API Reference Overview

The Math-Physics-ML MCP System provides 57 tools across 4 specialized MCP servers.

Quick Navigation

• Math MCP - 14 tools for symbolic algebra and numerical computing
• Quantum MCP - 12 tools for wave mechanics and simulations
• Molecular MCP - 15 tools for molecular dynamics
• Neural MCP - 16 tools for neural network training

Tool Categories

Math MCP

Category	Tools	Purpose
Discovery	info	Progressive capability discovery
Symbolic	symbolic_solve, symbolic_diff, symbolic_integrate, symbolic_simplify	Equation solving, calculus
Numerical	create_array, matrix_multiply, solve_linear_system	Array operations, linear algebra
Transforms	fft, ifft	Fast Fourier Transform
Optimization	optimize_function, find_roots	Function minimization, root finding

Quantum MCP

Category	Tools	Purpose
Discovery	info	Progressive capability discovery
Potentials	create_lattice_potential, create_custom_potential	Define quantum potentials
Wavepackets	create_gaussian_wavepacket, create_plane_wave	Initial states
Simulations	solve_schrodinger, solve_schrodinger_2d	Time evolution
Analysis	analyze_wavefunction, get_simulation_result	Extract observables
Visualization	render_video, visualize_potential	Generate plots/videos

Molecular MCP

Category	Tools	Purpose
Discovery	info	Progressive capability discovery
System	create_particles, add_potential	Define particle systems
Simulations	run_md, run_nvt, run_npt	Run MD in various ensembles
Analysis	compute_rdf, compute_msd, analyze_temperature, detect_phase_transition	Structural and thermodynamic analysis
Visualization	density_field, render_trajectory	Generate visualizations

Neural MCP

Category	Tools	Purpose
Discovery	info	Progressive capability discovery
Models	define_model, load_pretrained, get_model_summary	Model management
Data	load_dataset, create_dataloader	Dataset handling
Training	train_model, get_experiment_status	Training workflows
Evaluation	evaluate_model, compute_metrics	Model assessment
Tuning	tune_hyperparameters	Hyperparameter optimization
Visualization	plot_training_curves, confusion_matrix	Training analysis
Deployment	export_model	Model export

Common Parameters

Most tools support these common parameters:

GPU Acceleration

use_gpu: bool = True  # Use GPU if available, fallback to CPU

Progressive Discovery

info(topic: Optional[str] = None)
# topic=None          → List all categories
# topic='category'    → Show tools in category
# topic='tool_name'   → Detailed help for tool

Resource URIs

The system uses URI-based references for efficient data sharing:

URI Pattern	Source	Purpose
array://{id}	Math MCP	Large numerical arrays
potential://{id}	Quantum MCP	Quantum potentials
simulation://{id}	Quantum MCP	Completed simulations
system://{id}	Molecular MCP	Particle systems
trajectory://{id}	Molecular MCP	MD trajectories
model://{id}	Neural MCP	Neural network models
experiment://{id}	Neural MCP	Training experiments

Response Formats

All tools return JSON responses with a consistent structure:

Success Response

{
  "status": "success",
  "data": {
    // Tool-specific data
  }
}

Error Response

{
  "status": "error",
  "error": {
    "type": "ValueError",
    "message": "Clear error description",
    "suggestion": "How to fix the issue"
  }
}

Async Task Response

{
  "status": "submitted",
  "task_id": "task_abc123",
  "simulation_id": "sim_def456"  // Optional result ID
}

GPU Support

All numerical tools support GPU acceleration:

# Explicit GPU use
result = matrix_multiply(a, b, use_gpu=True)

# Automatic backend selection
xp = gpu_manager.get_array_module()
result = xp.matmul(a, b)

GPU Availability Check

# Via info tool
info(topic="gpu")
# Returns: {gpu_available: true, backend: "cuda", device_count: 1}

Error Handling

Common error types and solutions:

Error Type	Cause	Solution
ValueError	Invalid input parameters	Check parameter ranges and types
GPUMemoryError	Insufficient GPU memory	Reduce array size or use CPU
TimeoutError	Operation took too long	Increase timeout or reduce complexity
ResourceNotFoundError	Invalid URI reference	Check URI exists and is accessible

Rate Limits

Default resource limits (configurable in config.kdl):

• Max array size: 100M elements
• Max particles: 10M
• Max time steps: 1M
• Max epochs: 1000
• Symbolic operation timeout: 30 seconds

Next Steps

Explore the detailed API documentation for each server:

1. Math MCP API - Start here for foundational operations
2. Quantum MCP API - Quantum simulations
3. Molecular MCP API - Classical MD
4. Neural MCP API - Deep learning