digital twin and uncertainty quantification** — [10.48550/arXiv.2306.14430](https://doi.org/10.48550/arXiv.2306.14430)
  - Type: indirect | Citations: 24
  - Demonstrates multi-fidelity surrogate models for digital twins, which can be adapted for LES UQ.
- **[2024] Multi-fidelity Gaussian process surrogate modeling for regression problems in physics** — [10.1088/2632-2153/ad7ad5](https://doi.org/10.1088/2632-2153/ad7ad5)
  - Type: indirect | Citations: 24
  - Provides methods for multi-fidelity surrogate modeling that can be applied to LES to reduce computational cost.
- **[2020] Bayesian learning of orthogonal embeddings for multi-fidelity Gaussian Processes** — [10.1016/j.cma.2021.114147](https://doi.org/10.1016/j.cma.2021.114147)
  - Type: indirect | Citations: 21
  - Presents advanced multi-fidelity GP methods that could be used for LES UQ.
- **[2019] Deep Gaussian Processes for Multi-fidelity Modeling**
  - Type: indirect | Citations: 130
  - Provides a deep multi-fidelity model that can capture complex relationships between fidelities, applicable to LES.

### 2.3 Contre-preuves et limitations connues

- **[minor] Large Eddy Simulation of Premixed Combustion: Sensitivity to Subgrid Scale Velocity Modeling**
  - LES results are sensitive to SGS velocity models, but the paper does not address formal UQ; it may indicate that model-form uncertainty is significant and difficult to quantify.

### 2.4 Evaluation de nouveaute

- **Score**: 0.7/1.0
- **Verdict**: novel

## 3. Predictions falsifiables

| # | Prediction | Borne quantitative | Methode | H0 | Test statistique |
|---|-----------|-------------------|---------|-----|-----------------|
| 1 | Applying QUEENS multi-fidelity UQ to LES will yield a 90% confidence interval for the Nusselt number with a width of ±5% of the mean, using at least 10 times fewer high-fidelity LES runs than brute-force Monte Carlo. | Reduction of at least 10-fold in number of high-fidelity LES runs required to achieve a coefficient of variation of 0.05 in the Nusselt number. | Compare the number of high-fidelity LES runs needed for QUEENS-based UQ vs. Monte Carlo to achieve the same confidence interval width in Nu. | H0: The number of high-fidelity LES runs required for QUEENS-based UQ is not significantly less than that for Monte Carlo (i.e., ratio ≤ 1). | Paired t-test on the ratio of runs across multiple test cases, alpha=0.05 |
| 2 | The uncertainty in the Strouhal number, as quantified by the standard deviation, will be less than 0.02 when input uncertainties are propagated using QUEENS, and this value will be within 20% of the uncertainty obtained from a brute-force Monte Carlo with 1000 samples. | Standard deviation of St ≤ 0.02, and within 20% of Monte Carlo reference. | Compute St from LES time series for each sample; estimate standard deviation from surrogate predictions and from Monte Carlo. | H0: The standard deviation of St from QUEENS is not significantly different from that of Monte Carlo (i.e., difference > 20%). | Two-sample F-test for variances, alpha=0.05 |

## 4. Protocole experimental

**Timeline globale**: 8-14 months
**Budget global**: €20k-80k

### 4.1 Phase 1 — In Silico Validation

**Objectif**: Determine if the QUEENS multi-fidelity Bayesian UQ framework can accurately predict QoIs (Nu, St) with reduced computational cost compared to Monte Carlo, using existing LES data and synthetic test cases.

**Methodologie**: 1. Acquire existing LES datasets for turbulent flows (e.g., channel flow, flow over a cylinder) with varying grid resolutions and SGS coefficients. 2. Implement a multi-fidelity surrogate (e.g., linear autoregressive GP) using QUEENS or GPyTorch. 3. Train surrogates on subsets of the data, simulating low- and high-fidelity runs. 4. Propagate input uncertainties (Cs, N, inlet turbulence) via Monte Carlo on the surrogate and compare to brute-force Monte Carlo on the actual LES solver (if feasible) or to reference DNS/experimental data. 5. Compute metrics: number of high-fidelity runs needed to achieve a 90% CI width of ±5% of mean Nu, and standard deviation of St. 6. Perform sensitivity analysis to identify key parameters.

