sim-to-real encoder training

In data-scarce real-world scenarios, synthetic data can enhance model generalization, yet excessive incorporation degrades performance due to distributional shift—e.g., increased Wasserstein distance—between synthetic and real domains. Method: We propose the first analytical framework grounded in algorithmic stability and regularization theory to quantify how the mixture ratio of synthetic to real data affects generalization error. Our analysis reveals, for the first time, a U-shaped relationship between test error and synthetic data proportion, and derives the theoretically optimal mixing ratio. Crucially, we incorporate the Wasserstein distance into the generalization bound for kernel ridge regression, extending it to domain adaptation settings. Results: Experiments on CIFAR-10 and clinical brain MRI datasets validate our theory: models trained with the predicted optimal ratio achieve significantly lower test error and demonstrate improved robustness and generalization—both in-domain and cross-domain.

This study addresses the lack of theoretical guidance regarding per-domain sample sufficiency conditions in cross-domain learning. Overcoming the limitations of classical learning theory, this work establishes a theoretical criterion for per-domain sample requirements through generalization bound analysis and statistical learning theory derivations. The results demonstrate that the required sample size depends critically on the number of training domains, revealing an inverse-linear scaling law between domain count and sample complexity that elucidates the underlying principles of data sufficiency assumptions. These findings provide a rigorous theoretical foundation for evaluating existing datasets and constructing new ones, while offering deep insights into the intrinsic connection between in-domain learning and out-of-domain generalization.

This work addresses the challenge of rapidly generalizing models to new tasks in transfer learning. We propose a geometric transfer learning framework grounded in Hilbert space theory. Methodologically, we introduce the first functional-space geometric characterization of transfer learning, unifying interpolation, linear extrapolation, and nonlinear extrapolation under a single theoretical umbrella. We further propose a novel function encoder paradigm, rigorously proving its universal approximation property, and integrate kernel methods with functional analysis to enable efficient least-squares training. Empirically, our approach achieves state-of-the-art performance across four benchmark tasks, consistently outperforming leading methods—including Transformers and meta-learning approaches—both in generalization accuracy and adaptation speed. Key contributions include: (i) a principled geometric formalism for transfer learning in reproducing kernel Hilbert spaces; (ii) a theoretically grounded, trainable function encoder; and (iii) empirical validation demonstrating superior sample efficiency and cross-task generalization.

Convolutional neural networks (CNNs) for surrogate modeling of high-dimensional partial differential equations (PDEs) suffer from prohibitive computational costs due to reliance on large-scale, high-fidelity numerical simulations. Method: We propose a cross-dimensional transfer learning framework featuring a novel hybrid-dimensional (d- and (d−1)-dimensional) joint training paradigm. It leverages approximate solutions of lower-dimensional PDEs to guide training of high-dimensional CNN surrogates, enabling knowledge transfer and error compensation. The architecture employs a fully convolutional encoder–decoder, multi-scale transfer mechanisms, and PDE-informed dimensionality-reduced data generation, augmented with uncertainty quantification. Contribution/Results: On multiphase flow benchmark problems, our method achieves higher accuracy than Monte Carlo methods using only a few times fewer simulation budgets. Forward inference is negligible in cost, dramatically improving the cost-effectiveness and practicality of PDE surrogates.

Meta-learning surrogate models for black-box optimization faces significant challenges in cross-task transfer under few-shot settings, primarily due to unmodeled domain misalignment and rigid linear assumptions. Method: This paper proposes a bi-level optimization framework that jointly models nonlinear domain warping—via a Beta-CDF-based mapping—and unspecified affine transformations, thereby unifying their coupled effects without relying on traditional linear approximations. The method enables rapid adaptation of pre-trained surrogates using only a few target-domain observations, optimizing an empirical loss via learnable parameters. Contribution/Results: Evaluated on the BBOB benchmark and real-world industrial black-box optimization tasks, the approach achieves substantial performance gains—up to 37%–62% improvement—over both the original pre-trained surrogate and from-scratch models. These results demonstrate its effectiveness and generalizability in data-scarce regimes.

本文解决如何用最少的真实数据测试合成数据集对AI模型训练效果的影响，提出了一种自适应e-过程符号翻转测试方法。

针对神经算子在新环境下精度下降的问题，提出LatentDDM方法，通过预训练局部预测器和轻量级组合模块适应新设置，减少高精度模拟需求。

This study addresses the structural degradation of pretrained neural operators during simulation-to-real (Sim2Real) transfer and proposes the R²NO framework. The method freezes the fine-tuned source predictor and introduces a shared repair module, innovatively formulating adaptation depth as the selective activation of Fourier-domain units learned independently from real data. It further integrates orthogonal Fourier projection, spectral ensembling, and ridge regression to fuse multiple candidate refinements. Experiments on RealPDEBench across six backbone architectures demonstrate that R²NO consistently outperforms full fine-tuning and iterative refinement baselines, achieving robust Sim2Real transfer for neural operators.

This study addresses the limited cross-geometry and cross-scenario generalization of neural CFD surrogate models and the prohibitive cost of generating new training data. We propose a few-shot efficient fine-tuning method based on cross-domain pre-training and multi-source data pooling. Our findings demonstrate that simply pooling diverse steady-state datasets significantly enhances model generalization, an advantage that proves architecture-agnostic and scales with both model size and data diversity. Experimental results show that, compared to training from scratch, the proposed approach reduces prediction error by 2–3× under identical sample budgets, or achieves equivalent accuracy with 8× fewer samples. This work establishes an efficient transfer learning paradigm for CFD surrogate modeling.

研究针对物理领域中模拟与实验数据分布差异的问题，提出一种自适应域适应方法，通过重新加权模拟事件来专注于实际物理不匹配。