Physics MCP Server

--- title: Machine Learning & AI Augmentation Tools kind: reference header_svg: src: "/assets/svg/tool-ml-hero.svg" static: "/assets/svg/tool-ml-hero-static.svg" title: "Machine Learning & AI Augmentation Tools" animate: true theme_variant: "auto" reduced_motion: "auto" --- {% assign header_svg = page.header_svg %} {% include header-svg.html %} # Machine Learning & AI Augmentation Tools The ML & AI Augmentation tool provides advanced machine learning capabilities specifically designed for physics applications, including symbolic regression, physics-informed neural networks, and scientific pattern recognition. ## Core Capabilities ### Symbolic Regression - **PySR Integration**: Genetic programming for equation discovery - **Physics-Informed**: Incorporates physical constraints and units - **Interpretable Models**: Human-readable mathematical expressions - **Uncertainty Quantification**: Error bars and confidence intervals ### Physics-Informed Neural Networks (PINNs) - **PDE Solving**: Solve partial differential equations with neural networks - **Boundary Conditions**: Enforce physical constraints automatically - **Multi-Physics**: Handle coupled physics problems - **Real-time Simulation**: Fast inference for interactive applications ### Scientific Pattern Recognition - **Image Analysis**: Detect features in scientific images - **Signal Processing**: Identify patterns in time-series data - **Classification**: Categorize experimental results - **Anomaly Detection**: Find unusual patterns in data ### Derivation Explanation - **Mathematical Proofs**: Generate step-by-step derivations - **LaTeX Output**: Professional mathematical formatting - **Interactive Explanations**: Guided problem-solving - **Educational Content**: Student-friendly explanations ## Usage Examples ### Symbolic Regression ```json { "tool": "ml_ai_augmentation", "params": { "action": "symbolic_regression_train", "data_x": [1, 2, 3, 4, 5], "data_y": [1, 4, 9, 16, 25], "target_complexity": 10, "max_iterations": 1000 } } ``` ### Physics-Informed Neural Network ```json { "tool": "ml_ai_augmentation", "params": { "action": "surrogate_pde_train", "pde_type": "heat_equation", "boundary_conditions": { "initial": "sin(x)", "boundary": "0" }, "training_points": 1000, "epochs": 1000 } } ``` ### Pattern Recognition ```json { "tool": "ml_ai_augmentation", "params": { "action": "pattern_recognition_infer", "image_data": "base64_encoded_image", "task": "detection", "model_type": "yolo", "confidence_threshold": 0.7 } } ``` ### Derivation Explanation ```json { "tool": "ml_ai_augmentation", "params": { "action": "explain_derivation", "problem": "Derive the time-independent Schrödinger equation", "level": "undergraduate", "include_steps": true } } ``` ## Educational Applications ### Equation Discovery - **Student Data**: Let students discover physical laws from their own data - **Historical Context**: Show how famous equations were discovered - **Parameter Estimation**: Find unknown constants in physical models - **Model Validation**: Test theoretical predictions against data ### Interactive Learning - **Real-time Fitting**: Instant parameter estimation during experiments - **Visual Feedback**: See how models fit data in real-time - **Error Analysis**: Understand uncertainty in measurements - **Hypothesis Testing**: Test student predictions against data ### Research Applications - **Data Mining**: Find hidden patterns in large datasets - **Model Selection**: Choose best physical models for data - **Parameter Optimization**: Fine-tune theoretical models - **Prediction**: Forecast future behavior of physical systems ## Advanced Features ### GPU Acceleration - **Automatic Detection**: Use GPU when available - **Memory Management**: Efficient handling of large datasets - **Batch Processing**: Process multiple problems simultaneously - **Performance Monitoring**: Real-time performance metrics ### Model Interpretability - **Feature Importance**: Understand which variables matter most - **Uncertainty Quantification**: Reliable error estimates - **Sensitivity Analysis**: How sensitive are results to input changes - **Physical Constraints**: Ensure models obey physical laws ### Integration with Physics Tools ```json { "tool": "ml_ai_augmentation", "params": { "action": "symbolic_regression_train", "data_source": "plot_output", "physical_constraints": { "units": "energy", "symmetries": ["time_reversal"] } } } ``` ## Performance Optimization ### Training Efficiency - **Early Stopping**: Prevent overfitting automatically - **Learning Rate Scheduling**: Adaptive learning rates - **Regularization**: Prevent overfitting with physics constraints - **Parallel Processing**: Use multiple CPU cores when available ### Memory Management - **Chunked Processing**: Handle datasets larger than memory - **Lazy Loading**: Load data only when needed - **Cache Management**: Intelligent caching of intermediate results - **Garbage Collection**: Automatic cleanup of unused resources ## Error Handling and Validation ### Data Validation - **Input Checking**: Ensure data is in correct format - **Range Validation**: Check for reasonable parameter values - **Unit Consistency**: Verify units are compatible - **Missing Data**: Handle incomplete datasets gracefully ### Model Validation - **Cross-Validation**: Test models on unseen data - **Physical Constraints**: Ensure models obey physical laws - **Uncertainty Estimation**: Provide reliable error estimates - **Robustness Testing**: Test models under various conditions ## Integration Examples ### Complete Analysis Pipeline ```json { "tool": "experiment_orchestrator", "params": { "dag": [ { "tool": "data", "action": "import_hdf5", "file": "experiment_data.h5" }, { "tool": "ml_ai_augmentation", "action": "symbolic_regression_train", "data": "from_previous_step" }, { "tool": "export_tool", "export_type": "overleaf", "results": "from_previous_step" } ] } } ``` ### Real-time Analysis ```json { "tool": "ml_ai_augmentation", "params": { "action": "pattern_recognition_infer", "streaming_data": true, "real_time": true, "output_format": "live_plot" } } ``` ## Best Practices ### Data Preparation - **Clean Data**: Remove outliers and handle missing values - **Feature Engineering**: Create meaningful input features - **Normalization**: Scale data appropriately for training - **Validation Split**: Reserve data for testing ### Model Selection - **Start Simple**: Begin with basic models before complex ones - **Physical Constraints**: Incorporate known physics into models - **Regularization**: Prevent overfitting with appropriate penalties - **Cross-Validation**: Use multiple validation sets ### Interpretation - **Uncertainty**: Always report uncertainty in results - **Physical Meaning**: Ensure results make physical sense - **Sensitivity**: Test how sensitive results are to inputs - **Validation**: Compare with known analytical solutions when possible