Deep Learning as an Implementation of Mathematical Theory for Modeling Sentiment Dynamics: The Case of Pertamina’s “BBM Oplosan” Issue

Abstrak

Public sentiment dynamics provide a quantitative reflection of how societal trust and perception evolve during crises. This study implements mathematical theory through deep learning techniques to model changes in public sentiment surrounding Pertamina’s “BBM Oplosan” (fuel adulteration) issue, which went viral in Indonesia in early 2025. Twitter (X) data containing the keyword “Pertamina” were collected across two temporal windows—before and after the issue’s emergence. Sentiment was classified into positive, neutral, and negative categories using both lexicon-based analysis (InSet Lexicon) and deep learning architectures, including Convolutional Neural Networks (CNN), Long Short-Term Memory (LSTM), and a hybrid CNN-LSTM model. From a mathematical standpoint, deep learning serves as a functional approximation framework that minimizes loss through gradient-based optimization—an implementation of multivariable calculus and linear algebra principles. Results show that negative sentiment increased from 23.5% to 48.2%, while positive sentiment declined from 44.6% to 26.2%, indicating a significant erosion of public trust. The CNN model achieved the highest validation accuracy (~63%), though it exhibited signs of overfitting. This research demonstrates how mathematical models underlying deep learning can be effectively applied to analyze real-world social phenomena, offering a robust quantitative framework for monitoring and interpreting public opinion dynamics during corporate crises.