Heteroscedastic regression models a Gaussian variable's mean and variance as a function of covariates. Parametric methods that employ neural networks for these parameter maps can capture complex relationships in the data. Yet, optimizing network parameters via log likelihood gradients can yield suboptimal mean and uncalibrated variance estimates. Current solutions side-step this optimization problem with surrogate objectives or Bayesian treatments. Instead, we make two simple modifications to optimization. Notably, their combination produces a heteroscedastic model with mean estimates that are provably as accurate as those from its homoscedastic counterpart (i.e.~fitting the mean under squared error loss). For a wide variety of network and task complexities, we find that mean estimates from existing heteroscedastic solutions can be significantly less accurate than those from an equivalently expressive mean-only model. Our approach provably retains the accuracy of an equally flexible mean-only model while also offering best-in-class variance calibration. Lastly, we show how to leverage our method to recover the underlying heteroscedastic noise variance.

The identification of material parameters occurring in constitutive models has a wide range of applications in practice. One of these applications is the monitoring and assessment of the actual condition of infrastructure buildings, as the material parameters directly reflect the resistance of the structures to external impacts. Physics-informed neural networks (PINNs) have recently emerged as a suitable method for solving inverse problems. The advantages of this method are a straightforward inclusion of observation data. Unlike grid-based methods, such as the finite element method updating (FEMU) approach, no computational grid and no interpolation of the data is required. In the current work, we aim to further develop PINNs towards the calibration of the linear-elastic constitutive model from full-field displacement and global force data in a realistic regime. We show that normalization and conditioning of the optimization problem play a crucial role in this process. Therefore, among others, we identify the material parameters for initial estimates and balance the individual terms in the loss function. In order to reduce the dependence of the identified material parameters on local errors in the displacement approximation, we base the identification not on the stress boundary conditions but instead on the global balance of internal and external work. In addition, we found that we get a better posed inverse problem if we reformulate it in terms of bulk and shear modulus instead of Young's modulus and Poisson's ratio. We demonstrate that the enhanced PINNs are capable of identifying material parameters from both experimental one-dimensional data and synthetic full-field displacement data in a realistic regime. Since displacement data measured by, e.g., a digital image correlation (DIC) system is noisy, we additionally investigate the robustness of the method to different levels of noise.

多分辨率的深度学习方法，例如U-NET体系结构，在分类和分割图像中已经达到了高性能。但是，这些方法不能提供潜在的图像表示形式，也不能用于分解，denoise和重建图像数据。 U-NET和其他卷积神经网络（CNNS）通常使用合并来扩大接受场，这通常会导致不可逆的信息丢失。这项研究建议包括riesz-quincunx（RQ）小波变换，结合1）高阶Riesz小波变换和2）在U-NET体系结构内正交Quincunx小波（两者都用于减少医学图像中的模糊） ，以减少卫星图像及其时间序列中的噪音。在变换的特征空间中，我们提出了一种变异方法，以了解特征的随机扰动如何影响图像以进一步降低噪声。结合两种方法，我们引入了一种用于减少卫星图像中噪声的图像和时间序列分解的混合Rqunet-VAE方案。我们提出了定性和定量的实验结果，表明与其他最先进的方法相比，我们提出的Rqunet-VAE在降低卫星图像中的噪声方面更有效。我们还将我们的方案应用于多波段卫星图像的多个应用程序，包括：通过扩散和图像分割分解图像denoising，图像和时间序列分解。

多尺度模拟在计算资源方面要求。在连续微力学的背景下，多尺度问题源于从微观尺度上推断宏观材料参数。如果通过微观扫描明确给出了基础微观结构，则可以使用卷积神经网络来学习微观结构 - 绘图映射，这通常是从计算均质化获得的。 CNN方法提供了显着的加速，尤其是在异质或功能分级材料的背景下。另一个应用是不确定性量化，需要进行许多扩展的评估。但是，这种方法的一种瓶颈是所需的大量训练微观结构。这项工作通过提出针对三维微观结构生成的生成对抗网络来缩小这一差距。轻量级算法能够从单个微分扫描中学习材料的基本属性，而无需明确的描述符。在预测时间内，网络可以在几秒钟内且始终高质量生产具有原始数据具有相同特性的独特三维微观结构。