An automatic uncertainty quantification analysis method and system based on a large language model drive

Abstract

The application discloses an automatic uncertainty quantification analysis method and system based on a large language model driving, and the method comprises the following steps: an LLM driving stage, a proxy model is constructed through a double-branch architecture, an explicit equation is extracted, translated into Python code, and Sobol compatible coding rules are forced to be executed, and a normalized additive polynomial proxy model is constructed to avoid variance compression; a numerical calculation stage, an unbiased Saltelli Sobol estimator is used for global sensitivity analysis, a pooling estimation is used instead of a cross product item to reduce the bias from O (1 / √N) to O (1 / N), and uncertainty propagation and first-order second-moment reliability evaluation are carried out through sampling; an LLM report stage, a structured conclusion report is generated. The application also supports direct import of CSV engineering data. The application shortens the UQ analysis time from several hours to 8-10 minutes, and is suitable for multiple engineering fields such as mechanics, materials, acoustics and thermology.

Description

Technical Field

[0002] This invention belongs to the field of engineering uncertainty quantification (UQ) analysis technology, specifically involving an automated uncertainty quantification analysis method and system driven by a large language model (LLM), which is used to automatically complete the entire process of parameter extraction, model building, sensitivity analysis, uncertainty propagation and reliability assessment from scientific research paper texts or engineering data. Background Technology

[0004] Uncertainty quantification (UQ) plays a crucial role in engineering design, used to systematically assess how input parameter variability propagates through computational models and affects final performance predictions. A complete UQ workflow typically includes five steps: (i) manually identifying uncertain parameters and their numerical ranges from relevant literature; (ii) constructing surrogate models or configuring physical simulators; (iii) sampling the input parameter space using sampling methods such as Latin Hypercube Sampling (LHS); (iv) calculating global sensitivity indices to rank parameter importance; and (v) evaluating reliability using the First Order Second Moment (FOSM) method. Manually executing this workflow requires both engineering domain expertise and UQ methodological knowledge, typically taking several hours to days per paper, and the results from different analysts on the same paper often vary significantly, resulting in low reproducibility.

[0005] Existing UQ software tools, such as Dakota developed by Sandia National Laboratories, OpenTURNS developed by EDF, and UQLab developed by ETH Zurich, provide robust implementations of sampling, sensitivity analysis, and reliability methods. However, these tools all require users to manually specify the model input function, parameter range, probability distribution type, and output definition, failing to automate the most critical initial step—extracting relevant information from the paper. This step is both the most time-consuming and error-prone part of the workflow. Furthermore, while probabilistic programming frameworks such as PyMC and Stan automate the Bayesian inference process, they require users to manually specify the model structure using domain-specific languages, similarly failing to automatically extract model information from the paper text.

[0006] In recent years, Large Language Models (LLMs) have demonstrated remarkable capabilities in automating scientific tasks. Domain-specific agent systems such as ChemCrow (chemical synthesis), MLAgentBench (machine learning experiments), and Boiko et al.'s autonomous chemistry research system have proven that LLMs can autonomously plan and execute multi-step scientific workflows, transforming from passive text generators into active scientific reasoning agents. However, existing systems do not provide dedicated capabilities for end-to-end uncertainty quantification, failing to automatically extract UQ parameters from papers, construct agent models, and perform sensitivity analysis.

[0007] In surrogate model construction, the commonly used weighted average formula `QoI = (Σw_i·f_i) / Σw_i` suffers from significant variance compression: the variance contribution of low-weight parameters is quadratically compressed by the sum of squares of all weights, making it almost invisible in the Sobol decomposition. For example, in a system with 7 parameters and a weight sum Σw_j = 2.65, the variance contribution of a parameter with weight w_i = 0.05 in the additive formula is w_i² = 0.0025, while in the weighted average formula it becomes 0.0025 / 7.02 ≈ 0.00036, a reduction of an order of magnitude. This compression effect makes the weighted average formula unable to correctly distinguish between important and unimportant parameters.

[0008] In calculating the Sobol sensitivity index, the standard Saltelli estimation method uses the product of the means of two independent samples, `f_0² = mean(f_A) · mean(f_B)`, to estimate the square of the overall mean, introducing a cross product bias of order O(1 / √N). This bias causes some parameters to fail to satisfy the fundamental mathematical constraint S_i ≤ ST_i, reducing the reliability of the sensitivity analysis results. Furthermore, the code generated by LLM, due to the lack of a unified coding standard, often uses operations such as np.clip, Boolean indexes, and if / else conditional branches, which create flat regions in Sobol analysis, causing derivative vanishing and severely affecting the accuracy of the sensitivity index calculation. Summary of the Invention

[0010] This invention provides an automated uncertainty quantification analysis method and system based on a large language model. Its purpose is to solve the shortcomings of existing uncertainty quantification tools, such as the need for manual extraction of paper parameters, variance compression in surrogate models, bias in Sobol estimation, and poor adaptation of LLM generated code. It relies on a large language model to achieve end-to-end automation from text and engineering data to complete UQ analysis, thereby improving the accuracy and efficiency of analysis.

[0011] This invention is achieved through the following technical solution:

[0012] An automated uncertainty quantification analysis method driven by a large language model, which specifically includes the following steps:

[0013] Step S1. Document parsing and information extraction: Receive a paper Markdown file or a CSV engineering data file, extract uncertain design parameters and their value ranges, target performance indicators and their value thresholds from the paper text through the large language model, extract existing sensitivity analysis data and reliability data from the paper, perform mapping from Greek letters to Latin letters and case unification normalization processing on the extracted parameter symbols;

[0014] Step S2. Baseline establishment: Extract the nominal value of each design parameter and the baseline performance value of each target performance indicator from the paper tables through the large language model, wherein the nominal value must be directly extracted from the paper tables;

[0015] Step S3. Boundary definition and distribution recommendation: Recommend a probability distribution type for each design parameter through the large language model, execute preset mapping rules according to the physical classification of the parameters, label each parameter as aleatory uncertainty or epistemic uncertainty type, and establish a limit state function for each target performance indicator according to its threshold and direction;

[0016] Step S4. UQ method selection: Automatically select a sampling method, a sensitivity analysis method, a reliability method and a sample size according to the parameter dimension through the large language model, execute a three-way branching rule according to the dimension, wherein when the number of parameters d≤5, tensor product PCE combined with Gaussian integration is selected, when 5<d≤20, Smolyak sparse grid is selected, and when d>20, Latin hypercube sampling is selected;