- Cout: €500-2000
- Duree: 4-6 weeks
- Equipement: High-performance computing cluster (optional for initial tests)
- Logiciels: QUEENS (or GPyTorch, scikit-learn), OpenFOAM or Nek5000 for LES (if needed), Python with numpy, scipy, matplotlib

**Criteres de succes :**

- Reduction in number of high-fidelity LES runs: At least 10-fold reduction compared to Monte Carlo to achieve same CI width (90% CI ±5% of mean Nu)
- Accuracy of St uncertainty: Standard deviation of St ≤ 0.02 and within 20% of Monte Carlo reference (1000 samples)

- **GO**: Both success criteria met: at least 10-fold reduction in high-fidelity runs and St uncertainty within 20% of Monte Carlo.
- **NO-GO**: Reduction factor < 5 or St uncertainty deviates > 30% from Monte Carlo.
- **PIVOT**: If surrogate accuracy is poor (e.g., R^2 < 0.8), consider alternative multi-fidelity methods (e.g., deep GP) or refine input distributions.

### 4.2 Phase 2 — Minimal Experimental Validation

**Objectif**: Validate the QUEENS framework on a minimal set of actual LES runs for a canonical turbulent flow (e.g., flow over a cylinder at Re=10^4-10^5) to confirm the predicted reduction in computational cost and accuracy of UQ.

**Methodologie**: 1. Select a canonical test case: turbulent flow over a circular cylinder at Re=10^4 (subcritical regime) with incompressible flow. 2. Define input uncertainties: Cs (0.1-0.25), grid resolution (N: 1e6-1e7), inlet turbulence intensity (0.01-0.1). 3. Set up LES solver (e.g., OpenFOAM) with wall-modeled LES. 4. Run a small set of high-fidelity LES simulations (e.g., 10-20 runs) at different input combinations, and a larger set of low-fidelity runs (e.g., 50-100) with coarser grids. 5. Train multi-fidelity surrogate using QUEENS on these runs. 6. Perform UQ: propagate input distributions through surrogate to obtain distributions of Nu and St. 7. Compare with brute-force Monte Carlo using a limited number of high-fidelity runs (e.g., 100) to estimate the reference uncertainty. 8. Assess the reduction in high-fidelity runs required to achieve the same CI width.

- Cout: €2k-15k
- Duree: 1-3 months
- Equipement: High-performance computing cluster (e.g., 100+ cores)
- Logiciels: OpenFOAM (or Nek5000), QUEENS (or GPyTorch), Python with numpy, scipy, matplotlib

**Criteres de succes :**

- Reduction in high-fidelity runs: At least 10-fold reduction compared to Monte Carlo to achieve same CI width (90% CI ±5% of mean Nu)
- Accuracy of St uncertainty: Standard deviation of St ≤ 0.02 and within 20% of Monte Carlo reference (using 100 high-fidelity runs)

- **GO**: Both success criteria met: at least 10-fold reduction and St uncertainty within 20%.
- **NO-GO**: Reduction factor < 5 or St uncertainty deviates > 30% from Monte Carlo.
- **PIVOT**: If surrogate accuracy is poor, consider increasing number of high-fidelity runs or using a different multi-fidelity approach (e.g., nonlinear autoregressive).

### 4.3 Phase 3 — Full Experimental Protocol

**Objectif**: Perform a comprehensive validation of the QUEENS multi-fidelity UQ framework for LES across multiple turbulent flow cases, producing publishable results that demonstrate the framework's accuracy and computational efficiency.

