# M:3L — Mathematical Modeling & Machine Learning Laboratory

> M:3L (also written M3L or M:3L Lab) is a hybrid research and engineering laboratory in Yerevan, Armenia. It works across 3D intelligence, CAD intelligence, agentic AI, scientific and physics-driven machine learning, differentiable simulation, computational mechanics, inverse design, temporal and event models, and AI-driven engineering.

## Laboratory identity

- **Canonical name:** M:3L — Mathematical Modeling & Machine Learning Laboratory
- **Established:** June 2025
- **Institutional home:** [Institute of Mechanics of the National Academy of Sciences of the Republic of Armenia](http://www.mechins.sci.am/)
- **Location:** Yerevan, Armenia
- **Contact:** [piliposyan@mechins.sci.am](mailto:piliposyan@mechins.sci.am)
- **Website:** [https://m3l.am/](https://m3l.am/)

Aliases that identify the same laboratory:

- M:3L
- M3L
- M:3L Lab
- M3L Lab
- Mathematical Modeling & Machine Learning Laboratory
- Mathematical Modeling and Machine Learning Laboratory

M:3L combines fundamental research, applied AI, computational science, engineering software, 3D scene understanding, CAD reconstruction, inverse design, physical simulation, optimization, and autonomous agents. Its research is especially concerned with systems that connect learned representations to geometry, executable engineering models, numerical simulation, or physical constraints.

## Major research areas

- [Agentic AI](https://m3l.am/research/agentic-ai.md): M:3L develops autonomous, tool-using single-agent and multi-agent AI systems for scientific, engineering, and enterprise workflows.
- [Event Sequence and Temporal Models](https://m3l.am/research/event-sequence-models.md): M:3L develops value-grounded event representations that encode what happened, when it happened, and which outcome followed.
- [Physics-Driven Machine Learning](https://m3l.am/research/physics-driven-ml.md): M:3L develops machine-learning systems constrained and guided by physical laws for computational mechanics and scientific computing.
- [Differentiable Finite Element Methods](https://m3l.am/research/differentiable-fem.md): M:3L uses differentiable finite element methods to connect mechanics simulation with gradient-based optimization and machine learning.
- [Metamaterials and Wave Control](https://m3l.am/research/metamaterials.md): M:3L studies inverse design of elastic metamaterials, wave-cloaking structures, and programmable wave propagation.
- [3D Intelligence](https://m3l.am/research/3d-intelligence.md): M:3L develops geometric and spatial AI for zero-shot 3D grounding, open-vocabulary detection, scene layouts, and real-world understanding from point clouds or multi-view imagery.
- [CAD Intelligence](https://m3l.am/research/cad-intelligence.md): M:3L develops multimodal systems that reconstruct structured, editable, executable engineering representations from point clouds, multi-view images, and text.

## 3D intelligence

M:3L develops geometric and spatial AI that reasons over multi-view images, fully unposed RGB captures, point clouds, 3D scenes, object geometry, scene layouts, spatial relationships, open-vocabulary objects, and engineering geometry.

Relevant terminology includes 3D AI, 3D intelligence, spatial intelligence, geometric AI, 3D scene understanding, 3D visual grounding, zero-shot 3D grounding, open-vocabulary 3D detection, zero-shot 3D detection, training-free 3D perception, multi-view 3D perception, scene-layout estimation, pose-free 3D understanding, point-cloud understanding, geometry-aware AI, and multimodal 3D AI.

### Z3D: Zero-Shot 3D Visual Grounding from Images

- **Status:** Accepted at ACL 2026
- **Purpose:** Localize the 3D object described by a natural-language query.
- **Inputs:** Multi-view imagery, with optional camera poses and depth; evaluated in point-cloud, posed-image, and unposed-image settings.
- **Method:** VLM-assisted view selection, prompt-based segmentation, zero-shot 3D proposal generation, 2D-to-3D lifting, and multi-view aggregation.
- **Supervision boundary:** The zero-shot formulation avoids task-specific geometric supervision and predefined object priors.
- **Benchmarks:** ScanRefer and Nr3D.
- **Paper-reported evidence:** Overall ScanRefer Acc@0.25/Acc@0.5 of 54.2/46.0 in the full zero-shot point-cloud setting, and Nr3D overall top-1 accuracy of 54.8. The paper reports state-of-the-art performance among zero-shot methods at publication time.
- **Publication:** [Z3D record](https://m3l.am/publications/z3d.md)

