Using Linear Algebra to discover unknown Forces

[giodude]

In classical mechanics, it seems like solving force equations are a question of finding a solvable system of equations that accounts for all existing forces and masses in question. Therefore, I'm curious if this can be mixed with reinforcement learning to create a game and reward function through which a model can derive any remaining or unknown forces. The reward function that I believe would be useful is to have the model find a set of systems in the form of square, invertible matrices and then use those systems to enact the state change from state 1 of the physical system to the recorded state 2 of the physical system and find which best approximates it, until approaching some desired confidence interval. I'm new to physics so this is a half baked approach but I'm curious to get feedback and maybe spark a discussion about what the benefits and challenges of this approach may be!

 

[DaveE]

If you account for all existing forces, there won't be any unknown forces left to determine.
Sorry, kind of nitpicking there.

If by unknown forces you mean conceptually known to physics but unmeasured, then yes. This happens all the time in control systems, for example. Like how an airplane knows what the wind speed is based on the perturbations in it's navigation models. Kalman filtering is another good example, where future noise can be reduced in a system by identifying how the signal has been deviating from the expected model.

If you mean discover a force previously unknown to physicists, then this is way too simplistic compared to the sort of math and modelling that modern physicists do. However, the general concept is correct. Look for things that don't fit the model. For example, this is how we know there is something we call "dark matter" and "dark energy". Your game may come up with some description of what doesn't fit. The problem then is explaining it. There is no guarantee that what you get is correct, it would just be a description of the errors or perhaps a new model system with no ontological justification.

 

[BWV]

One could take a large enough dataset of properly constructed measurements of, say, projectile motion, and train a neural network that would then reproduce the correct (enough) classical mechanics answers to problems, the issue would be understanding how the model arrives at answers

 

[Baluncore]

The reward function that I believe would be useful is to have the model find a set of systems in the form of square, invertible matrices and then use those systems to enact the state change from state 1 of the physical system to the recorded state 2 of the physical system and find which best approximates it, until approaching some desired confidence interval.

There may be multiple solutions to the dataset. You could not know that, so would be overconfident in the one simple solution that was found.

Imagine you land on the shore of a mountainous island. Your strategy is to walk uphill until you get to the top of the mountain. It is dark when you get there, so you build a survey marker, then walk back down the mountain.

If you had reached the summit in daylight, you might have seen several other peaks higher than the one you were on.

If you marked your track on the way up, you could return to the same landing point. If you did not mark the track, you could end up on some other beach, or precipice.