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：我们提出了一种方法，通过热力学感知神经网络提高物理系统测量分辨率，并进而预测其时间演化。该方法采用对抗自编码器，将全阶模型降维至一组满足先验分布（如正态分布）的隐变量。对抗自编码器可视为生成模型，通过低分辨率输入训练生成高分辨率样本，从而解决超分辨率问题。随后，训练第二个神经网络以学习隐变量的物理结构并预测其时间演化。该神经网络称为保结构神经网络，通过学习系统的度量-泊松结构施加物理约束，确保热力学第一、第二定律成立。积分轨迹被解码至原始维度以及对抗自编码器产生的高维空间，并与真实解进行对比。该方法通过两个圆柱绕流案例进行验证，两个案例的流体物性参数存在差异。