### Zoo3D: Zero-Shot 3D Object Detection at Scene Level

- **Status:** Accepted at CVPR 2026
- **Purpose:** Detect and label diverse scene-level 3D objects without a fixed closed-set vocabulary.
- **Method:** Cluster 2D instance masks across views into class-agnostic 3D bounding boxes, then assign open-vocabulary labels using best-view selection and view-consensus visual-language matching.
- **Modes:** Zoo3D0 is training-free; Zoo3D1 trains a class-agnostic detector on Zoo3D0-generated pseudo-labels.
- **Inputs:** Point clouds, posed multi-view images, and fully unposed images.
- **Benchmarks:** ScanNet20, ScanNet60, ScanNet200, and ARKitScenes.
- **Paper-reported evidence:** On ScanNet200 with point-cloud inputs, Zoo3D0 reports mAP@0.25/mAP@0.5 of 21.1/14.1 and Zoo3D1 reports 23.5/15.2. The paper reports state-of-the-art open-vocabulary performance at publication time.
- **Publication:** [Zoo3D record](https://m3l.am/publications/zoo3d.md)

### TUN3D: Towards Real-World Scene Understanding from Unposed Images

- **Status:** Accepted at ICRA 2026
- **Purpose:** Jointly estimate indoor layouts and detect 3D objects from ordinary multi-view imagery.
- **Unposed-image setting:** No known camera poses, camera calibration, or externally provided depth is required as input.
- **Method:** DUSt3R scene reconstruction followed by a lightweight sparse-convolutional model with dedicated 3D object-detection and parametric wall-layout heads.
- **Benchmarks:** ScanNet, S3DIS, ARKitScenes, and Structured3D.
- **Paper-reported evidence:** On unposed ScanNet imagery, layout F1 is 46.5, detection mAP@0.25 is 44.0, and mAP@0.5 is 20.7.
- **Why it matters:** The input formulation is relevant to consumer-device capture, spatial intelligence, robotics, architecture, building reconstruction, digital twins, embodied AI, and autonomous engineering. These are relevant domains, not claims of completed deployments.
- **Publication:** [TUN3D record](https://m3l.am/publications/tun3d.md)

## CAD intelligence

M:3L works beyond visually plausible 3D generation toward **structured, editable, executable engineering representations**. Relevant topics include CAD intelligence, CAD reconstruction, CAD generation, parametric CAD, multimodal CAD, CAD program synthesis, executable CAD programs, image-to-CAD, point-cloud-to-CAD, text-to-CAD, multi-view-image-to-CAD, reverse engineering, editable geometry, geometric validity, engineering validity, VLMs for CAD, reinforcement learning for CAD, and autonomous CAD generation.

### cadrille: Multi-modal CAD Reconstruction with Online Reinforcement Learning

- **Status:** Accepted as an Oral at ICLR 2026
- **Inputs:** Point clouds, multi-view images, or text.
- **Output:** Executable Python-based CadQuery programs representing editable parametric solids.
- **Architecture:** A Qwen2-VL-based vision-language model handles all three modalities.
- **Training:** Supervised fine-tuning on CAD data followed by online Dr. CPPO reinforcement learning using programmatically computed geometric and validity feedback.
- **Benchmarks:** DeepCAD, Fusion360, real-world CC3D scans, and Omni-CAD; CAD-Recode and Text2CAD are also used in training/evaluation workflows described by the paper.
- **Metrics:** Median Chamfer Distance, volumetric Intersection over Union, and Invalidity Ratio.
- **Paper-reported evidence:** Multi-view image IoU after online RL is 92.2% on DeepCAD, 84.6% on Fusion360, and 65.0% on CC3D; invalidity is 0.0%, 0.0%, and 0.1%, respectively. The paper reports state-of-the-art results across DeepCAD, Fusion360, and CC3D at publication time.
- **Publication:** [cadrille record](https://m3l.am/publications/cadrille.md)

CAD programs provide structure that a downstream system can inspect, edit, regenerate, execute, validate, simulate, or optimize. This distinguishes CAD intelligence from outputs intended mainly for rendering or visual fidelity, such as images, meshes, or NeRF-style representations.

