Deep learning reveals key predictors of thermal conductivity in covalent organic frameworks

Abstract

The thermal conductivity of covalent organic frameworks (COFs), an emerging class of nanoporous polymeric materials, is crucial for many applications, yet the link between their structure and thermal properties remains poorly understood. Analysis of a dataset containing over 2,400 COFs reveals that conventional features such as density, pore size, void fraction, and surface area do not reliably predict thermal conductivity. To address this, an attention-based machine learning model was trained, accurately predicting thermal conductivities even for structures outside the training set. The attention mechanism was then utilized to investigate the model's success. The analysis identified dangling molecular branches as a key predictor of thermal conductivity, leading us to define the dangling mass ratio (DMR), a descriptor that quantifies the fraction of atomic mass in dangling branches relative to the total COF mass. Feature importance assessments on regression models confirm the significance of DMR in predicting thermal conductivity. These findings indicate that COFs with dangling functional groups exhibit lower thermal transfer capabilities. Molecular dynamics simulations support this observation, revealing significant mismatches in the vibrational density of states due to the presence of dangling branches.

Figures (7)

• Figure 1: Overview of this study. A COF structure consists of molecular substructures called linkers and knots arranged in a periodic pattern described by the topology. Through molecular dynamics, we construct a large dataset of 2,471 COFs (with diverse linkers, knots, and topologies) and their corresponding thermal conductivities. We demonstrate that conventional descriptors, such as density, pore size, void fraction, and surface area, fail to predict the thermal conductivity reliably. We employ a machine learning framework based on attention mechanism and transformer architecture to uncover a novel predictor, thus enhancing our understanding of the structure-property relationship of thermal conductivity of COFs.
• Figure 2: Distribution of (a) $\kappa$ versus density (with the color indicating data count per bin), (b) $\kappa$ versus largest pore diameter (LPD), (c) $\kappa$ versus void fraction, and (d) $\kappa$ versus gravimetric surface area (GSA). Also shown are four COF structures (i-iv) with contrasting properties, marked by green triangles in the plots above. The $r$-value indicates the Pearson correlation coefficient.
• Figure 3: Schematic of PMTransformer model. A sample COF structure is shown on the left. A crystal graph convolutional neural network computes local embeddings of the COF graph, while GRIDAY computes a three-dimensional energy grid of the structure, which becomes the global embeddings. These embeddings are combined and input into the PMTransformer (which includes a transformer encoder with attention mechanism and a prediction head) to predict $\kappa$. On the right, a parity plot compares $\kappa$ predictions with ground truth values. We report the mean and standard deviation of the goodness-of-fit across five random seeds. The random seeds affect the initialization of the prediction head, while the rest of the model is initialized from the pre-trained PMTransformer weights. The dashed line represents the ideal line with zero intercept and unit slope.
• Figure 4: An example pair of COFs with same topologies, similar geometric descriptors, but contrasting thermal conductivities. The first column illustrates the COF structures. The second column shows the atom-level attention score profile computed by the attention mechanism. The third column shows the same COF structure distinguishing atoms on the main branch and dangling atoms (with separate distinction for hydrogen atoms). The fourth column shows the VDOS profiles of various groups of atoms within the corresponding COF structure with the overlap metric $S$. The legend indicates the VDOS profile for main branch atoms $(.)$ and dangling atoms $(.)^{\text{(d)}}$. The reported thermal conductivities are obtained from NEMD simulations, rather than predicted by the PMTransformer model.
• Figure 5: An example pair of COFs with same topologies, similar geometric descriptors, but contrasting thermal conductivities. The first column illustrates the COF structures. The second column shows the atom-level attention score profile computed by the attention mechanism. The third column shows the same COF structure distinguishing atoms on the main branch and dangling atoms (with separate distinction for hydrogen atoms). The fourth column shows the VDOS profiles of various groups of atoms within the corresponding COF structure with the overlap metric $S$. The legend indicates the VDOS profile for main branch atoms $(.)$ and dangling atoms $(.)^{\text{(d)}}$. The reported thermal conductivities are obtained from NEMD simulations, rather than predicted by the PMTransformer model.