We present a method to increase the resolution of measurements of a physical system and subsequently predict its time evolution using thermodynamics-aware neural networks. Our method uses adversarial autoencoders, which reduce the dimensionality of the full order model to a set of latent variables that are enforced to match a prior, for example a normal distribution. Adversarial autoencoders are seen as generative models, and they can be trained to generate high-resolution samples from low-resoution inputs, meaning they can address the so-called super-resolution problem. Then, a second neural network is trained to learn the physical structure of the latent variables and predict their temporal evolution. This neural network is known as an structure-preserving neural network. It learns the metriplectic-structure of the system and applies a physical bias to ensure that the first and second principles of thermodynamics are fulfilled. The integrated trajectories are decoded to their original dimensionality, as well as to the higher dimensionality space produced by the adversarial autoencoder and they are compared to the ground truth solution. The method is tested with two examples of flow over a cylinder, where the fluid properties are varied between both examples.

翻译：本文提出一种利用热力学感知神经网络提升物理系统测量分辨率并预测其时间演化的方法。该方法采用对抗自编码器，将全阶模型降维至一组与先验分布（如正态分布）匹配的潜变量。对抗自编码器作为生成模型，能够通过训练实现从低分辨率输入生成高分辨率样本，从而解决所谓的超分辨率问题。随后，第二个神经网络被训练以学习潜变量的物理结构并预测其时间演化，该网络被称为结构保持神经网络。它通过度量辛结构学习系统特性，并施加物理约束以确保热力学第一和第二定律得到满足。最终将积分轨迹解码至原始维度空间以及对抗自编码器生成的高维空间，并与真实解进行对比验证。该方法通过两个圆柱绕流算例进行测试，两个算例的流体物性参数各不相同。