local sensitivity analysis

This work addresses the efficient and robust computation of gradients for numerical solutions of differential equations. We systematically survey four differentiable programming paradigms—adjoint methods, automatic differentiation (via source-to-source transformation and operator overloading), numerical perturbation, and symbolic-numeric hybrid approaches—and introduce, for the first time, a unified differentiability framework that bridges inverse problem solving and machine learning methodologies. We establish a cross-method comparative taxonomy and provide platform-specific best-practice guidelines for scientific computing libraries including SciPy, JAX, and TorchDiffeq. Our analysis rigorously characterizes trade-offs among accuracy, memory footprint, computational complexity, and applicability domains for each method. The results deliver both theoretical foundations and practical implementation pathways for differential-equation–data fusion modeling tasks, including parameter inversion, sensitivity analysis, and physics-informed neural networks (PINNs).

This work proposes a gradient-based active learning method to enhance the accuracy of global sensitivity analysis under limited computational budgets. By leveraging the posterior gradient distribution of a Gaussian process surrogate model, the approach introduces a novel acquisition function that explicitly accounts for correlations among partial derivatives, enabling intelligent selection of the most informative input samples within a constrained simulation budget. Compared to existing derivative-based global sensitivity measures (DGSM)-oriented strategies, the proposed method offers a more comprehensive and robust framework. Experimental results on multiple benchmark test functions and a real-world pesticide transport environmental model demonstrate that the method significantly outperforms state-of-the-art approaches, yielding notably improved estimates of both Sobol’ indices and DGSM sensitivity measures.

This study addresses the lack of a systematic framework for identifying critical input variables and conducting sensitivity analysis under uncertainty in complex simulations, particularly in military decision-making contexts. The authors propose a unified sensitivity analysis framework that integrates local and global methods—including variance-based, derivative-based, screening, and uncertainty quantification techniques—and strategically maps these approaches to specific decision objectives such as factor prioritization, fixing, variance reduction, and mapping. Innovatively, the framework introduces a “sensitivity audit” mechanism to enhance traceability of model assumptions and promote responsible model usage. By providing a structured guide for high-dimensional, complex simulation systems, this work significantly improves model interpretability, transparency, and the credibility of decisions derived from such models.

Neural network sensitivity to input perturbations remains poorly understood, limiting model interpretability—especially in clinical applications. Method: We propose a hierarchical sensitivity analysis framework: (1) for small feedforward networks on clinical diabetes data, we employ Sobol indices for global sensitivity analysis to identify discriminative features and enable dimensionality reduction with <1.2% accuracy loss; (2) for CNNs (VGG-16, ResNet-18) applied to ultrasound imaging, we integrate local pixel perturbation analysis, activation maximization, and Grad-CAM to quantify spatial consistency between saliency maps and decision-relevant regions (IoU > 0.78). Contribution/Results: Our framework bridges global feature importance and local decision localization, demonstrating anatomically plausible attention patterns in CNNs. It supports diverse model scales and data modalities while ensuring statistical robustness and visual interpretability—constituting the first quantitative validation of spatial alignment between perturbation-based and gradient-based explanations in medical ultrasound.

This work investigates the sensitivity of optimal score functions and generated samples in diffusion models to perturbations in the underlying data distribution—without requiring model retraining. We propose the first differentiable analytical framework that explicitly derives a closed-form expression for the directional derivative of the mapping from data distribution to score function. The method supports black-box access to pretrained models, requiring only their forward outputs and input gradients. By incorporating numerically stable differentiation techniques, it achieves sensitivity estimation with computational complexity matching that of standard sampling. Experiments on image diffusion models demonstrate high-precision prediction of how generated sample distributions respond to minor training-set perturbations. Predicted changes correlate strongly with actual changes observed after retraining or fine-tuning (Pearson *r* > 0.92), validating its fidelity. This framework provides a novel tool for model diagnostics, robustness analysis, and data editing in diffusion-based generative modeling.

This work addresses the challenge of estimating gradients of distribution parameters for random vectors in black-box simulators or expensive physical simulations. We propose Distributional Sensitivity Analysis (DistroSA), the first method to leverage derivatives of the conditional distribution inverse mapping for arbitrary-dimensional random vectors, combined with diagonal Jacobian approximation and four second-order numerical algorithms. DistroSA enables differentiable inference without requiring explicit model knowledge, prior sampling mechanisms, or high-dimensional integration. The resulting differentiable sampling subroutine framework is compatible with automatic differentiation and deep learning platforms, supporting efficient gradient propagation even when closed-form solutions are unavailable. Experiments validate its theoretical correctness and numerical robustness, demonstrating successful application to uncertainty quantification and parameter inversion for nuclear physics quantum correlation functions. The open-source DistroSA package ensures full reproducibility.

本文通过结合物理模型和实验数据，利用深度神经网络和高斯过程两种机器学习方法进行全局敏感性分析，以提高敏感性估计的准确性。

This work addresses the lack of interpretability in existing methods regarding the influence of hyperparameters in multi-objective optimization. The authors propose a novel game-theoretic framework that, for the first time, integrates Shapley effects with the Pareto front to enable objective-aware global sensitivity analysis, thereby uncovering key hyperparameters and their interactions under different optimization objectives. This approach not only identifies efficient hyperparameter configurations and substantially reduces the search space but also facilitates early-stage model performance estimation. The effectiveness and generalizability of the framework are empirically validated across three distinct neural network architectures and tasks.

Existing approaches struggle to effectively decompose the individual and interactive effects of aleatory and epistemic uncertainties in high-dimensional multi-output systems. This work proposes a dual-space tensor-product reproducing kernel Hilbert space (RKHS) framework that achieves an orthogonal decomposition of global dependencies through input–output factorized kernel functions. A concurrent dual Möbius inversion mechanism is introduced to preserve the structure of high-dimensional outputs, while inverse probability integral transforms combined with auxiliary variables enforce independence assumptions. Furthermore, a fully vectorized single-loop algorithm is developed to circumvent computationally expensive nested simulations. Numerical experiments on a modified multi-output Ishigami function and an aerodynamic pressure field problem demonstrate that the proposed method significantly enhances the accuracy, scalability, and computational efficiency of mixed uncertainty sensitivity analysis.

This work addresses the performance degradation of time series models in post-training quantization (PTQ), which arises from error propagation and amplification during quantization—particularly challenging in calibration-free or black-box settings where module sensitivity is hard to assess. To tackle this, the paper introduces discrete-time dynamical systems theory into quantization analysis for the first time. By modeling the inference process as a dynamical system, it proposes TQS, a quantizer-agnostic, prior-based sensitivity metric derived from trajectory sensitivity analysis, enabling calibration-free mixed-precision quantization budget allocation. The resulting TQS-PTQ framework significantly outperforms existing PTQ methods without relying on calibration data or second-order approximations, facilitating efficient low-bit deployment.

This study addresses the unclear mechanisms by which model quantization affects inversion attacks and its ambiguous relationship with data characteristics. For the first time, it decouples the information effects of quantization from optimization barriers, establishing a data-dependent sensitivity analysis framework. We propose a privacy-aware post-training quantization method that leverages Fisher sensitivity as a surrogate to optimize bit-width allocation, integrating activation calibration, weight rounding, and geometry-preserving regularization to jointly optimize security and utility. Experimental results demonstrate that under 4-bit quantization, ResNet-50 reduces the attack success rate to 26% with negligible accuracy degradation. Furthermore, combining this approach with SSD-based defenses suppresses the success rate to 37.33%.