Forward and inverse solid mechanics
Physics-informed models address linear elasticity, elastoplasticity, hyperelasticity, and fracture, as well as identification of material parameters, constitutive laws, and defects.
Read focus โAI for PDEs ยท computational mechanics
Learn from data.
Remain grounded in physics.
AI4PDE integrates governing equations, variational principles, and data to develop fast, physically consistent solvers for forward simulation, inverse analysis, and computational solid mechanics.
Continuum๐(u) = f
Variationalu* = arg min ฮ (u)
Operator๐ข: a(x) โฆ u(x)
Research framework
From equations
to reusable solvers.
We combine physics-informed networks, energy formulations, and operator learning to solve individual PDEs, learn across problem families, and accelerate trusted numerical methods.
Variational solvers made accessible
Deep energy methods use lower-order derivatives and fewer loss-balancing parameters. LM-DEM extends this approach with language-assisted geometry and an open interactive workflow.
Read focus โOperators for space, time, and warm starts
MHNO predicts full temporal trajectories in one forward pass, while PFEM uses physics-informed operators to provide efficient initial solutions for finite-element refinement.
Read focus โPretrain once, adapt with physics
Reusable models can learn broad PDE families, then adapt to new geometries, materials, and boundary conditions while retaining numerical verification and physical constraints.
Read vision โResearch translated into tools
Geometry, dynamics,
and numerical acceleration.
01
LM-DEM generates Gmsh-compatible geometry from natural-language descriptions or images
02
Built-in 2D/3D Poisson, screened Poisson, elasticity, and hyperelasticity workflows
03
MHNO captures long-term interfacial dynamics and predicts all time steps in one forward pass
04
PFEM couples data-free physics-informed pretraining with accurate finite-element refinement
Featured open platform ยท LM-DEM
Describe the geometry. Define the energy. Solve the PDE.
LM-DEM is an open-source Streamlit platform for variational PDEs. It combines large-model-assisted geometry generation, Deep Energy Method solutions, parallel finite-element references, and user-defined energy functionals in a workflow designed for both practitioners and beginners.