We propose a model-data asymptotic-preserving neural network(MD-APNN) method to solve the nonlinear gray radiative transfer equations(GRTEs). The system is challenging to be simulated with both the traditional numerical schemes and the vanilla physics-informed neural networks(PINNs) due to the multiscale characteristics. Under the framework of PINNs, we employ a micro-macro decomposition technique to construct a new asymptotic-preserving(AP) loss function, which includes the residual of the governing equations in the micro-macro coupled form, the initial and boundary conditions with additional diffusion limit information, the conservation laws, and a few labeled data. A convergence analysis is performed for the proposed method, and a number of numerical examples are presented to illustrate the efficiency of MD-APNNs, and particularly, the importance of the AP property in the neural networks for the diffusion dominating problems. The numerical results indicate that MD-APNNs lead to a better performance than APNNs or pure data-driven networks in the simulation of the nonlinear non-stationary GRTEs.

With the rapid advance of Machine Learning techniques and the deep increase of availability of scientific data, data-driven approaches have started to become progressively popular across science, causing a fundamental shift in the scientific method after proving to be powerful tools with a direct impact in many areas of society. Nevertheless, when attempting to analyze dynamics of complex multiscale systems, the usage of standard Deep Neural Networks (DNNs) and even standard Physics-Informed Neural Networks (PINNs) may lead to incorrect inferences and predictions, due to the presence of small scales leading to reduced or simplified models in the system that have to be applied consistently during the learning process. In this Chapter, we will address these issues in light of recent results obtained in the development of Asymptotic-Preserving Neural Networks (APNNs) for hyperbolic models with diffusive scaling. Several numerical tests show how APNNs provide considerably better results with respect to the different scales of the problem when compared with standard DNNs and PINNs, especially when analyzing scenarios in which only little and scattered information is available.

Neural program embedding can be helpful in analyzing large software, a task that is challenging for traditional logic-based program analyses due to their limited scalability. A key focus of recent machine-learning advances in this area is on modeling program semantics instead of just syntax. Unfortunately evaluating such advances is not obvious, as program semantics does not lend itself to straightforward metrics. In this paper, we introduce a benchmarking framework called COSET for standardizing the evaluation of neural program embeddings. COSET consists of a diverse dataset of programs in source-code format, labeled by human experts according to a number of program properties of interest. A point of novelty is a suite of program transformations included in COSET. These transformations when applied to the base dataset can simulate natural changes to program code due to optimization and refactoring and can serve as a "debugging" tool for classification mistakes. We conducted a pilot study on four prominent models--TreeLSTM [1], gated graph neural network (GGNN) [2], AST-Path neural network (APNN) [3], and DYPRO [4]. We found that COSET is useful in identifying the strengths and limitations of each model and in pinpointing specific syntactic and semantic characteristics of programs that pose challenges.

Instead, a signal space approach is used to gain new insights via ease of analysis and geometrical interpretation.

Instead, a signal space approach is used to gain new insights via ease of analysis and geometrical interpretation.

Instead, a signal space approach is used to gain new insights via ease of analysis and geometrical interpretation.