Deep learning techniques with neural networks have been used effectively in computational fluid dynamics (CFD) to obtain solutions to nonlinear differential equations. This paper presents a physics-informed neural network (PINN) approach to solve the Blasius function. This method eliminates the process of changing the non-linear differential equation to an initial value problem. Also, it tackles the convergence issue arising in the conventional series solution. It is seen that this method produces results that are at par with the numerical and conventional methods. The solution is extended to the negative axis to show that PINNs capture the singularity of the function at $\eta=-5.69$

在本文中，我们考虑了找到一种元学习在线控制算法的问题，该算法可以在面对$ n $（类似）控制任务的序列时可以在整个任务中学习。每个任务都涉及控制$ t $时间步骤的有限视野的线性动力系统。在采取控制动作之前，每个时间步骤的成本函数和系统噪声是对抗性的，并且控制器未知。元学习是一种广泛的方法，其目标是为任何新的未见任务开出在线政策，从其他任务中利用信息以及任务之间的相似性。我们为控制设置提出了一种元学习的在线控制算法，并通过\ textit {meta-regret}表征其性能，这是整个任务的平均累积后悔。我们表明，当任务数量足够大时，我们提出的方法实现了与独立学习的在线控制算法相比，$ d/d/d^{*} $较小的元regret，该算法不会在整个网上控制算法上进行学习任务，其中$ d $是一个问题常数，$ d^{*} $是标量，随着任务之间的相似性的增加而降低。因此，当任务的顺序相似时，提议的元学习在线控制的遗憾显着低于没有元学习的幼稚方法。我们还提出了实验结果，以证明我们的元学习算法获得的出色性能。

我们解决了通过在线后退地平线控制（RHC）的框架来控制控制未知线性动态系统的问题，以时代变化的成本函数。我们考虑控制算法不知道真正的系统模型的设置，并且只能访问固定长度（不与控制范围内的增长）预览未来成本函数。我们使用动态遗憾度量的算法表征了算法的性能，该算法被定义为算法产生的累积成本与后视行动中最佳动作顺序之间的差异。我们提出了两个不同的在线RHC算法来解决这个问题，即确定的等价RHC（CE-RHC）算法和乐观RHC（O-RHC）算法。我们表明，在模型估计的标准稳定假设下，CE-RHC算法实现$ \ Mathcal {O}（T ^ {2/3}）$动态遗憾。然后，我们将此结果扩展到通过提出O-RHC算法仅适用于真实系统模型的稳定假设。我们表明O-RHC算法实现$ \ Mathcal {O}（T ^ {2/3}）$动态遗憾，但有一些额外的计算。

在自动车辆（AVS）中，预警系统依赖于碰撞预测，以确保乘员安全。然而，使用深度卷积网络的最先进的方法在建模冲突中失败或者太昂贵/慢，使它们不太适合在AV边缘硬件上部署。为了解决这些限制，我们提出了SG2VEC，一种使用图形神经网络（GNN）和长短期内存（LSTM）层的时空场景图嵌入方法，以通过视觉场景感知来预测未来的碰撞。我们展示SG2VEC预测碰撞8.11％，比综合数据集的最新方法提前39.07％，在挑战现实世界碰撞数据集中更准确地进行29.47％。我们还表明，SG2VEC在将知识从合成数据集转移到现实世界驾驶数据集时更好。最后，我们证明SG2VEC更快地执行推论9.3X，较小的型号为88.0％，功率少32.4％，而且能量少于行业标准的NVIDIA驱动PX 2平台，制作它更适合在边缘实施。

Accurate determination of a small molecule candidate (ligand) binding pose in its target protein pocket is important for computer-aided drug discovery. Typical rigid-body docking methods ignore the pocket flexibility of protein, while the more accurate pose generation using molecular dynamics is hindered by slow protein dynamics. We develop a tiered tensor transform (3T) algorithm to rapidly generate diverse protein-ligand complex conformations for both pose and affinity estimation in drug screening, requiring neither machine learning training nor lengthy dynamics computation, while maintaining both coarse-grain-like coordinated protein dynamics and atomistic-level details of the complex pocket. The 3T conformation structures we generate are closer to experimental co-crystal structures than those generated by docking software, and more importantly achieve significantly higher accuracy in active ligand classification than traditional ensemble docking using hundreds of experimental protein conformations. 3T structure transformation is decoupled from the system physics, making future usage in other computational scientific domains possible.

