Deep Energy Method with Large Language Model assistance: an open-source Streamlit-based platform for solving variational PDEs

TL;DR

LM-DEM is an open-source Streamlit platform that leverages large language models to simplify geometry creation and solve variational PDEs using the deep energy method, making energy-form PINNs more accessible.

Contribution

The paper introduces LM-DEM, a user-friendly platform integrating LLMs for geometry modeling and energy-based PDE solving, filling a gap in dedicated software for energy-form PINNs.

Findings

Supports multiple PDE types including Poisson and elasticity

Enables geometry generation from natural language or images

Provides parallel finite element solutions

Abstract

Physics-informed neural networks (PINNs) in energy form, also known as the deep energy method (DEM), offer advantages over strong-form PINNs such as lower-order derivatives and fewer hyperparameters, yet dedicated and user-friendly software for energy-form PINNs remains scarce. To address this gap, we present \textbf{LM-DEM} (Large-Model-assisted Deep Energy Method), an open-source, Streamlit-based platform for solving variational partial differential equations (PDEs) in computational mechanics. LM-DEM integrates large language models (LLMs) for geometry modeling: users can generate Gmsh-compatible geometries directly from natural language descriptions or images, significantly reducing the burden of traditional geometry preprocessing. The solution process is driven by the deep energy method, while finite element solutions can be obtained in parallel. The framework supports built-in problems including Poisson, screened Poisson, linear elasticity, and hyperelasticity in two and three dimensions, as well as user-defined energy functionals analogous to the \texttt{UMAT} interface in Abaqus. The source code is available at https://github.com/yizheng-wang/LMDEM, and a web-based version is accessible at https://ai4m.llmdem.com. LM-DEM aims to lower the barrier for practitioners and beginners to adopt energy-form PINNs for variational PDE problems.