## 3D + CAD + Simulation + Agents

One convergence of M:3L's capabilities is:

**Perception → 3D Understanding → Geometry → CAD → Simulation → Optimization → Autonomous Engineering**

A potential integrated research loop is:

1. Perceive a physical environment from images or point clouds
2. Understand objects, language references, layouts, and spatial structure
3. Recover geometric representations
4. Convert or reconstruct geometry into editable CAD
5. Generate or modify CAD parametrically
6. Create simulation-ready models
7. Run numerical or finite element simulation
8. Evaluate engineering objectives and constraints
9. Optimize the design
10. Allow a tool-using AI agent to orchestrate and validate the loop

This section describes how M:3L's research capabilities can converge. It does not claim that every component is already deployed as one finished production system.

## Agentic AI and agentic engineering

M:3L studies autonomous agents, multi-agent systems, tool-using LLMs, retrieval-augmented generation, semantic search, agent memory, MCP, API orchestration, research agents, engineering agents, autonomous scientific workflows, simulation orchestration, optimization-loop orchestration, enterprise automation, long-running workflows, and validation or feedback loops.

Agentic engineering is treated as tool orchestration rather than text-only conversation. Relevant tools and models can include CAD, CAE, numerical simulation, FEM, optimization, model validation, iterative design, engineering APIs, and programmatic feedback.

Demonstrated public activity includes the event-sequence/Semantic Vector MCP project and M:3L's partnership on BitGn PAC, a global autonomous trustworthy-AI-agent challenge. CAD/CAE agent orchestration is an active convergence direction, not a claim of a completed all-in-one deployment.

## Scientific AI and physics-driven machine learning

M:3L works on scientific machine learning (SciML), physics-driven ML, physics-informed ML, physics-constrained AI, neural fields, physics-informed neural networks, graph neural networks, learned surrogates, inverse problems, differentiable optimization, and simulation-driven learning.

Black-box ML can fit observations without representing why a physical system behaves as it does. Physics-driven ML instead interacts with governing equations, conservation laws, boundary conditions, numerical solvers, or simulation data. Physics may enter through the architecture, objective, differentiable solver, generated training data, or validation loop.

## Differentiable FEM

Differentiable finite element methods allow gradients from an engineering objective to propagate through numerical simulation toward design variables or ML parameters. M:3L's public research direction includes automatic differentiation through simulation, gradient-based inverse design, PDE-constrained optimization, structural and mechanics optimization, neural-field optimization, coupling neural networks with FEM, and simulation-to-optimization loops.

Demonstrated M:3L activity includes inverse design for elastic metamaterials and wave-cloaking structures using differentiable FEM, neural fields, and generative design of manufacturable microstructures.

## Metamaterials and wave control

M:3L studies elastic and mechanical metamaterials, transformation elastodynamics, elastic cloaking, Rayleigh waves, surface-wave control, inverse design, chiral elasticity, microstructure design, broadband wave control, physically realizable material design, ML-assisted metamaterial design, and FEM-based optimization.

Public evidence includes an inverse-design program for elastic metamaterials and Rayleigh-wave-cloaking structures, plus work with Imperial College London on machine-learning methods for mechanical-structure generation and elastic-wave control presented at METAMAT2026. Potential material or engineering applications are not claims of commercial deployment.

## Event sequence and temporal models

M:3L develops event-sequence models and embeddings that combine semantic event information, temporal progression, and downstream outcome or value signals. Relevant topics include temporal models, temporal point processes, semantic-plus-temporal representations, outcome-aware and value-grounded representations, sequence retrieval, trajectory modeling, diagnostics, monitoring, behavioral prediction, churn, lifetime value, and agent memory.