**Methodologie**: 1. Select a suite of test cases: (a) turbulent channel flow at Re_tau=1000, (b) flow over a backward-facing step at Re=10^5, (c) flow over a cylinder at Re=10^5. 2. For each case, define input uncertainties (Cs, N, inlet turbulence) based on literature and expert judgment. 3. Generate training data: run a set of low-fidelity LES (coarse grids) and high-fidelity LES (fine grids) at various input combinations. Use design of experiments (e.g., Latin hypercube) to sample inputs. 4. Train multi-fidelity surrogates (e.g., linear autoregressive GP, deep GP) using QUEENS. 5. Perform UQ: propagate input distributions through surrogates to obtain distributions of Nu and St. 6. Validate against reference data: DNS or experimental data for each case. 7. Compare with brute-force Monte Carlo (using a sufficient number of high-fidelity runs, e.g., 500-1000) to assess accuracy and computational cost. 8. Perform sensitivity analysis to identify key parameters. 9. Document results and prepare publication.

- Cout: €15k-100k+
- Duree: 6-12 months
- Equipement: High-performance computing cluster (e.g., 1000+ cores)
- Logiciels: OpenFOAM or Nek5000, QUEENS (or GPyTorch), Python with numpy, scipy, matplotlib, Paraview for visualization

**Criteres de succes :**

- Reduction in high-fidelity runs: At least 10-fold reduction compared to Monte Carlo to achieve same CI width (90% CI ±5% of mean Nu) for each test case
- Accuracy of St uncertainty: Standard deviation of St ≤ 0.02 and within 20% of Monte Carlo reference (using 1000 high-fidelity runs) for each test case
- Agreement with reference data: Predicted mean Nu and St within 5% of DNS/experimental values, and 90% CI covers the reference value

- **GO**: All success criteria met for at least two of the three test cases.
- **NO-GO**: Reduction factor < 5 or St uncertainty deviates > 30% from Monte Carlo for all cases.
- **PIVOT**: If surrogate accuracy is poor, consider alternative multi-fidelity methods or increase number of high-fidelity runs; if computational cost is prohibitive, reduce number of test cases.

### 4.4 Quick start : comment demarrer aujourd'hui

- **Peut demarrer maintenant**: Oui
- **Premiere action**: Download and install QUEENS (or GPyTorch) and acquire public LES datasets from JHTDB or NASA Turbulence Modeling Resource.
- **Outils**: QUEENS (or GPyTorch), Python with numpy, scipy, matplotlib, JHTDB access
- **Donnees ouvertes**: Johns Hopkins Turbulence Databases (JHTDB), NASA Turbulence Modeling Resource

## 5. Analyse d'impact

### 5.1 Impact scientifique

Novelty score: 0.7/1.0 (novel)

### 5.2 Applications industrielles et marche

**Score industriel**: 7.5/10

**Forces :**
- Clear market need in aerospace, energy, and automotive sectors where LES is used for design and certification, and where quantifying uncertainty is critical for safety and performance. Companies like Airbus, Rolls-Royce, and Siemens Energy are investing in UQ for CFD.
- Multi-fidelity Bayesian UQ offers a significant computational cost reduction (at least 10x) compared to brute-force Monte Carlo, enabling practical UQ for complex turbulent flows that are otherwise intractable. This provides a strong competitive advantage for early adopters.

**Faiblesses :**
- The main barrier is the need for domain expertise in both LES and Bayesian UQ, which may slow adoption in industrial settings where such skills are scarce. Integration with existing LES solvers and workflows will require customization.
- The commercial timeline is uncertain: while the protocol suggests 8-14 months for validation, achieving a production-ready product with robust performance across multiple flow cases may take longer, potentially 2-3 years, which could impact ROI expectations.

**Recommandation**: Proceed with Phase 1 validation to confirm the technical feasibility. Simultaneously, engage with potential industrial partners (e.g., via joint research projects) to understand their specific UQ needs and co-develop use cases. This will help tailor the solution and build a business case. If Phase 1 is successful, consider spinning off a specialized software tool or service offering, leveraging the QUEENS framework as a unique selling point.

