Neural physics: Using AI libraries to develop physics-based solvers for incompressible computational fluid dynamics
Year: 2026
Type: article
Abstract: Numerical discretisations of partial differential equations (PDEs) can be written as discrete convolutions, which, themselves, are a key tool in AI libraries and used in convolutional neural networks (CNNs). We therefore propose to implement numerical discretisations as convolutional layers of a neural network, where the weights or filters are determined analytically rather than by training. Furthermore, we demonstrate that these systems can be solved entirely by functions in AI libraries, either by using Jacobi iteration or multigrid methods, the latter realised through a U-Net architecture. Some advantages of the Neural Physics approach are that (1) the methods are platform agnostic; (2) the resulting solvers are fully differentiable, ideal for optimisation tasks; and (3) writing CFD solvers as (untrained) neural networks means that they can be seamlessly integrated with trained neural networks to form hybrid models. We demonstrate the proposed approach on a number of test cases of increasing complexity from advection-diffusion problems, the non-linear Burgers equation to the Navier-Stokes equations. We validate the approach by comparing our results with solutions obtained from traditionally written code and common benchmarks from the literature. We show that the proposed methodology can solve all these problems using repurposed AI libraries in an efficient way, without training, and presents a new avenue to explore in the development of methods to solve PDEs with implicit methods.
Source: Computers & Fluids
Institution: Imperial College London
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,700
Awards: Health assessment across biological length scales for personal pollution exposure and its mitigation (INHALE), PREdictive Modelling with QuantIfication of UncERtainty for MultiphasE Systems (PREMIERE), G2552696663, New Generation Modelling Suite for the Survivability of Wave Energy Convertors in Marine Environments (WavE-Suite), G5750141071, AI for Personalised respiratory health and pollution (AI-Respire), Enabling CO2 capture and storage using AI
OpenAlex ID: W7125487442