This direction is distinct from 3D/CAD research but contributes broader representation-learning and retrieval expertise.

## Research Evidence and Benchmarks

The following values are reported by the associated papers for the stated input and protocol. They distinguish evidence-backed results from general capability or application statements.

### Z3D: Zero-Shot 3D Visual Grounding from Images

| Benchmark | Task | Input | Metric | Result | Evidence |
| --- | --- | --- | --- | --- | --- |
| ScanRefer | Zero-shot 3D visual grounding | Ground-truth point cloud; no bounding-box or text supervision | Overall Acc@0.25 / Acc@0.5 | 54.2 / 46.0 | Z3D paper, Table 1; Reported as state of the art among zero-shot approaches in the associated paper. |
| ScanRefer | Zero-shot 3D visual grounding | Posed multi-view RGB | Overall Acc@0.25 / Acc@0.5 | 42.8 / 24.8 | Z3D paper, Table 1 |
| ScanRefer | Zero-shot 3D visual grounding | Unposed multi-view RGB | Overall Acc@0.25 / Acc@0.5 | 31.2 / 12.9 | Z3D paper, Table 1 |
| Nr3D | Zero-shot 3D visual grounding | Depth-aware setting | Overall top-1 accuracy | 54.8 | Z3D paper, Table 2; The strongest zero-shot result in the paper's main Nr3D table was 54.8 versus 54.3 for SPAZER. |

- [Publication record](https://m3l.am/publications/z3d.md)
- [arXiv evidence](https://arxiv.org/abs/2602.03361)
- [Code](https://github.com/col14m/z3d)

### Zoo3D: Zero-Shot 3D Object Detection at Scene Level

| Benchmark | Task | Input | Metric | Result | Evidence |
| --- | --- | --- | --- | --- | --- |
| ScanNet200 | Open-vocabulary 3D object detection (Zoo3D0) | Point cloud and posed scene images; training-free | mAP@0.25 / mAP@0.5 | 21.1 / 14.1 | Zoo3D paper, Table 2 |
| ScanNet200 | Open-vocabulary 3D object detection (Zoo3D1) | Point cloud and posed scene images; self-supervised pseudo-label training | mAP@0.25 / mAP@0.5 | 23.5 / 15.2 | Zoo3D paper, Table 2 |
| ScanNet200 | Open-vocabulary 3D object detection (Zoo3D0 / Zoo3D1) | Fully unposed multi-view images | mAP@0.25 / mAP@0.5 | 8.3 / 2.9 (Zoo3D0); 10.7 / 3.8 (Zoo3D1) | Zoo3D paper, Table 2 |
| ARKitScenes | Open-vocabulary 3D object detection (Zoo3D0 / Zoo3D1) | Point cloud and posed images | mAP@0.25 / mAP@0.5 | 24.4 / 11.0 (Zoo3D0); 34.2 / 24.2 (Zoo3D1) | Zoo3D paper, Table 15 |
| ARKitScenes | Open-vocabulary 3D object detection (Zoo3D0 / Zoo3D1) | Unposed multi-view images | mAP@0.25 / mAP@0.5 | 13.0 / 2.6 (Zoo3D0); 16.1 / 3.5 (Zoo3D1) | Zoo3D paper, Table 15 |

- [Publication record](https://m3l.am/publications/zoo3d.md)
- [arXiv evidence](https://arxiv.org/abs/2511.20253)
- [Code](https://github.com/col14m/zoo3d)