[0017] Step S5. Equation extraction and model construction: Automatically select the first branch or the second branch to construct an executable surrogate model according to whether the paper contains an explicit governing equation;

[0018] The first branch: When the paper contains a governing equation from parameters to target performance indicators, extract the explicit governing equation in the paper, identify the equation type as one of closed-form algebra, multi-step chain, implicit root-finding, piecewise condition, coupled system or integro-differential, translate it into Python numerical code, and enforce Sobol-compliant coding rules;

[0019] The second branch: When the paper only provides qualitative trend descriptions, construct a normalized additive polynomial surrogate model, whose mathematical form is QoI_k = Σ_{i=1}^{n} w_i · f_i(X_{n,i}) + B_k, where X_{n,i} is a parameter normalized to the [0,1] interval, f_i is a trend function mapped according to the qualitative description of the paper, w_i is a sensitivity weight, and B_k is a baseline constant;

[0020] Step S6, Model Validation: Perform nominal value validation and K-fold cross-validation on the constructed proxy model to generate a model quality rating;

[0021] Step S7, Sensitivity Analysis and Uncertainty Propagation: Generate parameter samples using Latin hypercube sampling, perform uncertainty propagation on the surrogate model, calculate the mean, standard deviation and confidence interval of each target performance index, and use the unbiased Saltelli Sobol estimator to calculate the global sensitivity index.

[0022] Step S8, Reliability Analysis: Based on the propagation results, the failure probability and reliability index of each target performance index are calculated using the first-order quadratic moment method. The system reliability is calculated using a cascade model, and samples that meet the thresholds of all target performance indices are selected as the satisfactory parameter range.

[0023] Step S9, Visualization: Automatically generate Sobol sensitivity bar chart, parameter probability density distribution chart, target performance index probability density distribution chart, reliability dashboard and cross-validation result chart;

[0024] Step S10: Conclusion Report Generation: Read all calculation results through the large language model and generate a structured analysis conclusion report that includes an execution summary, key findings, parameter importance ranking, optimization suggestions, value analysis, and limitation analysis.

[0025] As a preferred embodiment, step S1 further includes a parameter self-verification step: by calling the large language model a second time, it is verified whether each extracted parameter and each target performance indicator has supporting evidence in the Results, Discussion and Conclusion sections of the paper. Parameters without evidence are removed and missing parameters are supplemented.

[0026] As a preferred embodiment, when the input is a CSV engineering data file, step S1 further includes the following sub-steps: automatically identifying the input and output columns through keyword matching, calculating the mean, standard deviation, coefficient of variation, and quantiles of each column, fitting three distributions (Normal, Uniform, and Lognormal) and selecting the optimal distribution type using the AIC criterion, automatically selecting the surrogate model construction method based on the number of parameters (multinomial chaotic expansion OLS fitting when the number of parameters n≤10, and Gaussian process regression Cholesky fitting when the number of parameters n>10), and reusing the complete process of the paper mode in subsequent steps S6 to S10.

[0027] In a preferred embodiment, the mapping rule for the probability distribution type in step S3 is as follows: for geometric dimension parameters, a Normal or Uniform distribution is recommended; for material property parameters, a Normal or Lognormal distribution is recommended; for ratio / fraction parameters, a Uniform or Beta distribution is recommended; for environmental condition parameters, a Uniform or Normal distribution is recommended; and for load parameters, a Gumbel or Weibull distribution is recommended.

[0028] As a preferred embodiment, the normalized additive polynomial surrogate model in the second branch of step S5 has a trend function f_i mapped to one of the following six standard forms according to the qualitative description in the paper: proportional function f(X_n) = X_n, decreasing function f(X_n) = 1 - X_n, saturation function f(X_n) = √(X_n), acceleration function f(X_n) = e^{X_n} - 1, peak function f(X_n) = 1 - 4(X_n - 0.5)², threshold function f(X_n) = 1 / (1 + e^{-10(X_n - 0.5)}); the weights w_i are assigned according to the sensitivity conclusions in the paper: dominant parameter w_i ∈ [0.7, 1.0], significant parameter w_i ∈ [0.3, 0.7], and low-impact parameter w_i ∈ [0.05, 0.25].

[0029] In a preferred embodiment, after constructing the normalized additive multinomial surrogate model in the second branch of step S5, a calibration loop is executed: the surrogate model is evaluated at the nominal design point. If the deviation between the predicted target performance index value and the paper report value exceeds 20%, only the Scale and Baseline constants are adjusted through the large language model, without modifying the weight w_i or the trend function f_i, and the iteration is repeated up to 3 times.

[0030] As a preferred embodiment, the Sobol-compatible encoding rules for the first branch in step S5 include: prohibiting the use of the np.clip function to generate flat regions that cause derivatives to disappear; prohibiting the use of Boolean index assignment arr[mask] = value; prohibiting the use of if / else for array operations, and requiring the use of np.where instead; requiring the use of smoothing nonlinear functions such as np.exp, np.log, np.sqrt, and np.power; adding 1e-10 to the denominator to prevent division by zero; and specifying the interface of model_func as Xshape (N, n) → return shape (N, m), where N is the number of samples, n is the number of parameters, and m is the number of target performance indicators.

[0031] In a preferred embodiment, the model quality rating in step S6 is divided into four levels: reliable indicates nominal deviation <20% and cross-validation R²>0.8, low_confidence indicates nominal deviation <20% but R²≤0.8, unverified indicates nominal deviation between 20% and 50% and is a second-branch model, and unreliable indicates nominal deviation ≥50% and is a first-branch model.

[0032] In a preferred embodiment, the unbiased Saltelli Sobol estimator in step S7 uses pooling estimation to replace the cross product term in the standard Saltelli method. Specifically, it calculates the overall mean using f_bar = (1 / 2N) Σ_{k=1}^{2N} f_k, replacing mean(f_A)·mean(f_B) in the original method with f_bar², where {f_k}_{k=1}^{2N} is the concatenation of two independent sample matrices f(A) and f(B), reducing the estimation bias from O(1 / √N) to O(1 / N) and halving the estimator variance. The unbiased Saltelli Sobol estimator in step S7 is calculated 5 times using 5 different random seeds, and the median is taken as the final result to further reduce Monte Carlo noise. The sample size is set to max(5000, n × 2000), where n is the number of parameters.

[0033] An automated uncertainty quantification analysis system based on a large language model is provided for executing the aforementioned analysis method. The system includes an input module, a large language model-driven extraction module, a numerical calculation module, a visualization module, and a report generation module.

