M:3L Lab
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M:3L research

Physics-Driven Machine Learning

M:3L develops machine-learning systems constrained and guided by physical laws for computational mechanics and scientific computing.

Overview

The laboratory combines differentiable finite element solvers, physics-informed neural networks, graph neural networks, neural fields, and generative methods. These approaches connect data-driven learning with governing equations and numerical simulation.

Current applications include virtual system modeling and diagnostics, inverse design of elastic metamaterials, wave-cloaking structures, and manufacturable microstructures.

Demonstrated M:3L research

  • Inverse design work combining differentiable FEM, neural-field optimization, and generative design for elastic metamaterials and wave-cloaking structures.
  • A Yerevan State University collaboration on digital engineering and simulation-trained models for virtual-system modeling and diagnostics.

Technical capabilities

  • Differentiable finite element methods
  • Physics-informed neural networks
  • Graph neural networks for physical systems
  • Neural-field optimization
  • Simulation-trained machine-learning models

Physics-driven versus black-box ML

Ordinary black-box machine learning can fit input-output observations without representing why a physical system behaves as it does. Physics-driven ML instead interacts with governing equations, numerical solvers, conservation laws, boundary conditions, or simulation data so predictions and designs can be assessed against physical constraints.

M:3L combines learned models with finite element simulation and numerical optimization. Depending on the problem, physics may enter through the architecture, loss function, differentiable solver, generated training data, or validation loop.

Research directions

  • Physics-informed neural networks and neural fields
  • Graph neural networks and learned surrogates for physical systems
  • Simulation-driven learning and inverse problems
  • Differentiable optimization under governing equations and engineering constraints

Potential applications

  • Virtual-system modeling and diagnostics
  • Engineering digital twins
  • Inverse material and structure design
  • Computational mechanics
  • Scientific computing

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

Connected research

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

New Collaboration with YSU

We are partnering with Yerevan State University's Physical-Technical Laboratory and Department of Radiophysics and Telecommunications to build a digital engineering platform for virtual system modeling and diagnostics. The platform will create digital twins of real experimental systems that scientists can query in plain language for fast, accurate answers, powered by machine-learning models trained on thousands of physics simulations. The project is funded by the Higher Education and Science Committee of RA MESCS, with co-financing from the Enterprise Incubator Foundation.