### 5.3 Opportunites de financement

| Programme | Agence | Fit | Budget type | Taux succes |
|-----------|--------|-----|-------------|-------------|
| ANR JCJC (Jeunes Chercheuses et Jeunes Chercheurs) 2026 | Agence Nationale de la Recherche (France) | 0.85 | €150k-250k | ~15% |
| ERC Starting Grant 2026 | European Research Council | 0.7 | €1.5M-2.5M | ~10% |
| PRACE (Partnership for Advanced Computing in Europe) Tier-1 Access | PRACE aisbl | 0.9 | Not a direct grant; provides computational resources | ~40% |

- **ANR JCJC (Jeunes Chercheuses et Jeunes Chercheurs) 2026** (Agence Nationale de la Recherche (France)): This program supports early-career researchers and is ideal for a proof-of-concept project. The budget is sufficient for a postdoc and computing costs, and the focus on methodological innovation aligns well.
- **ERC Starting Grant 2026** (European Research Council): If the initial validation succeeds, this could be positioned as a high-risk/high-gain project to develop a comprehensive UQ framework for LES. The ERC values novelty and ambition, and the multi-fidelity approach has potential for broad impact.
- **PRACE (Partnership for Advanced Computing in Europe) Tier-1 Access** (PRACE aisbl): The project requires significant computational resources for LES runs. PRACE provides access to supercomputers, which is essential for the high-fidelity simulations. This is a complementary resource to secure alongside funding.

**Recommandation financement**: Target the ANR JCJC (Jeunes Chercheuses et Jeunes Chercheurs) for a 24-month project to develop the framework and validate on canonical cases, while simultaneously applying for a PRACE (Partnership for Advanced Computing in Europe) allocation for computational resources. If initial results are promising, leverage them for an ERC Starting Grant in the next call.

## 6. Panel Review Summary

| Reviewer | Score | Verdict | Point cle |
|----------|-------|---------|-----------|
| methodologist | 6.5/10 | weak_accept | The protocol clearly defines falsifiable predictions with quantitative bounds (e.g., 10-fold reduction in high-fidelity runs, St uncertainty within 20% of Monte Carlo) and specifies statistical null hypotheses, which is commendable for rigorous testing. |
| domain_expert | 7.8/10 | accept | The hypothesis clearly identifies a practical need (systematic UQ in LES) and proposes a concrete solution (transfer of QUEENS framework) that leverages mature multi-fidelity surrogate methods, aligning with current trends in UQ for computational fluid dynamics. |
| contrarian | 4.0/10 | weak_reject | The multi-fidelity Bayesian UQ approach is a promising direction to reduce computational cost for LES uncertainty quantification, as it leverages correlations between different fidelity levels. |
| industrialist | 7.5/10 | accept | Clear market need in aerospace, energy, and automotive sectors where LES is used for design and certification, and where quantifying uncertainty is critical for safety and performance. Companies like Airbus, Rolls-Royce, and Siemens Energy are investing in UQ for CFD. |
| funding_strategist | 7.2/10 | accept | Strong methodological novelty: transferring a multi-fidelity Bayesian UQ framework to LES is timely and addresses a critical need for systematic error propagation in computational fluid dynamics. |

**Consensus score**: 6.6/10
**Verdict final**: publish_brief

### 6.1 Consensus

- The hypothesis addresses a critical need for systematic UQ in LES, and the multi-fidelity Bayesian approach is promising for reducing computational cost.
- The phased validation approach with clear GO/NO-GO criteria is well-structured and de-risks the project.

### 6.2 Points de desaccord

- The methodologist and contrarian question the statistical rigor and the assumption of deterministic LES, while the domain expert and industrialist see the approach as feasible and valuable.
- The contrarian argues that the chaotic nature of LES and model form uncertainty may invalidate the surrogate approach, while others believe these can be managed with careful design.

