Machine learning applications in reservoir modeling are hindered by the limited availability of well log data, a common challenge in the oil and gas industry. We propose VAEc-tMC, a domain-informed Conditional Variational Autoencoder that generates synthetic well-log data conditioned on rock type. Addressing a critical gap by existing generative models that rely solely on statistical reconstruction, our model embeds geological domain knowledge into the latent space, and optimizes a modified objective with an adaptive Student-t reconstruction loss and a beta-weighted KL regularizer, improving stability under heavy-tailed data. When used for data augmentation, the synthetic samples preserve inter-log dependencies and substantially enhance downstream classification, accuracy 39→63%, F1-score 36→68%, AUC 0.46→0.80 on a held-out well. Beyond the geological context, the proposed approach illustrates a generalizable strategy where domain-aware generative models with adaptive loss functions provide a robust solution for data-efficient learning in scientific domains facing data scarcity, noise, and heavy-tailed distributions.

The generation of synthetic well log data is crucial for enhancing the understanding and exploration of subsurface reservoirs. This paper introduces a novel Generative Adversarial Network (GAN) model that incorporates a Principal Component Analysis (PCA)-based loss function to improve the quality of synthetic well log data. The proposed method is distinguished by its ability to generate complete well log datasets, rather than just individual logs or completing partial logs. Traditional GANs utilize cross-entropy loss but often fail to capture the complex structural patterns inherent in well logs. By integrating PCA into the loss function, our model not only distinguishes real from synthetic data but also ensures that the synthetic data retains the intrinsic variability and relationships observed in real logs. We validate our approach using histograms, correlation heatmaps, dimensionality reduction techniques (PCA and t-SNE), and a discriminative task. Results show that synthetic data generated with PCA-based loss aligns closely with real data, demonstrating superior preservation of statistical and structural characteristics. This advancement in synthetic data generation holds promise for enriching subsurface data analysis and exploration.