An AI-based Approach for Constructing Custom Thermodynamics

By Samudrapom DamReviewed by Susha Cheriyedath, M.Sc.Jan 3 2024

In an article recently published in the journal Nature Computational Science, researchers proposed an artificial intelligence (AI) platform that automatically learns a clear and concise thermodynamic description of complex, non-equilibrium systems from microscopic trajectory observations.

Understanding complex non-equilibrium systems

A universal approach is adopted by the modern scientific method to ensure a non-conflicting and stable progression of understanding of nature. New theories must be hypothesized and evaluated on previously accumulated data, compatible with fundamental scientific principles, and provable by experiments.

However, no general algorithmic method currently exists to implement this approach to promote discovery in complex systems. Until now, only the basic physical phenomena that are in equilibrium and static have been described using an intuitive equations’ set.

Several non-equilibrium dynamic phenomena that determine functionality in chemistry, biology, and soft-condensed matter are described using approximate, empirical laws. Advances in machine learning (ML) and AI have improved the prospects of identifying a data-driven solution to this issue.

Automated scientific discovery based on previously amassed data and restrictions provided by known physical principles, including conservation laws and symmetries, can be realized using AI. Such automated creation and verification of hypotheses can assist researchers in investigating complex phenomena where conventional physical intuition is ineffective.

The proposed AI-based approach

In this study, researchers developed a platform based on a generalized Onsager principle, designated as Stochastic OnsagerNet (S-OnsagerNet), to directly learn arbitrary stochastic dissipative systems’ macroscopic dynamical descriptions from their microscopic trajectory observations.

Specifically, the proposed AI platform can discover a closed and interpretable thermodynamic description of arbitrary stochastic dissipative dynamical systems by analyzing their microscopic trajectories. The method constructs reduced thermodynamic coordinates and interprets the dynamics on these coordinates simultaneously.

Unstructured and structured approaches are used to predict and understand the dynamical processes’ behavior from data. Unstructured approaches primarily parameterize the dynamical equations using a generic set of building blocks, such as fixed polynomials, and determine the most suitable associated parameters for the observations.

In the fitting process, physical insights can be added as regularizers. However, the generality of unstructured approaches affects long-term stability, predictive accuracy, and interpretability. The problem can be addressed using structured approaches, where the physical insights guide the model architecture design directly.

This work focused on structured approaches due to lacking a general structured approach to model noisy, non-equilibrium, and dissipative dynamics that emerge in applications such as biophysics and soft matter. The methodology proposed was based on the classical Onsager principle, which has been customized to such problems.

The physical systems’ macroscopic thermodynamic descriptions can provide valuable insights. However, constructing an intuitive thermodynamic description that allows subsequent control and analysis for a general complex dynamical system is significantly challenging.

The proposed approach overcame this challenge by learning a macroscopic thermodynamic description for specific microscopic dynamics through constructing low-dimensional partially interpretable closure coordinates and a time evolution law on these constructed coordinates simultaneously.

Moreover, the developed platform inherently limits the search to physically relevant evolution laws, unlike general AI approaches. Specifically, researchers ensured compatibility with the current scientific knowledge by constructing a generalized Onsager principle-based neural network architecture.

Significance of this research

The method's effectiveness was demonstrated by investigating theoretically and validating experimentally the stretching of long polymer chains in an externally applied field. Three interpretable thermodynamic coordinates were learned and a dynamical polymer stretching landscape, including regulating the stretching rate and identifying transition and stable states, was built successfully.

Specifically, the stretching dynamics of polymer chains having 900 degrees of freedom were learned and condensed into a thermodynamic description that involved only three macroscopic coordinates, which governed the polymer stretching dynamics in both experimental and computational data.

Additionally, a macroscopic evolution energy landscape was built that revealed the presence of transition and stable states, which can be considered as a dynamic equation of state. Verification computational experiments, such as the thermodynamic coordinate interpretation and the control of polymer stretching rate, can be designed by mastering such equations.

Results from the single-molecule deoxyribonucleic acid (DNA) stretching experiments displayed that the thermodynamic description constructed in the study could be effectively used to distinguish slow and fast stretching polymers, which is much beyond the existing human-labeling capabilities.

Moreover, the free-energy landscape-derived predicted fluctuation correlations matched with the experimental data. Physical experiments validated some qualitative predictions of the constructed thermodynamic description.

To summarize, the findings of this study demonstrated that the proposed AI-based methodology can be feasibly applied to general complex dissipative processes, such as glassy systems and protein folding, apart from the polymer and epidemic dynamics.