### 6.3 Critical path

The success hinges on demonstrating that the multi-fidelity surrogate can accurately capture the input-output relationship for chaotic LES, and that the computational cost reduction is real in practice, which requires a rigorous validation on a canonical test case.

**Recommandation finale**: The panel is cautiously optimistic about the hypothesis. The methodological concerns about statistical power and bias must be addressed in the brief, but the overall approach is sound and timely. We recommend publishing the brief to proceed with Phase 1 validation, with the expectation that the protocol will be refined based on initial results.

## 7. Gap Manifest residuel

### 7.1 Data gaps

- Need for explicit demonstration of QUEENS applied to LES, as no paper directly uses QUEENS.
- Need for handling categorical uncertainties (e.g., SGS model choice) in UQ frameworks.

### 7.2 Competence gaps

- Phase 1: Bayesian statistics
- Phase 1: Gaussian processes
- Phase 1: LES simulations
- Phase 1: Python programming
- Phase 2: LES simulation expertise
- Phase 2: HPC usage
- Phase 2: Bayesian UQ
- Phase 2: Python programming
- Phase 3: LES simulation expertise
- Phase 3: Bayesian UQ
- Phase 3: Multi-fidelity modeling
- Phase 3: HPC usage
- Phase 3: Scientific writing

### 7.3 Epistemic gaps

- The optimal choice of multi-fidelity surrogate (e.g., deep GP vs. linear autoregressive) for LES is unknown.
- The impact of correlated input uncertainties on the UQ results is not fully understood.

## References

[1] S. Rezaeiravesh, T. Mukha, et al. (2018). *Systematic study of accuracy of wall-modeled large eddy simulation using uncertainty quantification techniques*. DOI: [10.1016/j.compfluid.2019.03.025](https://doi.org/10.1016/j.compfluid.2019.03.025)
[2] Di Zhou, H. Bae (2023). *Sensitivity analysis of wall-modeled large-eddy simulation for separated turbulent flow*. DOI: [10.1016/j.jcp.2024.112948](https://doi.org/10.1016/j.jcp.2024.112948)
[3] S. Rezaeiravesh, Mattias Liefvendahl Division of Scientific Computing, et al. (2018). *Effect of grid resolution on large eddy simulation of wall-bounded turbulence*. DOI: [10.1063/1.5025131](https://doi.org/10.1063/1.5025131)
[4] Jayant Mukhopadhaya, Brian T. Whitehead, et al. (2019). *MULTI-FIDELITY MODELING OF PROBABILISTIC AERODYNAMIC DATABASES FOR USE IN AEROSPACE ENGINEERING*. DOI: [10.1615/int.j.uncertaintyquantification.2020032841](https://doi.org/10.1615/int.j.uncertaintyquantification.2020032841)
[5] A. Desai, N. Navaneeth, et al. (2023). *Enhanced multi-fidelity modelling for digital twin and uncertainty quantification*. DOI: [10.48550/arXiv.2306.14430](https://doi.org/10.48550/arXiv.2306.14430)
[6] Kislaya Ravi, Vladyslav Fediukov, et al. (2024). *Multi-fidelity Gaussian process surrogate modeling for regression problems in physics*. DOI: [10.1088/2632-2153/ad7ad5](https://doi.org/10.1088/2632-2153/ad7ad5)
[7] Panagiotis Tsilifis, Piyush Pandita, et al. (2020). *Bayesian learning of orthogonal embeddings for multi-fidelity Gaussian Processes*. DOI: [10.1016/j.cma.2021.114147](https://doi.org/10.1016/j.cma.2021.114147)
[8] Kurt Cutajar, Mark Pullin, et al. (2019). *Deep Gaussian Processes for Multi-fidelity Modeling*.
[9] I. Langella, N. Swaminathan, et al. (2017). *Large Eddy Simulation of Premixed Combustion: Sensitivity to Subgrid Scale Velocity Modeling*. DOI: [10.1080/00102202.2016.1193496](https://doi.org/10.1080/00102202.2016.1193496)