[0034] The input module is used to receive Markdown files of academic papers or CSV project data files;

[0035] The large language model-driven extraction module is used to execute steps S1 to S5 as described in claim 1, including parameter extraction, self-verification, baseline establishment, distribution recommendation, method selection, and bi-branch model construction.

[0036] The numerical calculation module includes a built-in algorithm library for performing steps S6 to S8 of claim 1, including model verification, Latin hypercube sampling, unbiased Saltelli Sobol sensitivity analysis, uncertainty propagation, and FOSM reliability calculation.

[0037] The visualization module is used to execute step S9 of claim 1, and automatically generate a Sobol sensitivity bar chart, a parameter probability density distribution chart, a target performance index probability density distribution chart, a reliability dashboard, and a cross-validation result chart.

[0038] The report generation module is used to perform step S10 of claim 1, and generate a structured analysis conclusion report through a large language model;

[0039] The built-in algorithm library in the numerical calculation module contains more than 55 algorithms in 9 modules, covering sampling methods, random expansion, sensitivity analysis, reliability methods, Gaussian processes, prediction models, regression regularization, adjoint methods, and cognitive uncertainty quantification.

[0040] The technical principle of this invention is as follows: This invention provides an automated uncertainty quantification analysis method and system driven by a large language model. It constructs an end-to-end automated uncertainty quantification analysis framework based on a large language model. First, raw materials such as engineering text and experimental data are input. The large language model automatically extracts literature parameters, replacing the traditional manual parameter extraction process. This invention calls multiple uncertainty quantification tool components through the model to construct a proxy model on the input data. Simultaneously, variance compression correction is performed on the proxy model output to eliminate model output bias. Addressing the inherent bias problem in Sobol index estimation, a bias elimination calculation module is integrated to correct the sensitivity index calculation results. The large language model automatically generates runnable UQ analysis code according to task requirements, completing the entire process of data preprocessing, proxy model training, sensitivity analysis, and uncertainty propagation, avoiding the problems of poor code adaptability and cumbersome debugging inherent in traditional code. The framework automatically parses the calculation results and outputs visual charts and quantification reports, fully reproducing the entire uncertainty quantification process. The entire process eliminates the need for researchers to manually write code or extract literature parameters, achieving fully automated output from raw input to analysis reports, improving the calculation accuracy and efficiency of engineering uncertainty quantification.

[0041] Compared with the prior art, the present invention has the following beneficial effects:

[0042] (1) End-to-end automation of the entire UQ analysis process has been achieved, reducing the UQ analysis time for a single paper from several hours to 8-10 minutes, without the need for manual intervention. The accuracy of parameter extraction is guaranteed by the LLM self-validation mechanism, and repeatability is achieved through weight standardization and calibration loop.

[0043] (2) The dual-branch architecture enables the system to process any paper, regardless of whether there is an explicit equation. Branch A covers about 40% of the papers (with explicit equations), and Branch B covers about 60% of the papers (with only qualitative trends), with a total coverage of 100%.

[0044] (3) The normalized additive surrogate model fundamentally avoids the variance compression problem of the weighted average formula, keeps low-weight parameters visible in Sobol decomposition, correctly distinguishes important parameters from unimportant parameters, even if the parameter weights span multiple orders of magnitude.

[0045] (4) The unbiased Saltelli Sobol estimator replaces the cross product term with pooling estimation, reducing the bias from O(1 / √N) to O(1 / N). It satisfies the mathematical constraint S_i ≤ ST_i in more than 94% of the parameter-QoI pairs, thus improving the credibility of the sensitivity analysis results.

[0046] (5) The Sobol-compatible coding rules ensure that the Python code generated by LLM can be directly used for Sobol sensitivity analysis, avoiding errors in sensitivity index calculation caused by code implementation issues.

[0047] (6) CSV dual mode supports direct import of engineering data, and AIC distribution fitting and PCE / GP automatic selection enable data from non-paper sources to also perform complete UQ analysis.

[0048] (7) Through 40 stability tests (20 tests × 2 papers), the parameter sign consistency reached 100% after normalization, the proportion of models rated as reliable reached 88.9%-100%, the chart generation success rate reached 100%, and the consistency of the key parameter sorting set reached 100%. Attached Figure Description

[0050] Figure 1 This is a schematic diagram of the overall system architecture of an embodiment of the present invention, showing the process of a 10-stage automated UQ pipeline and the division of the three stages (LLM-driven extraction stage, deterministic calculation stage, and LLM reporting stage).

[0051] Figure 2 This is a schematic diagram of a dual-branch model architecture according to an embodiment of the present invention, showing the decision path and process of Branch A (explicit equation extraction, 6 types of equations) and Branch B (qualitative trend modeling, 6 types of trend functions).

[0052] Figure 3 This is a schematic diagram comparing the variance of a normalized additive surrogate model and a weighted average model according to an embodiment of the present invention, demonstrating how the additive formula avoids the secondary compression of the variance of low-weight parameters.

[0053] Figure 4 This is a flowchart of the computation of the unbiased Saltelli Sobol estimator in one embodiment of the present invention, showing the improved method of using pooling estimation to replace the cross product term and the 5-round median aggregation process.

[0054] Figure 5 This is a flowchart of a CSV engineering data mode in one embodiment of the present invention, showing the complete process of automatic column identification, AIC distribution fitting, and automatic PCE / GP selection. Detailed Implementation

[0056] The embodiments of the present invention will be described in detail below with reference to the accompanying drawings: These embodiments are implemented based on the technical solution of the present invention, and provide detailed implementation methods and specific operation processes, but the protection scope of the present invention is not limited to the following embodiments.

[0057] like Figure 1 As shown, an automated uncertainty quantification analysis method based on a large language model includes the following steps:

[0058] Step S1, Document Parsing and Information Extraction: Receive the paper's Markdown file or CSV project data file, and execute a three-step extraction protocol using a large language model. The first step extracts uncertain design parameters, with extraction conditions including: parameters having a defined numerical range; parameters directly affecting performance output; parameters being design variables or uncertain parameters rather than fixed constants; and parameter symbols originating from mathematical symbols or table column headings in the original paper. The second step extracts the target performance index (Quantity of Interest, QoI), including the numerical thresholds for each QoI, directional definitions (">" indicates larger is better, "<" indicates smaller is better), and physical units. The third step extracts existing sensitivity analysis and reliability data from the paper, including the Sobol index, parameter importance ranking, failure probability, etc. After extraction, post-processing normalization is performed on all parameter symbols, including mapping from Greek letters to Latin letters (δ→delta, σ→sigma, α→alpha, θ→theta) and case unification.

