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Differentiable Finite Element Methods

M:3L uses differentiable finite element methods to connect mechanics simulation with gradient-based optimization and machine learning.

Overview

Differentiable FEM is part of the laboratory's physics-driven machine-learning work. Automatic differentiation through a finite element simulation allows gradients from an engineering objective to propagate toward design variables or machine-learning parameters.

This creates simulation-to-optimization loops that retain governing equations, boundary conditions, constitutive models, and finite element structure rather than replacing mechanics with an unconstrained predictor.

M:3L applies this capability to elastic metamaterials, wave-cloaking structures, neural-field optimization, and generative design of manufacturable microstructures.

Demonstrated M:3L research

  • Differentiable-FEM-based inverse design for elastic metamaterials and wave-cloaking structures.
  • Neural-field optimization and generative design of manufacturable microstructures supported by NVIDIA H100 computing access through Armenia's AI Virtual Institute.

Technical capabilities

  • Automatic differentiation through simulation
  • Gradient-based inverse design
  • PDE-constrained and structural optimization
  • Neural networks coupled with finite element models
  • Simulation-to-optimization loops
  • Elastic metamaterial optimization
  • Wave-cloaking structure design

Gradient path

A differentiable simulation exposes the sensitivity of an objective to upstream parameters. In an engineering loop, an objective such as wave attenuation, stiffness, displacement, or another response can be differentiated through the numerical model so an optimizer can update geometry, material parameters, boundary conditions, or learned representations.

Research directions

  • Automatic differentiation through mechanics solvers
  • PDE-constrained optimization and inverse design
  • Coupling neural fields or neural networks with FEM
  • Gradient-based structural and material optimization

Potential applications

  • Metamaterial and microstructure design
  • Wave-control structures
  • Structural optimization
  • Inverse engineering design
  • Scientific AI workflows

These are relevant application domains, not claims that every application is deployed.

Connected research

  • Physics-Driven Machine Learning: M:3L develops machine-learning systems constrained and guided by physical laws for computational mechanics and scientific computing.
  • Metamaterials and Wave Control: M:3L studies inverse design of elastic metamaterials, wave-cloaking structures, and programmable wave propagation.
  • Agentic AI: M:3L develops autonomous, tool-using single-agent and multi-agent AI systems for scientific, engineering, and enterprise workflows.

Related projects and news

M:3L Secures HTI AI Virtual Institute Grant for High-Performance GPU Computing

M:3L has received access to NVIDIA H100 GPUs through the AI Virtual Institute, a program of Armenia's Ministry of High-Tech Industry. This support expands our capacity to design elastic metamaterials and wave-cloaking structures. The research combines differentiable FEM, neural-field optimisation, and generative design to create manufacturable microstructures for broadband Rayleigh-wave cloaking and chiral metamaterials.