Variational autoencoders model high-dimensional data by positing low-dimensional latent variables that are mapped through a flexible distribution parametrized by a neural network. Unfortunately, variational autoencoders often suffer from posterior collapse: the posterior of the latent variables is equal to its prior, rendering the variational autoencoder useless as a means to produce meaningful representations. Existing approaches to posterior collapse often attribute it to the use of neural networks or optimization issues due to variational approximation. In this paper, we consider posterior collapse as a problem of latent variable non-identifiability. We prove that the posterior collapses if and only if the latent variables are non-identifiable in the generative model. This fact implies that posterior collapse is not a phenomenon specific to the use of flexible distributions or approximate inference. Rather, it can occur in classical probabilistic models even with exact inference, which we also demonstrate. Based on these results, we propose a class of latent-identifiable variational autoencoders, deep generative models which enforce identifiability without sacrificing flexibility. This model class resolves the problem of latent variable non-identifiability by leveraging bijective Brenier maps and parameterizing them with input convex neural networks, without special variational inference objectives or optimization tricks. Across synthetic and real datasets, latent-identifiable variational autoencoders outperform existing methods in mitigating posterior collapse and providing meaningful representations of the data.

Differentiable Architecture Search (DARTS) has attracted considerable attention as a gradient-based Neural Architecture Search (NAS) method. Since the introduction of DARTS, there has been little work done on adapting the action space based on state-of-art architecture design principles for CNNs. In this work, we aim to address this gap by incrementally augmenting the DARTS search space with micro-design changes inspired by ConvNeXt and studying the trade-off between accuracy, evaluation layer count, and computational cost. To this end, we introduce the Pseudo-Inverted Bottleneck conv block intending to reduce the computational footprint of the inverted bottleneck block proposed in ConvNeXt. Our proposed architecture is much less sensitive to evaluation layer count and outperforms a DARTS network with similar size significantly, at layer counts as small as 2. Furthermore, with less layers, not only does it achieve higher accuracy with lower GMACs and parameter count, GradCAM comparisons show that our network is able to better detect distinctive features of target objects compared to DARTS.

The Government of Kerala had increased the frequency of supply of free food kits owing to the pandemic, however, these items were static and not indicative of the personal preferences of the consumers. This paper conducts a comparative analysis of various clustering techniques on a scaled-down version of a real-world dataset obtained through a conjoint analysis-based survey. Clustering carried out by centroid-based methods such as k means is analyzed and the results are plotted along with SVD, and finally, a conclusion is reached as to which among the two is better. Once the clusters have been formulated, commodities are also decided upon for each cluster. Also, clustering is further enhanced by reassignment, based on a specific cluster loss threshold. Thus, the most efficacious clustering technique for designing a food kit tailored to the needs of individuals is finally obtained.

Learning efficient and interpretable policies has been a challenging task in reinforcement learning (RL), particularly in the visual RL setting with complex scenes. While neural networks have achieved competitive performance, the resulting policies are often over-parameterized black boxes that are difficult to interpret and deploy efficiently. More recent symbolic RL frameworks have shown that high-level domain-specific programming logic can be designed to handle both policy learning and symbolic planning. However, these approaches rely on coded primitives with little feature learning, and when applied to high-dimensional visual scenes, they can suffer from scalability issues and perform poorly when images have complex object interactions. To address these challenges, we propose \textit{Differentiable Symbolic Expression Search} (DiffSES), a novel symbolic learning approach that discovers discrete symbolic policies using partially differentiable optimization. By using object-level abstractions instead of raw pixel-level inputs, DiffSES is able to leverage the simplicity and scalability advantages of symbolic expressions, while also incorporating the strengths of neural networks for feature learning and optimization. Our experiments demonstrate that DiffSES is able to generate symbolic policies that are simpler and more and scalable than state-of-the-art symbolic RL methods, with a reduced amount of symbolic prior knowledge.

Tumor-stroma ratio (TSR) is a prognostic factor for many types of solid tumors. In this study, we propose a method for automated estimation of TSR from histopathological images of colorectal cancer. The method is based on convolutional neural networks which were trained to classify colorectal cancer tissue in hematoxylin-eosin stained samples into three classes: stroma, tumor and other. The models were trained using a data set that consists of 1343 whole slide images. Three different training setups were applied with a transfer learning approach using domain-specific data i.e. an external colorectal cancer histopathological data set. The three most accurate models were chosen as a classifier, TSR values were predicted and the results were compared to a visual TSR estimation made by a pathologist. The results suggest that classification accuracy does not improve when domain-specific data are used in the pre-training of the convolutional neural network models in the task at hand. Classification accuracy for stroma, tumor and other reached 96.1$\%$ on an independent test set. Among the three classes the best model gained the highest accuracy (99.3$\%$) for class tumor. When TSR was predicted with the best model, the correlation between the predicted values and values estimated by an experienced pathologist was 0.57. Further research is needed to study associations between computationally predicted TSR values and other clinicopathological factors of colorectal cancer and the overall survival of the patients.