A molecule can look ready to stretch, yet take a very different path from another molecule that looks identical. This study teaches artificial intelligence to uncover the hidden information that explains why. Many important natural processes are too complicated for scientists to describe with a simple set of equations.

The study asks whether artificial intelligence can learn useful rules from observations while still obeying known physical principles. The approach is tested on the stretching of long polymer chains in an externally applied field. It learns three interpretable thermodynamic coordinates and builds a landscape of the stretching process.

The central problem is that flexible data-fitting systems can predict behavior, yet their generic rules may be difficult to interpret, while their generality can reduce long-term accuracy and stability. S-OnsagerNet is an artificial intelligence platform that discovers an interpretable description of a changing system directly from microscopic trajectories.

The method keeps the macroscopic quantity of interest, then learns additional closure coordinates and an evolution law on the combined coordinates, making the system more predictable and understandable. For a stretching polymer, the visible quantity can be its extension. The learned coordinates are combined with it to create an evolution law that supports understanding, checking against experiments, and control.

It extends the classical Onsager principle with a time-evolution law in which a positive semidefinite matrix models energy dissipation in the system. This extension targets dynamics far from equilibrium and substantial stochastic behavior, with an antisymmetric component modeling conservative forces in the dynamics.

Its diffusion matrix and white-noise process represent thermal fluctuations, adding randomness to the model's description of the system over time. The unknown parts are represented by trainable deep neural networks, while required physical constraints are preserved.

Another network generates the additional coordinates. The test begins with chains that have similar extension lengths, but they subsequently stretch at vastly different rates. The learned description predicts the true statistics of those different paths.

It also captures the distribution of the time taken to reach a reference extension length, rather than only following one average trajectory. The landscape explains why nearly identical chains can unfold differently: one route heads directly toward a stable stretched state, while another lingers near a bottleneck before escaping.

That hidden terrain turns different stretching behaviours into predictable paths. A folded polymer can be guided past the barrier that normally delays stretching: the flow briefly stops while random motion brings it into a useful position, then resumes to push it onward.

The trajectories show this guidance makes unfolding happen more quickly and reliably. The strongest test comes from physical experiments with individual DNA molecules. Two samples initially appear similar, making their later stretching behavior impossible to distinguish by eye.

When the samples are placed in the learned coordinates, subtle differences become visible and lead to different predicted stretching statistics. This improves on human labeling, which can happen only much later. The same relation between the learned coordinates near the stretched state also applies to experimental data from two sources, including the current experiments and previously available data.

The map is not merely a fit to simulated motion: its qualitative predictions are confirmed by physical experiments, including single-molecule observations of DNA stretching. Together, these results demonstrate the promise of using the learned description to enable physical understanding and control of real polymer dynamics.

The approach has limits. It is less suited to chaotic systems, and its current theory assumes that thermal noise is small compared with the other forces. Its accuracy also depends on the observations covering the important regions of the landscape, so future versions could choose new data more actively and systematically.

More broadly, the practical promise is that this approach could be applied to learn macroscopic thermodynamics in other systems of scientific interest. The same approach may eventually learn large-scale thermodynamic descriptions for other systems of scientific interest, beyond polymer stretching.

The system turns microscopic motion into a small, interpretable map that predicts different stretching behavior and works on real DNA. That could help scientists understand and control complicated moving systems.