Predictive analysis of physicochemical properties using novel weighted Sombor indices and comparative machine learning approach

The pharmaceutical industry currently faces a “combinatorial explosion” of potential drug-like molecules. Predicting their physical properties quickly is essential for modern drug discovery. Testing millions of theoretical compounds in a physical laboratory exceeds the capacity of traditional laboratory testing. Therefore, researchers need fast mathematical models to screen these chemicals before they are synthesized. Traditional Quantitative Structure-Property Relationship (QSPR) models rely on basic 2D graph theory to transform chemical structures into numerical data. However, standard unweighted topological indices treat all atoms identically, lacking to capture the unique physical differences between atoms like carbon and oxygen. To overcome this, our study introduces a “Physico-Topological” framework using Weighted Sombor Indices, modifying the geometric graph with atomic mass, radius, electronegativity, and ionization energy. We tested 28 novel descriptors on 200 pharmaceutical compounds, comparing classical Multiple Linear Regression (MLR) against advanced machine learning algorithms (Random Forest, XGBoost, ANN). Results show that linear models accurately predict size-dependent properties like Molar Refractivity ( $$\:{R}^{2}\approx\:0.98$$ ). Conversely, electronic properties like Polarizability require the non-linear architecture of Artificial Neural Networks ( $$\:{R}^{2}=\:0.93$$ ). While models achieved moderate accuracy for Boiling Point ( $$\:{R}^{2}=\:0.75$$ ), they failed for Density ( $$\:{R}^{2}<\:0.20$$ ). This proves that 2D invariants successfully map basic connectivity but miss 3D crystal packing and intermolecular forces. These weighted indices offer a highly efficient prescreening filter, though properties governed by spatial arrangement require hybridization (mixing two different things) with 3D geometric descriptors.