[0059] Step S1.5, Parameter Self-Verification: Through a second call to the large language model, verify whether each parameter and QoI extracted in step S1 has supporting evidence in the Results, Discussion, and Conclusion sections of the paper. Parameters without evidence are removed, and missing parameters are added. This step serves as a quality gate before model construction, reducing the risk of erroneous parameters caused by the LLM illusion.

[0060] Step S2, Baseline Establishment: Extract the nominal value of each design parameter and the baseline performance value of each QoI from the tables in the paper using a large language model. Nominal values ​​must be extracted directly from the tables; taking the midpoint of the parameter range or inferring from textual descriptions is prohibited. When multiple tables in the paper contain the same parameter, prioritize them as follows: Results Table > Parameter Table > Textual Description.

[0061] Step S3, Boundary Definition and Distribution Recommendation: Recommend a suitable probability distribution type for each design parameter using a large language model. Execute mapping rules based on parameter physical classification: For geometric dimensions (thickness, radius, length), recommend Normal or Uniform distribution; for material properties (modulus, strength, density), recommend Normal or Lognormal distribution; for ratios / fractions (volume fraction, porosity), recommend Uniform or Beta distribution; for environmental conditions (temperature, pressure), recommend Uniform or Normal distribution; for loads / load conditions, recommend Gumbel or Weibull distribution (extreme value distribution is suitable for extreme load conditions). Simultaneously, label each parameter with its uncertainty type: aleatory (intrinsic random fluctuation, CV ≥ 5%) or epistemic (insufficient knowledge, CV < 5%). For each QoI, establish a limit state function based on its threshold and direction: when the direction is ">", g = QoI - threshold (g > 0 is safe); when the direction is "<", g = threshold - QoI (g > 0 is safe); when the direction is "target", g = tolerance - |QoI - target|.

[0062] Step S4, UQ Method Selection: The optimal UQ method combination is automatically selected based on the problem dimension using a large language model. A three-way branching rule is executed according to the dimension: When the number of parameters d ≤ 5, tensor product PCE combined with Gaussian integral is selected for sampling, the Sobol exponent is calculated analytically using PCE coefficients, and the reliability uses the FOSM→FORM→SORM method chain; when 5 < d ≤ 20, Smolyak sparse grid is selected for sampling, the Sobol global sensitivity is calculated based on an alternative model, and the reliability uses the AFOSM (Rosenblatt transform + HL-RF iteration) method; when d > 20, LHS is selected for sampling, the Sobol exponent is calculated after filtering the active parameter subset using Lasso regression, and the reliability uses a subset simulation method.

[0063] Step S5, Equation Extraction and Model Building: Based on the paper's content, one path in the dual-branch architecture is automatically selected to build the surrogate model. When the paper contains control equations that translate parameters into QoI, Branch A—the explicit equation extraction branch—is executed to identify the equation type and translate it into Python numerical code. When the paper only provides a qualitative trend description, Branch B—the qualitative trend modeling branch—is executed to build a normalized additive multinomial surrogate model.

[0064] Step S5A, Branch A: Explicit Equation Extraction: Scan the entire paper to find numbered equations, distinguishing between governing equations (physical relationships between parameters and QoI) and definition formulas (only redefinition or normalization). Classify the governing equations into six structural types: Type 1: Closed algebras directly translated into NumPy code; Type 2: Multi-step chained equations, calculating intermediate variables sequentially; Type 3: Implicit root finding using `scipy.optimize.fsolve`; Type 4: Piecewise conditions transformed using `np.where`; Type 5: Coupled systems solved using `fsolve`; Type 6: Integral / differential equations processed using `scipy.integrate`. All coefficients must be directly extracted from the original paper and cannot be fabricated. The source of the equation is marked as "explicit_formula".

[0065] Step S5B, Branch B Normalized Additive Surrogate Model Construction: When the paper does not have explicit governing equations, a normalized additive polynomial surrogate model is constructed, the mathematical form of which is:

[0066] QoI_k = Σ_{i=1}^{n} w_i · f_i(X_{n,i}) + B_k,

[0067] Where X_{n,i} = (X_i - X_{i,min}) / (X_{i,max} - X_{i,min}) ∈ [0,1] are normalization parameters, f_i is the trend function, w_i is the sensitivity weight, and B_k is the baseline constant. The trend function is qualitatively described in the paper and mapped to 6 standard mathematical forms: proportional (f = X_n), decreasing (f = 1 - X_n), saturation (f = √X_n), acceleration (f = e^{X_n} - 1), peak (f = 1 - 4(X_n - 0.5)²), and threshold (f = 1 / (1+e^{-10(X_n-0.5)})). Weights are assigned based on the sensitivity conclusions of the papers: dominant parameters (top 3) w_i ∈ [0.7, 1.0], significant parameters w_i ∈ [0.3, 0.7], and low-impact parameters w_i ∈ [0.05, 0.25]. When there is an interaction effect between the parameters described in the papers, the interaction term w_ij · X_i · X_j is added.

[0068] The key advantage of the additive formula over the weighted average formula lies in its variance behavior. For an independent trend function, the variance contribution of parameter i is w_i²·Var[f_i] / Σ_j w_j²·Var[f_j], while in the weighted average formula it is w_i²·Var[f_i] / (Σ_j w_j)². The denominator of the additive formula is the sum of squares rather than the square of the sum, avoiding secondary compression of the variance contribution of low-weight parameters, keeping low-weight parameters visible in the Sobol decomposition, and correctly distinguishing important and unimportant parameters.

[0069] Step S5C, Calibration Cycle: After the Branch B model is built, the surrogate model is evaluated at the nominal design point. If the deviation between the predicted QoI value and the value reported in the paper exceeds 20%, only the Scale and Baseline constants are adjusted through the large language model, without modifying the weights w_i or the trend function f_i. This process is repeated a maximum of 3 times.

[0070] Step S5D, Sobol-compatible coding rules: All Python code generated in step S5A must adhere to the following coding rules to ensure its usability for Sobol sensitivity analysis: The use of `np.clip` is prohibited (it creates flat regions that cause derivative vanishing, biasing the Sobol exponent); Boolean index assignment is prohibited (`arr[mask] = value`); if / else statements for array operations are prohibited; `np.where` must be used instead; smoothing nonlinear functions such as `np.exp`, `np.log`, `np.sqrt`, and `np.power` must be used; 1e-10 must be added to all denominators to prevent division by zero; the interface specification for `model_func` is `X shape (N, n) → return shape(N, m)`, where N is the number of samples, n is the number of parameters, and m is the number of QoI values, such as... Figure 2 As shown.

