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.

使用具有热力学感知能力的神经网络，通过增加物理系统的测量分辨率并预测其时间演化。该方法使用对抗自编码器将完全有序模型的维数降低到一组隐变量中，并确保这些变量符合先验（例如正态分布）。然后，利用第二个神经网络学习隐变量的物理结构和预测其时序演变，该神经网络称为结构保持神经网络。通过将整合轨迹解码为其原始维度以及由对抗自编码器产生的高维空间，将其与真实解进行比较。该方法在两个流体在圆柱上的例子中进行了测试，液体属性在两个例子之间存在变化。

稀缺时间动力学数据的热力学优化超分辨率