## Annexes

### A. Detailed Reviewer Reports

#### Methodologist

- **Score**: 6.5/10 | **Verdict**: weak_accept | **Confidence**: 0.8
- **Strengths**: The protocol clearly defines falsifiable predictions with quantitative bounds (e.g., 10-fold reduction in high-fidelity runs, St uncertainty within 20% of Monte Carlo) and specifies statistical null hypotheses, which is commendable for rigorous testing.; The phased approach (in silico, minimal, full) allows for iterative validation and risk mitigation, with explicit GO/NO-GO criteria and pivot strategies, enhancing the practical feasibility of the study.
- **Weaknesses**: The protocol lacks a detailed power analysis: it does not specify the number of samples needed to detect the claimed reduction in high-fidelity runs with adequate statistical power, nor does it account for variability in the reduction factor across test cases.; Potential biases are not systematically addressed: selection bias in choosing existing LES datasets (Phase 1) and test cases (Phase 3) may favor the framework; confirmation bias could arise from subjective interpretation of surrogate accuracy; measurement bias in estimating St from LES time series is not discussed.; The protocol does not include blinding or independent validation of the surrogate predictions against a held-out set of high-fidelity runs, which is critical for assessing overfitting and generalizability.
- **Questions**: How will you determine the number of high-fidelity runs required for the Monte Carlo reference to achieve a stable estimate of the 90% CI width? What is the margin of error on this estimate, and how does it affect the comparison with QUEENS?; What specific measures will you take to mitigate selection bias in choosing test cases and datasets? Will you pre-register the test cases and success criteria before seeing results?; How will you handle the non-monotonic relationship between inputs (e.g., Cs) and QoIs (Nu, St) in the multi-fidelity surrogate? Have you considered using non-stationary kernels or other methods to capture this behavior?
- **Recommendation**: The protocol is well-structured with clear falsifiable predictions and a phased approach, but it requires more rigorous statistical planning and bias mitigation. I recommend revising the protocol to include a formal power analysis, pre-registration of test cases and criteria, and a validation strategy using held-out data. With these improvements, the study could provide strong evidence for the effectiveness of the multi-fidelity UQ framework.

#### Domain Expert

- **Score**: 7.8/10 | **Verdict**: accept | **Confidence**: 0.85
- **Strengths**: The hypothesis clearly identifies a practical need (systematic UQ in LES) and proposes a concrete solution (transfer of QUEENS framework) that leverages mature multi-fidelity surrogate methods, aligning with current trends in UQ for computational fluid dynamics.; The mechanistic steps are logically structured and grounded in established UQ methodologies (e.g., GP surrogates, Bayesian inference), and the evidence base includes recent, relevant studies that demonstrate the feasibility of both UQ in LES and multi-fidelity modeling in similar contexts.
- **Weaknesses**: The hypothesis assumes that LES model inputs can be treated as independent random variables with known distributions, but in practice, input uncertainties are often correlated and poorly characterized, which could undermine the accuracy of the UQ results.; The claim of 'at least an order of magnitude reduction in computational cost' is not rigorously justified; the actual speedup depends on the correlation between fidelities and the complexity of the surrogate, which are not quantified in the hypothesis.; The evidence base lacks direct applications of multi-fidelity Bayesian UQ to LES; most cited works are either UQ on LES without multi-fidelity or multi-fidelity on other applications, leaving a gap in demonstrating the specific integration.
- **Questions**: How would the framework handle correlated input uncertainties (e.g., between SGS coefficients and grid resolution) that are common in LES, and what impact would that have on the accuracy of the propagated uncertainty?; What is the expected computational cost reduction in practice, given that training a multi-fidelity surrogate itself requires a set of LES runs at different fidelities, and how does this compare to brute-force Monte Carlo for a typical turbulent flow problem?; How would the framework validate the uncertainty estimates against DNS or experimental data, and what metrics would be used to assess the quality of the UQ predictions (e.g., coverage probability, calibration)?
- **Recommendation**: The hypothesis is promising and well-aligned with current research directions, but it requires further specification of the input uncertainty characterization and a more quantitative analysis of the computational savings. I recommend accepting it as a basis for a research proposal, with the suggestion to include a pilot study on a canonical turbulent flow to demonstrate the feasibility and cost benefits.