[0071] Step S5.5, Model Validation: Perform a three-step validation on the constructed surrogate model. Step 1: Nominal Value Validation: Compare the model's predicted values ​​at the nominal parameter values ​​with the values ​​reported in the paper. If the deviation exceeds 50%, it is marked as failed. Step 2: K-fold Cross-validation: Fit model_func using higher-order PCE, calculate R² and RMSE, and output statistical results such as R²=0.94±0.13, RMSE=0.23. Step 3: Model Quality Rating: Based on the nominal value deviation and cross-validation results, classify the model quality into four levels: reliable (deviation <20% and R²>0.8), low confidence (deviation <20% but R²≤0.8), unverified (deviation 20%-50% and Branch B), and unreliable (deviation ≥50% and Branch A). Figure 3 As shown.

[0072] Step S6, Sensitivity Analysis and Uncertainty Propagation: N=5000 parameter samples were generated using Latin hypercube sampling, with a fixed random seed of 42 to ensure reproducibility. Uncertainty propagation was performed on the surrogate model, calculating the mean, standard deviation, coefficient of variation (CV), and 95% confidence interval for each QoI. A three-branch Sobol calculation method was used: if the paper contains Sobol values, they were directly cited (Branch A); if the surrogate model is PCE, the Sobol exponent was calculated analytically from the PCE coefficients (Branch B); otherwise, the unbiased Saltelli Monte Carlo method was used (Branch C).

[0073] The core improvement of the unbiased Saltelli Sobol estimator (Branch C) lies in the following: The standard Saltelli estimator uses the product of the means of two independent samples, f_0² = mean(f_A)·mean(f_B), to estimate the squared total mean, introducing a cross product bias of order O(1 / √N). This invention uses pooling estimation instead.

[0074] f_bar = (1 / 2N) Σ_{k=1}^{2N} f_k, f_0² = f_bar²,

[0075] Where {f_k}_{k=1}^{2N} is the concatenation of f(A) and f(B). This correction reduces the bias to O(1 / N) and halves the estimator variance. The corrected Sobol formula is:

[0076] S_i = ((1 / N) Σ f(A_k)·f(BA_{i,k}) - f_0²) / Var[{f_k}],

[0077] ST_i = 1 - ((1 / N) Σ f(A_k)·f(AB_{i,k}) - f_0²) / Var[{f_k}],

[0078] Where BA_i represents the i-th column of matrix B replaced by the i-th column of matrix A, and AB_i represents the i-th column of matrix A replaced by the i-th column of matrix B. The calculation is repeated 5 times using different random seeds, and the median is taken as the final result to further reduce Monte Carlo noise.

[0079] Step S6 also includes multi-objective analysis: automatically identifying non-dominated solutions in the Pareto front for multi-QoI problems (m≥2), and selecting the parameter distribution intervals of the top-10% best samples as the optimal parameter intervals, such as... Figure 4 As shown.

[0080] Step S7, Reliability Analysis: Based on the propagation results from Step S6, calculate the reliability index β and failure probability Pf for each QoI using the FOSM method. For QoIs with a direction of ">", z = (threshold - μ) / σ; for QoIs with a direction of "<", z = (μ - threshold) / σ. Pf = Φ(-z), β = -Φ⁻¹(Pf). When no threshold is specified, t = μ and Pf = 0.5 are set as neutral default values. System reliability is calculated using a cascade model: Pf_sys = 1 - Π(1 - Pf_j). Risk levels are classified according to the Pf threshold: Pf < 1% is Low, 1%-10% is Medium, and Pf ≥ 10% is High. Samples satisfying all QoI thresholds are selected as the satisfactory parameter range.

[0081] Step S8, Visualization: Automatically generate 5 publication-quality visualization charts with a resolution of 300 DPI. Fig 1 is a Sobol sensitivity bar chart (S1 and ST are displayed side by side, with a sub-chart for each QoI, and error bars representing the median fluctuation over 5 rounds); Fig 2 is a probability density distribution chart of design parameters (histogram with KDE curve, labeled with P5 / P50 / P95 quantiles); Fig 3 is a probability density distribution chart of QoI (labeled with threshold lines and colored safe / failure regions); Fig 4 is a reliability dashboard (Pf ring chart, β labeling, risk level color coding, system reliability summary, and satisfactory parameter interval table); Fig 5 is a cross-validation result chart (R² and RMSE bar charts for each QoI, with error bars representing K-fold fluctuations).

[0082] Step S9, Conclusion Report Generation: Read all calculation results through the large language model and generate a structured analysis conclusion report, including an executive summary, key findings (each finding must include three fields: finding, evidence, and implication), parameter importance ranking (sorted by Sobol ST value, including recommended measures), optimization suggestions (including measures, expected improvements, and priorities), UQ value analysis, and limitation analysis.

[0083] Step S10, CSV Engineering Data Mode: When the input is a CSV structured data file, the system automatically executes the following processes: Automatically identifies input and output columns through keyword matching; calculates the mean, standard deviation, CV, and quantiles (P5 / P50 / P95) for each column; fits Normal, Uniform, and Lognormal distributions respectively, using the AIC criterion to select the optimal distribution type; CV < 5% is marked as cognitive uncertainty, and CV ≥ 5% is marked as random uncertainty; automatically selects the surrogate model construction method based on the number of parameters: Multinomial Chaotic Expansion (PCE) OLS fitting is used when n ≤ 10, and Gaussian Process Regression (GP) Cholesky fitting is used when n > 10; subsequent steps S5.5 to S9 reuse the complete logic of the paper mode, such as... Figure 5 As shown.

[0084] Example 1: Input Uncertainty Analysis of Honeycomb Sandwich Panels

[0085] This embodiment uses a 3D-printed TPU honeycomb energy-absorbing structure as an example to analyze the impact of manufacturing tolerances on energy absorption performance. This embodiment corresponds to the Branch A (explicit equation) mode.

[0086] Step 1: Receive the paper's Markdown file and extract parameters. Extract three design parameters from the paper: wall thickness t ∈ [0.75, 0.85] mm, where "t" comes from the column header of the paper's tables; yield strength σ_ys ∈ [37, 43] MPa, where "σ_ys" comes from the paper's formula; and elastic modulus E_s ∈ [42.2, 46.7] MPa, where "E_s" comes from the paper's formula. Extract four QoIs: platform stress σ_pl (direction ">", threshold 0.2 MPa), equivalent elastic modulus E* (direction ">", threshold 0.05 MPa), compacted strain ε_D (direction ">", threshold 0.6), and specific energy absorption SEA (direction ">", threshold 1.0 kJ / kg).

