LRX-PINN: Neural Network with Cauchy Activations for Dominant Convection

The simulation of physical phenomena where convection dominates over diffusion presents a classic challenge in computational fluid dynamics. In these problems, solutions develop extremely thin boundary layers with steep gradients that traditional numerical methods —including physics-informed neural networks (PINNs)— fail to capture efficiently. Faced with this limitation, an innovative proposal has emerged: the LRX-PINN neural network, which employs activation functions based on the Cauchy distribution to resolve the misalignment between the network's basis and the structure of convection layers. Instead of using generic activation functions like ReLU or sigmoids, LRX-PINN incorporates Cauchy integral activations that, at the solution level, act as smooth transitions, while their derivatives recreate localized kernels, mimicking the behavior of boundary layers. This allows the network to learn with far fewer parameters —less than 30% of those required by other architectures like PIKAN or PINNs with Fourier features— and achieve superior accuracy on convective benchmarks. From a business perspective, this type of advancement in artificial intelligence applied to the simulation of physical processes opens doors for AI for businesses seeking to optimize industrial designs, reduce physical prototypes, and accelerate decision-making. The ability to model phenomena with boundary layers compactly and accurately can be integrated into simulation tools that support multiple sectors: from aeronautics to chemical process engineering. At Q2BSTUDIO, as a software and technology development company, we understand that an approach like LRX-PINN is not only relevant for academic research but also for developing custom applications in environments where numerical simulation is critical. Our artificial intelligence services allow us to build models tailored to specific needs, combining cutting-edge techniques with robust implementation on modern infrastructures. Furthermore, we complement this capability with AWS and Azure cloud services to scale training and deployment computations, and with business intelligence services like Power BI to visualize simulation results. Integrating physics-based models with autonomous AI agents can automate design and validation cycles, an area where we offer process automation solutions. Even in the field of cybersecurity, protecting data generated by industrial simulations is part of our portfolio. Ultimately, the LRX-PINN proposal demonstrates that aligning the neural representation with the problem's structure drastically reduces computational complexity. This principle, applied to the development of custom software, allows for creating more efficient and accurate tools for engineers and scientists. The intersection of artificial intelligence and physical simulation is redefining what is possible, and at Q2BSTUDIO we accompany companies in that transformation.