FEALPy: A Cross-platform Intelligent Numerical Simulation Engine

TL;DR

FEALPy is a versatile, cross-platform numerical simulation engine that unifies various algorithms and supports multiple backends, enabling efficient and integrated simulations across different computational environments.

Contribution

Introduces FEALPy, a modular simulation framework with a unified tensor abstraction supporting multiple backends and deep learning workflows, addressing fragmentation in numerical simulation software.

Findings

Supports CPU and GPU computations seamlessly.

Enables integration of diverse numerical methods.

Demonstrated effectiveness in multiple application domains.

Abstract

In resent years, the software ecosystem for numerical simulation still remains fragmented, with different algorithms and discretization methods often implemented in isolation, each with distinct data structures and programming conventions. This fragmentation is compounded by the growing divide between packages from different research fields and the lack of a unified, universal data structure, hindering the development of integrated, cross-platform solutions. In this work, we introduce FEALPy, a numerical simulation engine built around a unified tensor abstraction layer in a modular design. It enables seamless integration between diverse numerical methods along with deep learning workflows. By supporting multiple computational backends such as NumPy, PyTorch, and JAX, FEALPy ensures consistent adaptability across CPU and GPU hardware systems. Its modular architecture facilitates the entire simulation pipeline, from mesh handling and assembly to solver execution, with built-in support for automatic differentiation. In this paper, the versatility and efficacy of the framework are demonstrated through applications spanning linear elasticity, high-order PDEs, moving mesh methods, inverse problems and path planning.