#### Contrarian

- **Score**: 4.0/10 | **Verdict**: weak_reject | **Confidence**: 0.85
- **Strengths**: The multi-fidelity Bayesian UQ approach is a promising direction to reduce computational cost for LES uncertainty quantification, as it leverages correlations between different fidelity levels.; The hypothesis is specific and testable, with clear predictions for the Nusselt number and Strouhal number, and a defined baseline (Monte Carlo) for comparison.
- **Weaknesses**: FAIL REASON #1: The assumption that LES is a deterministic function of the uncertain inputs is flawed. LES is inherently chaotic and sensitive to initial conditions; small perturbations in inputs can lead to divergent flow states, making the input-output mapping non-smooth and non-deterministic. This violates the smoothness assumption of Gaussian process surrogates, likely leading to poor surrogate accuracy and unreliable uncertainty estimates.; FAIL REASON #2: The hypothesis does not account for model form uncertainty. LES itself is an approximation; even with perfect input distributions, the surrogate will propagate only input uncertainty, not the structural error of the LES model. The comparison to DNS/experiments may show large discrepancies that are not due to input uncertainty, making the UQ results misleading and potentially invalid.; FAIL REASON #3: The claimed order-of-magnitude reduction in computational cost is optimistic. Multi-fidelity methods require a sufficient number of high-fidelity runs to anchor the surrogate, and for turbulent flows, the number of high-fidelity LES runs needed to capture the variability may still be large. Additionally, the cost of training the surrogate and performing Bayesian inference may offset the savings, especially for complex geometries and high Reynolds numbers.
- **Questions**: How do you plan to handle the chaotic nature of LES? Specifically, how will you ensure that the LES runs are deterministic with respect to the uncertain inputs, and how will you address the sensitivity to initial conditions that can lead to different flow realizations for the same input parameters?; What is the actual computational cost of training the multi-fidelity surrogate and performing Bayesian inference for a realistic LES case? Can you provide a detailed cost breakdown showing that the total cost (including surrogate training and inference) is indeed an order of magnitude lower than brute-force Monte Carlo?
- **Recommendation**: To strengthen the hypothesis, the authors should demonstrate the method on a simpler test case where LES is more deterministic (e.g., forced turbulence) and quantify the impact of model form uncertainty. They should also provide a detailed cost analysis and compare the surrogate predictions against a large Monte Carlo reference to validate the claimed accuracy and cost reduction.

#### Industrialist

- **Score**: 7.5/10 | **Verdict**: accept | **Confidence**: 0.75
- **Strengths**: Clear market need in aerospace, energy, and automotive sectors where LES is used for design and certification, and where quantifying uncertainty is critical for safety and performance. Companies like Airbus, Rolls-Royce, and Siemens Energy are investing in UQ for CFD.; Multi-fidelity Bayesian UQ offers a significant computational cost reduction (at least 10x) compared to brute-force Monte Carlo, enabling practical UQ for complex turbulent flows that are otherwise intractable. This provides a strong competitive advantage for early adopters.
- **Weaknesses**: The main barrier is the need for domain expertise in both LES and Bayesian UQ, which may slow adoption in industrial settings where such skills are scarce. Integration with existing LES solvers and workflows will require customization.; The commercial timeline is uncertain: while the protocol suggests 8-14 months for validation, achieving a production-ready product with robust performance across multiple flow cases may take longer, potentially 2-3 years, which could impact ROI expectations.
- **Questions**: What is the specific target market segment (e.g., aerospace vs. energy) and what is the estimated size in terms of potential licenses or services revenue?; How will the IP be protected? Is there a possibility of patenting the multi-fidelity UQ framework applied to LES, or will it be based on trade secrets and know-how?; What is the expected cost of a full commercial deployment (including support and maintenance) and what pricing model (e.g., per-seat license, cloud subscription) would be viable?
- **Recommendation**: Proceed with Phase 1 validation to confirm the technical feasibility. Simultaneously, engage with potential industrial partners (e.g., via joint research projects) to understand their specific UQ needs and co-develop use cases. This will help tailor the solution and build a business case. If Phase 1 is successful, consider spinning off a specialized software tool or service offering, leveraging the QUEENS framework as a unique selling point.

