Quantasio: A Generalized Neural Framework for Solving 3-D Navier–Stokes Dynamics

Partial Differential Equations form the cornerstone of numerous scientific and engineering domains, modeling phenomena such as fluid dynamics, heat transfer, and electro-magnetics. Traditional numerical solvers, while accurate, are computationally expensive and often impractical for real-time applications or high-dimensional systems. Recent advancements in Physics-Informed Neural Networks (PINNs) have demonstrated promise in addressing these limitations; however, existing PINN frameworks face challenges in achieving convergence, enforcing boundary conditions, and scaling to multivariate, highdimensional PDEs. This paper introduces Quantasio, a PINN-based framework that leverages a residual network-inspired architecture with domain-specific reparameterization to achieve efficient and accurate solutions to PDEs across diverse spatiotemporal scenarios and specially Navier-Stokes dynamics in 3 spatial dimensions. Quantasio addresses key limitations in traditional PINNs by incorporating adaptive loss weighting, advanced gradient stabilization techniques, and robust boundary condition enforcement. Its performance is evaluated on a wide range PDEs, including diffusion-reaction, wave equations, and fluid dynamics, demonstrating superior accuracy, achieving up to a 60% reduction in convergence time while maintaining physical consistency. Quantasio reduces peak GPU memory by 50%, and attains a lower residual compared to leading PINN and operator-learning baselines. Our experiments demonstrate robust handling of turbulent flows and complex geometries, positioning Quantasio as an efficient and scalable solver for real-time 3D Navier–Stokes dynamics, making it a versatile tool for real-time simulation in industrial and scientific applications.