[0087] Step 2: Perform parameter self-validation to verify that all parameters have supporting evidence in the Results section of the paper, and all parameters pass.

[0088] Step 3: Perform baseline establishment. Extract nominal values ​​from Table 1 of the paper: t = 0.8 mm, σ_ys = 40 MPa, E_s = 44.43 MPa. Extract baseline performance from the paper's results: σ_pl = 0.267 MPa, E* = 0.103 MPa, ε_D = 0.7, SEA = 1.61 kJ / kg;

[0089] Step 4: Perform boundary definition and distribution recommendations. Wall thickness *t* is the geometric dimension, recommended to be a Normal distribution, μ=0.8, σ=0.025, uncertainty_type=aleatory. Yield strength σ_ys is a material property, recommended to be a Normal distribution, μ=40, σ=1.5, uncertainty_type=aleatory. Elastic modulus *E_s* is a material property, recommended to be a Normal distribution, μ=44.43, σ=1.11, uncertainty_type=aleatory. Establish limit state functions: g_σ_pl = σ_pl - 0.2, g_E* = E* - 0.05, g_ε_D = ε_D - 0.6, g_SEA = SEA - 1.0;

[0090] Step 5: Perform UQ method selection, parameter number d=3 (≤5), select tensor product PCE + Gaussian integral sampling, Sobol exponent is calculated analytically through PCE coefficients, reliability is achieved using FOSM method, and sample size is set to 5000;

[0091] Step Six: Perform equation extraction and model building. Scan the paper to find governing equations and enter Branch A. Extract 6 governing equations, with the source of the equations marked as "explicit_formula":

[0092] Eq.1: ρ_rel = (2 / √3)·(t / l), a Type 1 closed algebra, to calculate the relative density;

[0093] Eq.2: σ_pl = 0.5·σ_ys·(ρ_rel)², Type 1 closed algebra, calculate the stress on the platform;

[0094] Eq.3: E* = 1.5·E_s·(ρ_rel)³, Type 1 closed algebra, calculate the equivalent elastic modulus;

[0095] Eq.4: ε_D = 1 - 1.4·ρ_rel, Type 1 closed algebra, calculate the compacted strain;

[0096] Eq.5: ρ* = ρ_rel·ρ_s, Type 1 closed algebra, calculate the equivalent density;

[0097] Eq.6: SEA = σ_pl·ε_D·10³ / ρ*, Type 1 closed algebra, calculate specific energy absorption.

[0098] All coefficients are from Chapter 4 of Gibson & Ashby (1997) Cellular Solids, including exponent parameters (exponent of ρ_rel is 2, exponent of ρ_rel is 3) and coefficient parameters (0.5, 1.5, 1.4, etc.).

[0099] Step 7: Sobol compatibility encoding check. The code contains no np.clip, no boolean indexes, and no if / else array operations. All passes.

[0100] Step 8: Perform model validation. Nominal value verification: Model prediction σ_pl = 0.268 MPa (paper report 0.267 MPa, bias 0.4%), E* = 0.104 MPa (paper report 0.103 MPa, bias 1.0%), passed. K-fold cross-validation R² = 0.98, RMSE = 0.05. Model quality rating: reliable;

[0101] Step 9: Perform sensitivity analysis and uncertainty propagation. LHS samples 5000 samples, and uncertainty propagation is performed on model_func. The results are shown in Tables 1 and 2 below:

[0102] Table 1 Statistical characteristics of each evaluation indicator

[0103] QoI metric mean Standard deviation Coefficient of variation (CV) 95% confidence interval CI σpl 0.268 MPa 0.039 MPa 14.5% [0.206, 0.334] E∗ 0.104 MPa 0.020 MPa 19.3% [0.073, 0.139] εD 0.70 0.015 2.2% [0.67, 0.73] SEA 1.61 kJ / kg 0.146 kJ / kg 9.1% [1.38, 1.86]

[0104] Table 2. Results of Sobol First-Order Sensitivity Index (S_1) Analysis

[0105] Input parameters σpl E∗ εD SEA Wall thickness t 72.4% 92.6% 99.3% 30.3% Yield strength σys 27.4% 0.5% 0.4% 69.5% Elastic modulus Es 0.2% 7.0% 0.3% 0.2%

[0106] Step 10: Perform reliability analysis, calculating with a σ_pl threshold of 0.2 MPa, Pf = 3.2%, β = 1.85, and a risk level of Medium. System reliability Pf_sys = 4.8%. Satisfactory parameter intervals: t ∈ [0.78, 0.82] mm, σ_ys ∈ [38, 42] MPa;

[0107] Step 11: Perform visualization to generate 5 publication-quality charts (300 DPI);

[0108] Step 12: Generate the conclusion report and output structured analysis conclusions in JSON format.

[0109] This embodiment compares the experimental data of aluminum honeycomb in the original work by Gibson & Ashby (1997). The predicted value falls within the experimental data band, and R² > 0.9, which verifies the accuracy of the method.

[0110] Example 2: Fatigue Life Analysis of Drive Shaft

[0111] This embodiment uses an SAE 1045 steel drive shaft as an example to analyze the prediction differences of different fatigue models under the same working conditions. This embodiment corresponds to the Branch A dual-model comparison mode.

[0112] Step 1: Parameter Extraction. Extract 6 design parameters: fatigue strength coefficient σ'_f = 948 MPa (Lognormal, CV=8%), fatigue strength index b = -0.092 (Normal, CV=10%), fatigue ductility coefficient ε'_f = 0.260 (Lognormal, CV=15%), fatigue ductility index c = -0.445 (Normal, CV=10%), elastic modulus E = 207 GPa (Normal, CV=3%), stress ratio R = -0.8 (Normal, σ=0.05). Extract 1 QoI: fatigue life N_f (direction ">");

[0113] Step 2: Equation Extraction (Branch A Dual Model), extracting two sets of governing equations:

[0114] Coffin-Manson model: Δε / 2 = (σ'_f / E)(2N_f)^b + ε'_f(2N_f)^c;

[0115] SWT model: σ_max·ε_a = (σ'_f)² / E·(2N_f)^(2b) + σ'_f·ε'_f·(2N_f)^(b+c);

[0116] Step 3: Model execution, total strain amplitude Δε / 2 = 0.5%. For symmetric cycles (R=-1): CM predicts N_f=122,854, SWT predicts N_f=75,006, bias 1.6 times, model uncertainty ≈0%. For asymmetric cycles (R=-0.8): CM predicts N_f=142,941, SWT predicts N_f=63,626, bias 2.2 times, model uncertainty 13.4%.