#### Funding Strategist

- **Score**: 7.2/10 | **Verdict**: accept | **Confidence**: 0.7
- **Strengths**: Strong methodological novelty: transferring a multi-fidelity Bayesian UQ framework to LES is timely and addresses a critical need for systematic error propagation in computational fluid dynamics.; Clear quantitative success criteria (10x reduction, 20% uncertainty) and a phased validation approach de-risk the project, making it attractive for seed funding.; Potential for high-impact publications in both computational physics and applied mathematics, with broad applicability to engineering and climate modeling.
- **Weaknesses**: TRL is low (1-2) as the framework is not yet validated for LES; the proposed budget and timeline may be insufficient to achieve convincing results.; The consortium is not yet defined; a single-institution effort may lack the complementary expertise in LES, UQ, and high-performance computing.; The hypothesis is narrowly focused on a specific QoI (Nusselt number) and may not demonstrate generalizability to other turbulent flow quantities.
- **Questions**: How will you ensure access to high-fidelity LES data and computational resources for validation, and what is the plan for scaling to larger test cases?; What is the novelty compared to existing multi-fidelity UQ methods applied to LES, and how will you position this work in the competitive landscape?; Have you considered partnering with experimental groups to provide validation data, which could strengthen the proposal and increase its impact?
- **Recommendation**: Target the ANR JCJC (Jeunes Chercheuses et Jeunes Chercheurs) for a 24-month project to develop the framework and validate on canonical cases, while simultaneously applying for a PRACE (Partnership for Advanced Computing in Europe) allocation for computational resources. If initial results are promising, leverage them for an ERC Starting Grant in the next call.

### B. Semantic Scholar Search Queries

- [novelty] `uncertainty quantification large eddy simulation` — Direct search for the core hypothesis of applying UQ to LES
- [novelty] `Bayesian inference LES turbulent flows` — Checks if Bayesian UQ methods have been applied to LES
- [novelty] `multi-fidelity UQ computational fluid dynamics` — Searches for multi-fidelity UQ in CFD, which is a key aspect of the transfer
- [novelty] `QUEENS uncertainty quantification framework` — Checks if QUEENS has been used for LES or similar applications
- [evidence] `sensitivity analysis subgrid-scale models` — Finds evidence of sensitivity of LES to SGS model choices
- [evidence] `grid resolution uncertainty LES` — Finds evidence of numerical errors due to grid resolution in LES
- [evidence] `polynomial chaos expansion turbulence modeling` — Finds evidence of surrogate-based UQ methods applied to turbulence models
- [evidence] `Gaussian process surrogate Reynolds-averaged Navier-Stokes` — Finds evidence of GP surrogates for RANS, which may be transferable to LES
- [cross_domain] `uncertainty quantification digital twin` — Finds precedents of UQ in digital twins, which is the origin of QUEENS
- [cross_domain] `multi-fidelity Bayesian inference engineering` — Finds cross-domain applications of multi-fidelity Bayesian inference
- [cross_domain] `surrogate modeling computational physics` — Finds general surrogate modeling techniques in computational physics

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*Generated by SPORE (Systeme de Production d'Opportunites de Recherche par Exploration) on 2026-08-26*