Implicit Neural Solver for Stable Surrogate Simulation of Fluid Dynamics*

Fluid simulations play a critical role in scientific and engineering domains, but their computational complexity has traditionally hindered real-time or many-query applications. Recent advances in scientific machine learning and neural solvers show promise in creating fast surrogate models using data, neural networks, and numerical techniques. However, most existing neural solvers rely on auto-regressive architectures to capture temporal dynamics, similar to explicit numerical methods, which can lead to error accumulation and limit their reliability for long-term predictions. To address this challenge, we propose an innovative implicit neural solver inspired by stable numerical implicit schemes. By adopting this approach, our neural network effectively mitigates the error accumulation problem, enabling accurate and dependable long-term trajectory predictions in fluid simulations. Through comprehensive numerical experiments, we demonstrate the effectiveness and merit of our proposed approach, showcasing the potential for advancing data-driven neural solvers in spatiotemporal simulations.