Deep learning still has great limitations, one of which is that it cannot incorporate prior knowledge, such as the basic laws of mathematics or physics. Usually, DL must be understood from the training set, which is difficult to really cover enough prior knowledge. One of the selling points of DL is that it does not need to be programmed with algorithms; instead, intelligence is extracted from these training sets through an optimized form. This method is very effective when the training set is large enough to cover the core of the target, but if other variables (such as rotation or movement) cannot be introduced well, this method is not very effective. This is a limitation that needs to be resolved urgently.
The easiest way to solve this problem is to expand the training range to cover more variables. For rotation, 108 * N training samples may be needed to cover 3 rotation axes and 36 directions (0, 10, 20, ... degrees) on each axis, and N samples are not enough. In other words, the number of training samples collected and labeled must be greatly increased. For the variable of movement, how to train ML to determine how other balls on the snooker table move when the cue ball is hit? Using training to rediscover what Newton had compiled more than 300 years ago seems to be a huge waste of creativity.
The best way to deal with these variables is to use prior knowledge of mathematics and physics in conjunction with ML. In computer graphics, we use algorithms based on mathematical formulas to infer the effect of rotation on the view. In the snooker example, we used Newton's law of motion, again encoded in the algorithm. These algorithms capture some simple equations, otherwise a large number of training sets are required when pursuing algorithm-free recognition, which is why the algorithm is eliminated.
A Stanford University paper used an understanding of projectile mechanics to identify and track the path of a thrown pillow in the room. It is reported that they first perform model recognition on a short path, and then use constraints to exclude a complete path that does not follow the expected second-order equation of motion. In fact, they used a classic formula as a constraint in the neural network structure. This research shows the promise of machine learning in the absence of supervision.
Another interesting paper from the Austrian Institute of Science and Technology uses a completely different approach (through ML) to model the safe operating conditions of robots (such as the range of moving arms or legs), which are based on known safe Learn simple formulas in range operations. These formulas allow results beyond the training range. They describe this as "a machine learning method that can accurately infer situations that cannot be accurately identified." In fact, this method is to establish one's prior knowledge in the form of simple linear equations by conducting experiments in a bounded space.
The third example comes from the Sorbonne University. They provided a diagram of the predicted sea surface temperature (SST). Sea surface temperature data has been generated from satellite imagery, which can provide a lot of information. Predicting how these data will develop requires timely updating of data based on partial differential equations (PDE), which is the basis of the standard method of prediction using numerical solution methods. The research team used a CDNN with a discretized version of the PDE equation to guide the weighting of time propagation in the network. Compared with numerical methods and some other NN methods, their research shows that it is more promising to see results.
Therefore, there are two methods to reduce or discretize prior physics knowledge into a mechanism suitable for the existing deep learning architecture through weighting. One method is to derive simple equations to form its own "a priori" knowledge base. However, in the author's opinion, the Sorbonne method seems to be the most scalable, because almost all problems in physics can be reduced to PDE.
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