Discovering State Variables Hidden in Experimental Data

Abstract: All physical laws are described as relationships between state variables that give a complete and non-redundant description of the relevant system dynamics. However, despite the prevalence of computing power and AI, the process of identifying the hidden state variables themselves has resisted automation. Most data-driven methods for modeling physical phenomena still assume that observed data streams already correspond to relevant state variables. A key challenge is to identify the possible sets of state variables from scratch, given only high-dimensional observational data. Here we propose a new principle for determining how many state variables an observed system is likely to have, and what these variables might be, directly from video streams. We demonstrate the effectiveness of this approach using video recordings of a variety of physical dynamical systems, ranging from elastic double pendulums to fire flames. Without any prior knowledge of the underlying physics, our algorithm discovers the intrinsic dimension of the observed dynamics and identifies candidate sets of state variables. We suggest that this approach could help catalyze the understanding, prediction and control of increasingly complex systems.

Music by Vincent Rubinetti.

[pion]

I fell in love with this concept back when I used Nutonian Eureqa (and lots of good pointers from M Schmidt). This is next level! There are few ML endeavors more beneficial to humanity than discerning physical theorems directly from data with no initial primer. Very excited to see where you take this next. Makes me want to use my physics education a bit more and get coding!

[therobotstudio]

Total genius, I love that fire has by far the highest ID.

[redpandachannel]

C'est peut-être la découverte du siècle le potentiel est presque infini !

[corpsdharmonie]

Incroyable découverte! Hâte de suivre l'évolution de vos recherches!! Votre IA semble très prometteuse 😍