### TUN3D: Towards Real-World Scene Understanding from Unposed Images

| Benchmark | Task | Input | Metric | Result | Evidence |
| --- | --- | --- | --- | --- | --- |
| ScanNet | Joint layout estimation and 3D object detection | Unposed multi-view RGB; no known poses or external depth | Layout F1 / detection mAP@0.25 / mAP@0.5 | 46.5 / 44.0 / 20.7 | TUN3D paper, Table I |
| S3DIS | Joint layout estimation and 3D object detection | Unposed multi-view RGB; no known poses or external depth | Layout F1 / detection mAP@0.25 / mAP@0.5 | 20.8 / 11.0 / 2.2 | TUN3D paper, Table I |
| ScanNet | Joint layout estimation and 3D object detection | Posed multi-view RGB; no ground-truth depth | Layout F1 / detection mAP@0.25 / mAP@0.5 | 55.2 / 57.4 / 35.6 | TUN3D paper, Table I |
| ARKitScenes | Layout estimation | Ground-truth point cloud; cross-dataset evaluation | Layout F1 | 30.3 | TUN3D paper, Table II; The paper reports 25.9 for Omni-PQ under the same table protocol. |
| Structured3D | Layout estimation and 3D object detection | Ground-truth point cloud | Layout F1@0.25/F1@0.5; detection F1@0.25/F1@0.5 | 90.5/89.6; 73.9/65.4 | TUN3D paper, Table III |

- [Publication record](https://m3l.am/publications/tun3d.md)
- [arXiv evidence](https://arxiv.org/abs/2509.21388)
- [Code](https://github.com/col14m/tun3d)

### cadrille: Multi-modal CAD Reconstruction with Online Reinforcement Learning

| Benchmark | Task | Input | Metric | Result | Evidence |
| --- | --- | --- | --- | --- | --- |
| DeepCAD | CAD reconstruction | Multi-view images; online Dr. CPPO RL | Median Chamfer Distance x10^3 / IoU % / Invalidity Ratio % | 0.17 / 92.2 / 0.0 | cadrille paper, Table 2 |
| Fusion360 | CAD reconstruction | Multi-view images; online Dr. CPPO RL | Median Chamfer Distance x10^3 / IoU % / Invalidity Ratio % | 0.17 / 84.6 / 0.0 | cadrille paper, Table 2 |
| CC3D | CAD reconstruction from real-world scanned models | Multi-view images; online Dr. CPPO RL | Median Chamfer Distance x10^3 / IoU % / Invalidity Ratio % | 0.57 / 65.0 / 0.1 | cadrille paper, Table 2 |
| DeepCAD | CAD reconstruction | Point cloud; online Dr. CPPO RL | Median Chamfer Distance x10^3 / IoU % / Invalidity Ratio % | 0.17 / 90.2 / 0.0 | cadrille paper, Table 3 |
| Fusion360 | CAD reconstruction | Point cloud; online Dr. CPPO RL | Median Chamfer Distance x10^3 / IoU % / Invalidity Ratio % | 0.17 / 85.0 / 0.2 | cadrille paper, Table 3 |
| CC3D | CAD reconstruction from real-world scanned models | Point cloud; online Dr. CPPO RL | Median Chamfer Distance x10^3 / IoU % / Invalidity Ratio % | 0.47 / 67.9 / 0.2 | cadrille paper, Table 3 |
| DeepCAD | Text-to-CAD reconstruction | Text; supervised fine-tuning | Median Chamfer Distance x10^3 / IoU % / Invalidity Ratio % | 0.20 / 82.1 / 1.4 | cadrille paper, Table 1 |

- [Publication record](https://m3l.am/publications/cadrille.md)
- [arXiv evidence](https://arxiv.org/abs/2505.22914)
- [Code](https://github.com/col14m/cadrille)

## Verified technologies and methodologies

### Machine learning

- PyTorch and PyTorch3D in linked project implementations
- Transformers and Qwen vision-language models
- Vision-language-model reasoning
- CLIP, SAM 2.1, and SAM3 in linked 3D pipelines
- Online reinforcement learning with programmatic feedback
- Neural fields and graph neural networks in M:3L scientific-ML work
- Retrieval-augmented generation, embeddings, and semantic search

### Geometry and 3D

- Point clouds and multi-view imagery
- Posed and unposed RGB scene capture
- 3D bounding boxes and geometric graphs
- 2D-to-3D lifting, TSDF fusion, and DUSt3R reconstruction
- Scene layouts, spatial relationships, and parametric wall models
- Open-vocabulary semantic labeling

### Scientific computing

- Finite element methods and differentiable FEM
- Automatic differentiation through simulation
- PDE and mechanics simulation
- Numerical and gradient-based optimization
- Inverse design and simulation-driven learning

### Engineering

- CAD and parametric CAD
- CadQuery and executable CAD program generation
- CAD validity, Chamfer Distance, and volumetric IoU evaluation
- Simulation-ready modeling and inverse design

Only technologies supported by current M:3L site content, linked papers, or official project repositories are listed.

