Mini-Enedina: A Domain-Specialized Small Language Model for Structural Shaft Analysis

Mini-Enedina is a monotropic language model -- deliberately small and intensively specialized -- with 37.5 million parameters, designed exclusively for structural shaft analysis according to Timoshenko beam theory.

Model Details

Parameter	Value
Parameters	37.57M
Layers	7
Attention Heads	8
Model Dimension	512
Feed-Forward Dimension	2048
Vocabulary Size	8,012 (8,000 BPE + 12 Harmony tokens)
Max Sequence Length	14,336 tokens
Positional Encoding	RoPE
Normalization	RMSNorm (pre-norm)
Activation	SiLU (SwiGLU)
Framework	MLX (Apple Silicon)
Precision	BFloat16
Model Size	143 MB

Training

• Dataset: 60,000 physically validated samples (621M tokens) of Timoshenko shaft analysis problems
• Training Strategy: Multidimensional curriculum learning with 4 phases (Foundation, Intermediate, Advanced, Full)
• Three Analysis Levels:
  • Bachelor: Deflection analysis (V, M, w, theta)
  • Master: + Von Mises stress analysis
  • Doctor: + Fatigue evaluation (Marin factors, Goodman criterion)
• Hardware: Apple M4 Pro, 48 GB unified memory
• Training Time: ~23 hours (14,920 steps)
• Optimizer: AdamW (lr=3e-4, cosine schedule with warmup)

Evaluation Results (6,000 held-out test samples)

Metric	Overall	Bachelor	Master	Doctor
Loss	0.0787	0.0733	0.0804	0.0825
Perplexity	1.08	1.08	1.08	1.09
Correct Stop Token	94%	97%	100%	85%
Valid Harmony Structure	100%	100%	100%	100%

Output Format: Harmony-Enedina

The model generates structured responses using the Harmony-Enedina format with two channels:

1. Analysis Channel: Chain-of-thought reasoning, problem classification, and qualitative analysis
2. Final Channel: Complete Python solver code with numerical grounding, quantitative results, and validation summary

Domain-specific tokens (<|shaft|>, <|python|>, <|numerical|>, <|latex|>) demarcate semantic boundaries within the output.

Inference Configuration

The model was trained without sliding window attention, repetition penalty, or n-gram blocking. These techniques must remain disabled during inference:

# CORRECT configuration (BASELINE)
use_sliding_window = False
repetition_penalty = 1.0
no_repeat_ngram_size = 0
temperature = 0.0  # greedy decoding

Enabling these techniques degrades performance from 94% to 8% correct stop tokens.

Intended Use

Mini-Enedina is designed for:

• Structural shaft analysis according to Timoshenko beam theory
• Engineering education and design iteration
• Generating complete, executable Python solver code
• Deployment on consumer hardware (edge, air-gapped environments)

Important: Model outputs should always be verified against independent calculations for safety-critical applications.

Limitations

• Handles exclusively shaft analysis according to Timoshenko theory
• Training language is Brazilian Portuguese
• Numerical accuracy is limited by tokenization granularity
• May struggle with support conditions or load combinations not represented in training

Citation

If you use this model, please cite:

@article{leitaofilho2026minienedina,
  title={Mini-Enedina: A Domain-Specialized Small Language Model for Structural Shaft Analysis Using Timoshenko Beam Theory},
  author={Leit{\~a}o Filho, Antonio de Sousa and Barros Filho, Allan Kardec Duailibe and Lima, Fabr{\'i}cio Saul and Santos, Selby Mykael Lima dos and Sousa, Rejani Bandeira Vieira},
  year={2026}
}

Acknowledgments

This work was supported by Aia Context Ltda. and by FINEP -- Funding Authority for Studies and Projects, a Brazilian government agency for science, technology, and innovation linked to the Ministry of Science, Technology and Innovation (MCTI), under Contract No. 03.25.0080.00.

License

CC-BY-4.0