FEALPy v3: A Cross-platform Intelligent Numerical Simulation Engine

TL;DR

FEALPy addresses fragmentation in numerical simulation software by introducing a tensor-centric, multi-backend engine that unifies data structures across NumPy, PyTorch, and JAX and enables automatic differentiation throughout the pipeline. Its four-layer architecture decouples mathematical abstractions from hardware-specific implementations, facilitating cross-backend execution and easy integration with DL workflows. The authors demonstrate the framework through elasticity, high-order PDEs, moving mesh, inverse problems, and path planning, and present SOPTX and FractureX as application packages built on FEALPy. The results indicate consistent backend performance enhancements, flexible multi-physics capabilities, and a scalable platform for next-generation computational science and AI integration.

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.

Figures (10)

• Figure 1: Software architecture of FEALPy
• Figure 2: For polygons, an additional pointer tensor is used to record the starting index of each polygon.
• Figure 3: Orientation of a 3D triangle is defined by the right-hand rule.
• Figure 4: Example of global DoF numbering ($p=4$) in a triangle in FEALPy.
• Figure 5: Hybrid COO: a batched sparse matrix containing many sparse matrices with the same non-zero pattern. This is useful in assembling matrices for batches of equations with different coefficients in FEM.