[0117] Step 4: This embodiment is consistent with the material parameters of the SAE J1099 standard and matches the trend of the SAE 1045 steel SN curve in the ASM Atlas of Fatigue Curves, verifying the reliability of the method.

[0118] Example 3: CSV Engineering Data Analysis Mode

[0119] This embodiment uses engineering test data in CSV format as input to verify the workflow of the CSV mode. The input CSV file contains 5 columns of input parameters (temperature, pressure, flow rate, concentration, pH value) and 2 columns of output performance indicators (conversion rate, selectivity).

[0120] Step 1: CSV column parsing, keyword matching automatically identifies the first 5 columns as input parameters and the last 2 columns as output QoI, load data matrices X (1000×5) and Y (1000×2);

[0121] Step 2: Distribution fitting. Fit Normal, Uniform, and Lognormal distributions for each column, and select the best value using AIC. The temperature column is fitted with a Normal distribution (μ=150, σ=12), and the pressure column is fitted with a Uniform distribution (min=1.0, max=2.5). CV=8.2% is marked as random uncertainty.

[0122] Step 3: Recommended method, number of parameters n=5 (≤10), select PCE branch. Normalize X to [-1,1], fit MultiDimensionalPCE with OLS (order=3), construct model_func to encapsulate PCE prediction;

[0123] Step 4: Subsequent steps S5.5 to S9 reuse the complete logic of the paper model to perform K-fold cross-validation, Sobol sensitivity analysis, uncertainty propagation, FOSM reliability assessment, visualization chart generation, and conclusion report generation.

[0124] An automated uncertainty quantification analysis system driven by a large language model is implemented in Python 3.13. LLM calls utilize the DeepSeek V4 Pro model, with the temperature parameter set to 0.0. The maximum output is 16,384 tokens, and the timeout is 1,800 seconds. Numerical computations are performed using NumPy 1.26 and SciPy 1.13, machine learning functions are implemented using scikit-learn 1.0, and charts are generated using Matplotlib 3.9 at a resolution of 300 dpi.

[0125] This invention's built-in algorithm library contains over 55 algorithms across 9 modules: the sampling_methods module provides Monte Carlo integration, Latin hypercube sampling, Saltelli Sobol sampling, and stratified sampling (including optimal allocation); the stochastic_expansion module provides Hermite / Legendre / Jacobi / Laguerre polynomial chaotic expansions, Smolyak sparse grid integration, and multidimensional PCE (OLS fitting + analytical Sobol exponentiation); the sensitivity_analysis module provides second-order Taylor expansion, finite difference gradient (forward / central), complex step differentiation (first-order / second-order), and variance propagation; and the reliability_methods module provides FOSM mean approximation, AFOSM (Rosenblatt transform + HL-RF iteration), SORM (Breitung / HRB formula), and limit state function. The `gaussian_process` module provides GP regression (Cholesky + jitter correction), RBF / PowerExp kernel functions, and feature space mapping; the `predictive_models` module provides MCMC (Metropolis-Hastings), Kennedy-O'Hagan models, multifidelity hierarchical models, and Bayesian calibration; the `regression_regularization` module provides OLS, Ridge, Lasso (coordinate descent), ElasticNet, and K-fold / LOOCV cross-validation; the `adjoint_methods` module provides linear adjoint, nonlinear time-inverse adjoint, discrete adjoint (finite difference Jacobian), and 1D FEM adjoint sensitivity; and the `epistemic_uncertainty` module provides P-Box, Dempster-Shafer evidence theory (including Yager conflict rules), KS test, and Cauchy distribution.

[0126] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.

Claims

1. An automated uncertainty quantification analysis method based on a large language model, characterized in that, Specifically, the following steps are included: Step S1, document parsing and information extraction: Receive a Markdown file of a paper or a CSV engineering data file, extract uncertain design parameters and their numerical ranges, target performance indicators and their numerical thresholds from the paper text through a large language model, extract existing sensitivity analysis data and reliability data from the paper, and perform mapping from Greek letters to Latin letters and normalization processing of case unification on the extracted parameter symbols; Step S2, baseline establishment: Extract the nominal value of each design parameter and the baseline performance value of each target performance indicator from the tables of the paper through the large language model, wherein the nominal values must be directly extracted from the tables of the paper; Step S3, boundary definition and distribution recommendation: Recommend a probability distribution type for each design parameter through the large language model, execute preset mapping rules according to the physical classification of the parameters, label each parameter as a random uncertainty or epistemic uncertainty type, and establish a limit state function for each target performance indicator according to its threshold and direction; Step S4, UQ method selection: Automatically select a sampling method, a sensitivity analysis method, a reliability method and a sample size according to the parameter dimension through the large language model, execute a three-way branching rule according to the dimension, wherein when the number of parameters d≤5, tensor product PCE combined with Gaussian integration is selected, when 5<d≤20, Smolyak sparse grid is selected, and when d>20, Latin hypercube sampling is selected; Step S5, equation extraction and model construction: Automatically select the first branch or the second branch to construct an executable surrogate model according to whether the paper contains an explicit governing equation; The first branch: When the paper contains a governing equation from parameters to target performance indicators, extract the explicit governing equation in the paper, identify the equation type as one of closed-form algebra, multi-step chain, implicit root finding, piecewise condition, coupled system or integro-differential, translate it into Python numerical code, and enforce Sobol-compatible coding rules; The second branch: When the paper only provides a qualitative trend description, construct a normalized additive polynomial surrogate model, whose mathematical form is QoI_k = Σ_{i=1}^{n} w_i · f_i(X_{n,i}) + B_k, where X_{n,i} is a parameter normalized to the interval [0,1], f_i is a trend function mapped according to the qualitative description of the paper, w_i is a sensitivity weight, and B_k is a baseline constant; Step S6, model validation: Perform nominal value verification and K-fold cross-validation on the constructed surrogate model, and generate a model quality rating; Step S7, sensitivity analysis and uncertainty propagation: Generate parameter samples using Latin hypercube sampling, perform uncertainty propagation on the surrogate model, calculate the mean, standard deviation and confidence interval of each target performance indicator, and calculate the global sensitivity index using the unbiased Saltelli Sobol estimator; Step S8, Reliability Analysis: Based on the propagation results, the failure probability and reliability index of each target performance index are calculated using the first-order quadratic moment method. The system reliability is calculated using a cascade model, and samples that meet the thresholds of all target performance indices are selected as the satisfactory parameter range. Step S9, Visualization: Automatically generate Sobol sensitivity bar chart, parameter probability density distribution chart, target performance index probability density distribution chart, reliability dashboard and cross-validation result chart; Step S10: Conclusion Report Generation: Read all calculation results through the large language model and generate a structured analysis conclusion report that includes an execution summary, key findings, parameter importance ranking, optimization suggestions, value analysis, and limitation analysis.