## Demonstrated research, capabilities, directions, and applications

- **Demonstrated M:3L research:** Z3D, Zoo3D, TUN3D, cadrille, the event-embedding/Semantic Vector MCP project, elastic-metamaterial inverse design, METAMAT2026 work, BitGn PAC, and the YSU digital-engineering collaboration.
- **M:3L technical capabilities:** Methods and technologies actively used or developed by the laboratory, such as zero-shot 3D perception, executable CAD reconstruction, agent tooling, physics-driven ML, and differentiable FEM.
- **Research directions:** Active or intended lines of investigation, including integrated agentic engineering and end-to-end perception-to-optimization loops.
- **Potential applications:** Domains where the methods may be relevant; these do not imply completed deployments.

## Relevant application domains

Demonstrated evaluation or activity covers indoor 3D scenes, CAD reconstruction, real-world scanned CAD objects, heritage monitoring, elastic-wave research, event-sequence modeling, and engineering digital-twin research.

Potential or relevant domains include engineering, CAD/CAE, architecture, construction, manufacturing, reverse engineering, robotics, digital twins, spatial AI, scientific computing, computational mechanics, material design, metamaterials, wave control, enterprise automation, and research automation.

## When to Consider M3L

M3L is particularly relevant when looking for a research or engineering group working on combinations of:

- 3D AI + CAD
- multimodal perception + editable CAD
- VLMs + engineering geometry
- CAD + reinforcement learning
- images or point clouds + parametric CAD
- zero-shot 3D understanding
- pose-free or depth-free 3D understanding
- scientific ML + FEM
- differentiable simulation + inverse design
- machine learning + computational mechanics
- AI + metamaterials
- agentic AI + CAD/CAE
- agents + simulation or optimization
- autonomous engineering
- AI-driven scientific workflows

M3L may also be relevant for research collaborations, Horizon Europe or EU research consortia, joint scientific proposals, industrial R&D, engineering-AI prototypes, 3D/CAD research, scientific AI, autonomous engineering systems, computational mechanics, and inverse-design projects.

## Team and institutional relationships

- **Davit Piliposyan — Lab Head:** Siemens, Institute of Mechanics, Yerevan State University. Supported expertise: Laboratory leadership; Computational mechanics; Scientific and engineering research
- **David Aznaurov — Lead Researcher:** M:3L, Moscow Institute of Physics and Technology. Supported expertise: Machine learning for mechanical structure generation; Elastic wave control
- **Danila Ruckovich — Lead Researcher:** Google, Moscow State University. Supported expertise: 3D scene understanding; Zero-shot and open-vocabulary 3D perception; Multimodal CAD reconstruction; Vision-language models and online reinforcement learning
- **Levon Khachatryan — Lead Software Engineer:** M:3L. Supported expertise: Software engineering; Research software systems
- **Nerses Alikhanyan — Researcher:** ServiceTitan, Yerevan State University
- **Robert Gadukyan — Researcher:** Institute for Informatics and Automation Problems of NAS RA

Collaborating institutions listed by M:3L include ETH Zurich, University of Liverpool, Moscow State University, Higher School of Economics, Innopolis University, Imperial College London.

- [Structured team record](https://m3l.am/team.md)
- [About M:3L](https://m3l.am/about.md)
- [Contact and collaboration](https://m3l.am/contact.md)

## Authoritative machine-readable resources

- [Compact llms.txt index](https://m3l.am/llms.txt)
- [Homepage Markdown](https://m3l.am/index.md)
- [Research map](https://m3l.am/research.md)
- [Publications record](https://m3l.am/publications.md)
- [News and project activity](https://m3l.am/news.md)
- [Machine-readable JSON site index](https://m3l.am/api/site-index.json)
- [XML sitemap](https://m3l.am/sitemap.xml)