The increasing demand for efficient energy systems and high-performance electronics necessitates the rapid identification of new materials and nanostructures with extreme transport properties. Traditional trial-and-error methods are becoming insufficient, leading to the adoption of machine learning (ML) and data informatics. While ML has successfully predicted material properties and accelerated nanostructure design for thermal transport optimization (e.g., maximizing disorder-induced Anderson phonon localization), its application in discovering new physics has been limited. This is due to the interpolative nature of traditional ML algorithms, which struggle to extrapolate beyond known data and physics. This research addresses this limitation by demonstrating an adaptive ML approach to discover unexpected thermal transport behavior in aperiodic superlattices (SLs). Binary SLs, composed of periodically alternating layers of two materials, exhibit lower lattice thermal conductivity (κ) than their constituent materials, making them attractive for thermoelectric applications. Randomizing layer thicknesses in periodic SLs (creating aperiodic superlattices or random multilayers, RMLs) further reduces κ, often below the random alloy limit. This reduction is attributed to destructive interference of coherent phonons and Anderson localization. While ML methods like Bayesian optimization and genetic algorithms (GAs) have efficiently identified RML structures with ultra-low thermal conductivities, the possibility of certain random distributions leading to higher κ than periodic SLs remains unexplored. A recent study using GAs found enhanced κ in disordered two-dimensional graphene nanomeshes, challenging the prevailing understanding of randomness and thermal conductivity. However, GA methods are computationally expensive for identifying low-probability solutions. This work aims to develop a systematic ML approach that can efficiently identify such exceptional solutions.

Existing literature extensively explores the reduced thermal conductivity in superlattices and random multilayers. Studies have demonstrated that the periodic arrangement of alternating layers in superlattices leads to a decrease in thermal conductivity compared to the constituent materials due to phonon scattering at interfaces [10-13]. Further reduction in thermal conductivity is observed when the layer thicknesses are randomized, leading to aperiodic superlattices or random multilayers [7, 17-23]. This reduction is often attributed to Anderson localization of phonons due to destructive interference at the randomly spaced interfaces [18, 24]. Previous work has utilized machine learning techniques such as Bayesian optimization [3] and genetic algorithms [25] to efficiently search for structures with ultra-low thermal conductivity. However, these studies primarily focused on minimizing thermal conductivity, leaving open the question of whether disorder could lead to enhanced thermal transport in specific configurations. A recent study by Wei et al. [25] showed an example of enhanced thermal conductivity in disordered graphene nanomeshes, highlighting the potential for exceptions to the general trend. This study motivates the search for similar exceptions in other well-understood systems such as one-dimensional superlattices.

This study uses an iterative machine learning approach to identify random multilayer (RML) structures with unexpectedly higher thermal conductivity (κ) than their corresponding periodic superlattices (SLs) with the same total length and average period. Non-equilibrium molecular dynamics (NEMD) simulations using the LAMMPS package with the Tersoff potential were employed to calculate the thermal conductivity of the nanostructures. To avoid strain issues arising from unequal lattice constants of Si and Ge, the Ge lattice constant was artificially set equal to Si's. A 6x6 unit cell cross-section was used for simulations, ensuring converged κ values at 300K. NEMD simulations involved establishing a temperature gradient across the SL/RML sandwiched between thermal reservoirs. Thermal conductivity (κ) and interfacial thermal resistance (R) were calculated from the steady-state heat flux and temperature profile. A convolutional neural network (CNN) was developed to rapidly predict κ for candidate structures. The CNN input was a binary array representing the Si/Ge layer sequence, processed through convolutional and max-pooling layers, culminating in a dense layer providing the predicted κ. The CNN was trained iteratively. The Mean Absolute Percentage Error (MAPE) was used as the loss function, with the Adamax algorithm for training, using 300-500 epochs. Early stopping prevented overfitting. The iterative process involved identifying RML structures with high κ, adding them to the training dataset, and retraining the CNN to improve prediction accuracy for structures with high κ, which are not initially present in the training data.

The iterative machine learning approach successfully identified RML structures exhibiting unexpectedly higher κ than their corresponding periodic SLs with the same average period. The enhanced κ in these RML structures is attributed to increased coherent phonon transport and reduced apparent interfacial thermal resistance at closely spaced interfaces. Analysis revealed that the randomization of layer thicknesses can have dual effects, either decreasing or enhancing κ depending on the specific arrangement and SL period. In short-period SLs, randomness causes phonon localization and reduces κ, while in longer-period SLs, certain forms of aperiodicity can enhance coherent phonon transport, leading to increased κ. Visual representation of the atomic structures and temperature profiles showed a clear correlation between closely spaced interfaces, reduced interfacial resistance, and enhanced κ in high-κ RMLs compared to the corresponding SLs. The exhaustive search strategy for finding optimal structures was computationally feasible in this study, adding minimal computational cost to the overall NEMD simulations and CNN training. However, the authors note that for systems with a larger number of design variables, more sophisticated optimization algorithms (such as Genetic Algorithms) in conjunction with the CNN predictor would be necessary.

The findings challenge the conventional understanding that randomization always reduces the thermal conductivity of superlattices. This study demonstrates that careful engineering of aperiodicity can lead to enhanced thermal transport, opening up new possibilities for thermal management in electronic devices. The success of the adaptive machine learning approach highlights its potential for discovering exceptional and low-probability solutions beyond the limitations of traditional methods. The iterative process of refining the CNN model based on newly discovered structures with unexpected properties is a significant advancement in ML-driven materials discovery. The results suggest that the interplay between coherent and incoherent phonon transport can be manipulated to achieve desired thermal properties. This work paves the way for exploring similar unexpected phenomena in other material systems and nanostructures. The ability to predict and discover such exceptions to the general trends using an ML approach can substantially reduce the computational cost and accelerate the discovery of novel materials with exceptional properties for advanced applications.

This research successfully employed an iterative machine learning approach to discover unexpected thermal conductivity enhancement in aperiodic superlattices. The study demonstrates the ability of active machine learning to identify low-probability solutions that challenge established understanding. The enhanced thermal conductivity is attributed to increased coherent phonon transport and reduced interfacial thermal resistance. Future work could explore larger design spaces with more design variables, requiring more sophisticated optimization algorithms. Investigating the impact of different types of disorder and exploring other material systems could further expand the understanding of thermal transport in aperiodic structures. The methodology used here provides a powerful framework for discovering novel materials with tailored thermal properties.

The current study is limited to a specific material system (Si/Ge) and a one-dimensional architecture. The transferability of these findings to other material systems and geometries requires further investigation. While the exhaustive search strategy was feasible here, the computational cost could become prohibitive for significantly larger design spaces with numerous design variables. Future studies should explore the use of more efficient optimization algorithms to handle larger design spaces.