Model-free quantification of completeness, uncertainties, and outliers in atomistic machine learning using information theory (2404.12367v2)

Abstract: An accurate description of information is relevant for a range of problems in atomistic ML, such as crafting training sets, performing uncertainty quantification (UQ), or extracting physical insights from large datasets. However, atomistic ML often relies on unsupervised learning or model predictions to analyze information contents from simulation or training data. Here, we introduce a theoretical framework that provides a rigorous, model-free tool to quantify information contents in atomistic simulations. We demonstrate that the information entropy of a distribution of atom-centered environments explains known heuristics in ML potential developments, from training set sizes to dataset optimality. Using this tool, we propose a model-free UQ method that reliably predicts epistemic uncertainty and detects out-of-distribution samples, including rare events in systems such as nucleation. This method provides a general tool for data-driven atomistic modeling and combines efforts in ML, simulations, and physical explainability.

• The paper demonstrates that information entropy computed from MD simulations can accurately estimate thermodynamic entropy changes in materials systems.
• It employs a novel non-parametric, model-free approach leveraging kernel density estimation to evaluate uncertainty and detect rare, out-of-equilibrium events.
• The study enhances data robustness for ML interatomic potentials by quantifying dataset redundancy and guiding efficient data sampling.

Information Theory Bridges Atomistic Machine Learning and Materials Thermodynamics

Overview

In the context of atomistic modeling and materials science, the integration of ML methodologies with classical thermodynamic and statistical mechanics principles provides a fertile ground for advancing predictive capabilities and understanding material behaviors under varied conditions. The paper introduces an information theoretical framework that effectively unifies the predictive modeling of phase transformations, kinetic events, and uncertainty quantification (UQ) in ML-driven simulations. By leveraging molecular dynamics (MD) simulations and non-parametric estimates of information entropy, the paper illuminates the deep connections between information entropy and thermodynamic entropy in atomistic systems.

Key Methodologies and Results

Leveraging Information Entropy for Thermodynamic Predictions

The paper leverages information entropy derived from distributions of atom-centered environments in MD simulations to predict changes in thermodynamic entropy. This approach is validated through comparisons with entropy differences obtained via traditional thermodynamic integration methods, demonstrating that information entropy can closely estimate these changes across various materials systems such as tin and copper under different phase conditions. Notably, the direct computation of information entropy from MD trajectories presents a computationally efficient alternative to rigorous free energy calculations.

Analytical Framework and Computational Methods

The proposed descriptor for representing atomic environments facilitates the non-parametric estimation of information entropy. This representation employs bijective mapping techniques and a concise vector representation derived from interatomic distances and angles. Kernel density estimation (KDE) methods form the crux of calculating the entropy of these distributions, demonstrating scale-appropriate estimations managed via varying kernel bandwidths related to atomic volumes.

Evaluating Rare Events and Out-of-Equilibrium Systems

In kinetic studies, like nucleation processes, the information entropy can act as an insightful "order parameter". The framework aptly handles the non-equilibrium conditions often encountered in material transformations such as nucleation and growth, offering a method to indirectly track these rare events through entropy calculations, aligning well with classical nucleation theory predictions.

Empirical Validation with Machine Learning Interatomic Potentials (MLIPs)

On the front of ML-driven simulations, employing information entropy proves to be powerful in dissecting and understanding the dataset characteristics essential for developing robust MLIPs. Notably, the paper embarks on quantifying the redundancy in datasets and rationalizing the efficiency of data sampling methods, which can significantly influence the training dynamics and performance of MLIPs. Furthermore, through a novel model-free UQ method based on non-parametric statistical treatments of the entropy, the paper introduces reliable detection of extrapolation regimes, transcending common model-dependent UQ approaches.

Practical Implications and Future Directions

Enhancing Data Efficiency and Model Reliability

This integrative information-theoretic approach enables a more nuanced understanding and crafting of atomistic datasets, potentially reducing computational overheads by identifying and trimming redundancy in ML training datasets. The insights into the role of dataset entropy in MLIP efficacy pave the way for more targeted and efficient data-driven modeling strategies.

Broad Applicability and Scalability

The framework's capacity to handle vast atom-centered datasets, scale to systems involving millions of atoms, and provide rigorous yet intuitive metrics for dataset integrity and model uncertainty underscores its adaptability. Future efforts might explore the expansion of this framework beyond crystalline materials to more complex disordered systems or multi-component alloys.

Integration with Existing and Emerging Technologies

While the paper firmly grounds itself in contemporary computational methodologies, its implications beckon integration with emerging quantum computing platforms and advanced statistical learning models. Such future convergences could further revolutionize the speed and accuracy of atomistic simulations and thermodynamic analyses.

Concluding Thoughts

The unification of information theory with atomistic machine learning and materials thermodynamics not only enhances our theoretical understanding but also recalibrates practical approaches to materials modeling. As we advance, the adaptability of this framework to new challenges and its integration with burgeoning computational technologies will likely be key drivers of its long-term relevance and impact in the field.