Seyed Kourosh Mahjour

Salah A Faroughi, Nikhil Pawar, Celio Fernandes et al.

Recent breakthroughs in computing power have made it feasible to use machine learning and deep learning to advance scientific computing in many fields, including fluid mechanics, solid mechanics, materials science, etc. Neural networks, in particular, play a central role in this hybridization. Due to their intrinsic architecture, conventional neural networks cannot be successfully trained and scoped when data is sparse, which is the case in many scientific and engineering domains. Nonetheless, neural networks provide a solid foundation to respect physics-driven or knowledge-based constraints during training. Generally speaking, there are three distinct neural network frameworks to enforce the underlying physics: (i) physics-guided neural networks (PgNNs), (ii) physics-informed neural networks (PiNNs), and (iii) physics-encoded neural networks (PeNNs). These methods provide distinct advantages for accelerating the numerical modeling of complex multiscale multi-physics phenomena. In addition, the recent developments in neural operators (NOs) add another dimension to these new simulation paradigms, especially when the real-time prediction of complex multi-physics systems is required. All these models also come with their own unique drawbacks and limitations that call for further fundamental research. This study aims to present a review of the four neural network frameworks (i.e., PgNNs, PiNNs, PeNNs, and NOs) used in scientific computing research. The state-of-the-art architectures and their applications are reviewed, limitations are discussed, and future research opportunities in terms of improving algorithms, considering causalities, expanding applications, and coupling scientific and deep learning solvers are presented. This critical review provides researchers and engineers with a solid starting point to comprehend how to integrate different layers of physics into neural networks.

Salah A Faroughi, Ramin Soltanmohammad, Pingki Datta et al.

Simulating solute transport in heterogeneous porous media poses computational challenges due to the high-resolution meshing required for traditional solvers. To overcome these challenges, this study explores a mesh-free method based on deep learning to accelerate solute transport simulation. We employ Physics-informed Neural Networks (PiNN) with a periodic activation function to solve solute transport problems in both homogeneous and heterogeneous porous media governed by the advection-dispersion equation. Unlike traditional neural networks that rely on large training datasets, PiNNs use strong-form mathematical models to constrain the network in the training phase and simultaneously solve for multiple dependent or independent field variables, such as pressure and solute concentration fields. To demonstrate the effectiveness of using PiNNs with a periodic activation function to resolve solute transport in porous media, we construct PiNNs using two activation functions, sin and tanh, for seven case studies, including 1D and 2D scenarios. The accuracy of the PiNNs' predictions is then evaluated using absolute point error and mean square error metrics and compared to the ground truth solutions obtained analytically or numerically. Our results demonstrate that the PiNN with sin activation function, compared to tanh activation function, is up to two orders of magnitude more accurate and up to two times faster to train, especially in heterogeneous porous media. Moreover, PiNN's simultaneous predictions of pressure and concentration fields can reduce computational expenses in terms of inference time by three orders of magnitude compared to FEM simulations for two-dimensional cases.

Seyed Kourosh Mahjour, Seyed Saman Mahjour

The petroleum industry faces unprecedented challenges in reservoir management, requiring rapid integration of complex multimodal datasets for real-time decision support. This study presents a novel integrated framework combining state-of-the-art large language models (GPT-4o, Claude 4 Sonnet, Gemini 2.5 Pro) with advanced prompt engineering techniques and multimodal data fusion for comprehensive reservoir analysis. The framework implements domain-specific retrieval-augmented generation (RAG) with over 50,000 petroleum engineering documents, chain-of-thought reasoning, and few-shot learning for rapid field adaptation. Multimodal integration processes seismic interpretations, well logs, and production data through specialized AI models with vision transformers. Field validation across 15 diverse reservoir environments demonstrates exceptional performance: 94.2% reservoir characterization accuracy, 87.6% production forecasting precision, and 91.4% well placement optimization success rate. The system achieves sub-second response times while maintaining 96.2% safety reliability with no high-risk incidents during evaluation. Economic analysis reveals 62-78% cost reductions (mean 72%) relative to traditional methods with 8-month payback period. Few-shot learning reduces field adaptation time by 72%, while automated prompt optimization achieves 89% improvement in reasoning quality. The framework processed real-time data streams with 96.2% anomaly detection accuracy and reduced environmental incidents by 45%. We provide detailed experimental protocols, baseline comparisons, ablation studies, and statistical significance testing to ensure reproducibility. This research demonstrates practical integration of cutting-edge AI technologies with petroleum domain expertise for enhanced operational efficiency, safety, and economic performance.