2. The automated uncertainty quantification analysis method based on a large language model as described in claim 1, characterized in that, Step S1 also includes a parameter self-verification step: by calling the large language model a second time, it is verified whether each extracted parameter and each target performance indicator has supporting evidence in the Results, Discussion and Conclusion sections of the paper. Parameters without evidence are removed and missing parameters are supplemented.

3. The automated uncertainty quantification analysis method based on a large language model as described in claim 1, characterized in that, When the input is a CSV engineering data file, step S1 further includes the following sub-steps: automatically identifying the input and output columns through keyword matching, calculating the mean, standard deviation, coefficient of variation, and quantiles of each column, fitting three distributions (Normal, Uniform, and Lognormal) and selecting the optimal distribution type using the AIC criterion, automatically selecting the surrogate model construction method based on the number of parameters (multinomial chaotic expansion OLS fitting when the number of parameters n≤10, and Gaussian process regression Cholesky fitting when the number of parameters n>10), and reusing the complete workflow of the paper mode in subsequent steps S6 to S10.

4. The automated uncertainty quantification analysis method based on a large language model as described in claim 1, characterized in that, The mapping rules for the probability distribution type in step S3 are as follows: for geometric dimension parameters, Normal or Uniform distribution is recommended; for material property parameters, Normal or Lognormal distribution is recommended; for ratio / fraction parameters, Uniform or Beta distribution is recommended; for environmental condition parameters, Uniform or Normal distribution is recommended; and for load parameters, Gumbel or Weibull distribution is recommended.

5. The automated uncertainty quantification analysis method based on a large language model as described in claim 1, characterized in that, The normalized additive polynomial surrogate model in the second branch of step S5 has a trend function f_i mapped to one of the following six standard forms according to the qualitative description in the paper: proportional function f(X_n) = X_n, decreasing function f(X_n) = 1 -X_n, saturation function f(X_n) = √(X_n), acceleration function f(X_n) = e^{X_n} - 1, peak function f(X_n) = 1 - 4(X_n - 0.5)², threshold function f(X_n) = 1 / (1 + e^{-10(X_n - 0.5)}); the weights w_i are assigned according to the sensitivity conclusions in the paper: dominant parameter w_i ∈ [0.7, 1.0], significant parameter w_i ∈ [0.3, 0.7], and low-impact parameter w_i ∈ [0.05, 0.25].

6. The automated uncertainty quantification analysis method based on a large language model as described in claim 1, characterized in that, In step S5, after constructing the normalized additive multinomial surrogate model in the second branch, a calibration loop is executed: the surrogate model is evaluated at the nominal design point. If the deviation between the predicted target performance index value and the paper report value exceeds 20%, only the Scale and Baseline constants are adjusted through the large language model, without modifying the weight w_i or the trend function f_i, and the iteration is repeated up to 3 times.

7. The automated uncertainty quantification analysis method based on a large language model as described in claim 1, characterized in that, The Sobol-compatible encoding rules for the first branch in step S5 include: prohibiting the use of the np.clip function to generate flat regions that cause derivatives to disappear; prohibiting the use of Boolean index assignment arr[mask] = value; prohibiting the use of if / else for array operations, and requiring the use of np.where instead; requiring the use of smoothing nonlinear functions such as np.exp, np.log, np.sqrt, and np.power; adding 1e-10 to the denominator to prevent division by zero; and specifying the interface of model_func as X shape (N, n) → return shape (N, m), where N is the number of samples, n is the number of parameters, and m is the number of target performance indicators.

8. The automated uncertainty quantification analysis method based on a large language model as described in claim 1, characterized in that, The model quality rating in step S6 is divided into four levels: reliable indicates nominal deviation <20% and cross-validation R²>0.8, low_confidence indicates nominal deviation <20% but R²≤0.8, unverified indicates nominal deviation between 20% and 50% and is a second-branch model, and unreliable indicates nominal deviation ≥50% and is a first-branch model.

9. The automated uncertainty quantification analysis method based on a large language model as described in claim 1, characterized in that, In step S7, the unbiased Saltelli Sobol estimator replaces the cross product term in the standard Saltelli method with pooling estimation. Specifically, it calculates the overall mean using f_bar = (1 / 2N) Σ_{k=1}^{2N} f_k, replacing mean(f_A)·mean(f_B) in the original method with f_bar², where {f_k}_{k=1}^{2N} is the concatenation of two independent sample matrices f(A) and f(B), reducing the estimation bias from O(1 / √N) to O(1 / N) and halving the estimator variance. The unbiased Saltelli Sobol estimator in step S7 is calculated 5 times using 5 different random seeds, and the median is taken as the final result to further reduce Monte Carlo noise. The sample size is set to max(5000, n × 2000), where n is the number of parameters.

10. An automated uncertainty quantification analysis system driven by a large language model, characterized in that, The tool for performing the analysis method according to any one of claims 1-9 includes an input module, a large language model-driven extraction module, a numerical calculation module, a visualization module, and a report generation module. The input module is used to receive Markdown files of academic papers or CSV project data files; The large language model-driven extraction module is used to execute steps S1 to S5 as described in claim 1, including parameter extraction, self-verification, baseline establishment, distribution recommendation, method selection, and bi-branch model construction. The numerical calculation module includes a built-in algorithm library for performing steps S6 to S8 of claim 1, including model verification, Latin hypercube sampling, unbiased Saltelli Sobol sensitivity analysis, uncertainty propagation, and FOSM reliability calculation. The visualization module is used to execute step S9 of claim 1, and automatically generate a Sobol sensitivity bar chart, a parameter probability density distribution chart, a target performance index probability density distribution chart, a reliability dashboard, and a cross-validation result chart. The report generation module is used to perform step S10 of claim 1, and generate a structured analysis conclusion report through a large language model; The built-in algorithm library in the numerical calculation module contains more than 55 algorithms in 9 modules, covering sampling methods, random expansion, sensitivity analysis, reliability methods, Gaussian processes, prediction models, regression regularization, adjoint methods, and cognitive uncertainty quantification.

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