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Features

Opifex provides extensive support for modern scientific machine learning paradigms, offering research-grade implementations designed for experimentation and development.

🧪 Supported Opifex Paradigms

Neural Operators

Discrete-Continuous Architectures:

  • Discrete-Continuous (DISCO) Convolutions: Continuous kernel convolutions for structured/unstructured grids
  • Grid Embeddings: Coordinate injection and positional encoding for enhanced spatial awareness

Core Architectures:

  • Fourier Neural Operators (FNO): Spectral convolution for operator learning
  • Deep Operator Networks (DeepONet): Branch-trunk architecture for function-to-function mapping
  • Graph Neural Operators: Message passing for irregular domains and unstructured meshes

FNO Variants:

  • Tensorized FNO (TFNO): Memory-efficient tensor decomposition (10-20x compression)
  • U-Fourier Neural Operator (U-FNO): Multi-scale encoder-decoder architecture
  • Spherical FNO (SFNO): Global climate and planetary science applications
  • Local FNO: Hybrid global-local processing for wave propagation
  • Amortized FNO (AM-FNO): High-frequency problems with neural kernel networks

Specialized Operators:

  • Geometry-Informed Neural Operator (GINO): Complex geometries and CAD domains
  • Multipole Graph Neural Operator (MGNO): Molecular dynamics and particle systems
  • Uncertainty Quantification Neural Operator (UQNO): Applications requiring uncertainty estimates

Classical Architectures:

  • Multi-Scale Fourier Neural Operators (MS-FNO): Hierarchical resolution handling for multi-scale physics
  • Latent Neural Operators (LNO): Attention-based compression with learnable latent representations
  • Wavelet Neural Operators (WNO): Multi-scale wavelet decomposition for time-frequency localization
  • Transform-Based Layers: Spectral convolution with FFT integration and factorization

Physics-Informed Neural Networks

  • Standard PINNs: Physics-constrained neural networks
  • Variants: XPINNs, VPINNs, cPINNs, Fourier PINNs
  • Multi-Physics Composition: Hierarchical loss composition with adaptive weighting
  • Conservation Laws: Mass, momentum, energy, and quantum conservation enforcement

Neural Density Functional Theory (Neural DFT)

  • Neural Exchange-Correlation Functionals: DM21-style equivariant functionals
  • ML-Accelerated SCF Methods: Neural convergence acceleration
  • Hybrid Classical-Neural DFT: Multi-fidelity quantum mechanical models
  • Chemical Accuracy: Sub-kcal/mol precision for molecular energies

Training Infrastructure

  • ModularTrainer: Component-based training architecture with pluggable components for flexible composition
  • BasicTrainer: Training framework with physics-informed capabilities and PINN integration
  • ErrorRecoveryManager: Robust error handling with gradient stability, NaN detection, and loss explosion recovery
  • FlexibleOptimizerFactory: Advanced optimizer creation (Adam, AdamW, SGD) with cosine, exponential, and linear scheduling
  • AdvancedMetricsCollector: Physics-aware metrics with convergence tracking, chemical accuracy monitoring, and SCF diagnostics
  • TrainingComponent: Base class for extensible training component development
  • TrainingConfig: Configuration management for quantum-aware training, loss configuration, and checkpointing
  • TrainingState: Enhanced state management with physics metrics, conservation violations, and recovery tracking
  • TrainingMetrics: Extensive metrics tracking including physics losses, chemical accuracy, and SCF convergence

Optimization

  • Learn-to-Optimize (L2O): Neural meta-learning framework with 158/158 tests passing
  • Parametric Programming Solver: Neural optimization with constraint handling
  • L2O Engine: Unified meta-optimization with problem encoding
  • Meta-Learning: MAML, Reptile, and gradient-based algorithms for few-shot adaptation
  • Multi-Objective Optimization: Pareto frontier approximation with learned scalarization
  • Reinforcement Learning: DQN-based optimization strategy selection with experience replay
  • Adaptive Learning Rates: Performance-aware scheduling with convergence monitoring
  • Meta-Optimizers: Learned optimization strategies with 100x+ potential speedup
  • Performance Monitoring: Thorough tracking and analytics with quality indicators

Benchmarking System

  • Domain-Specific Benchmarking: 8+ specialized components with physics-aware validation
  • BenchmarkRegistry: Configuration management with domain-specific settings
  • ValidationFramework: Reference comparison, convergence rate analysis, and error analysis
  • ChemicalAccuracyValidator: <1 kcal/mol energy accuracy for quantum chemistry applications
  • ConservationValidator: Energy, momentum, and mass conservation law validation
  • AnalysisEngine: Multi-operator comparison with statistical significance testing
  • ResultsManager: Publication-ready output with LaTeX/HTML table generation
  • BenchmarkRunner: End-to-end workflow orchestration with component integration
  • BaselineRepository: Historical baseline storage and regression detection
  • Adapters: Bridge to calibrax Run objects for cross-tool interoperability
  • Statistical Analysis: Welch t-test and Mann-Whitney U via calibrax for significance testing
  • Publication Pipeline: Automated generation of publication-ready figures and tables
  • Chemical Accuracy Validation: <1 kcal/mol energy accuracy for quantum chemistry applications

MLOps Integration

  • Multi-Backend Experiment Tracking: MLflow, Weights & Biases, Neptune, and custom Opifex backend
  • Physics-Informed Metadata: Domain-specific tracking for scientific computing applications
  • Neural Operator Metrics: Spectral accuracy, physics compliance, and conservation error tracking
  • L2O Metrics: Meta-learning performance, adaptation loss, and generalization metrics
  • Neural DFT Metrics: Chemical accuracy, SCF convergence, and density optimization tracking
  • PINN Metrics: Physics loss components, boundary condition compliance, and solution accuracy
  • Quantum Metrics: State fidelity, circuit depth, and quantum advantage measurements
  • Authentication Support: Pluggable authentication (planned; not yet implemented)
  • Deployment Infrastructure: Kubernetes-native MLOps infrastructure for scalable experiments
  • Unified API: Vendor-independent experiment tracking with comparative analysis capabilities

Probabilistic Numerics

  • Uncertainty Quantification: Multi-source uncertainty aggregation with adaptive weighting strategies
  • Epistemic Uncertainty: Ensemble disagreement methods and predictive diversity computation
  • Aleatoric Uncertainty: Distributional uncertainty for Gaussian, Laplace, and mixture distributions
  • Calibration Framework: Physics-aware temperature scaling with constraint enforcement
  • Physics-Aware Constraints: Energy conservation, mass conservation, positivity, and boundedness enforcement
  • Physics-Informed Priors: Conservation law constraints and boundary condition enforcement
  • Domain-Specific Priors: Quantum chemistry, fluid dynamics, and materials science parameter distributions
  • Hierarchical Bayesian Framework: Multi-level uncertainty modeling with adaptive propagation
  • Physics-Aware Uncertainty Propagation: Constraint-preserving uncertainty propagation
  • Uncertainty Quality Assessment: Coverage probability, calibration metrics, and reliability estimation
  • Bayesian Inference: Parameter estimation with BlackJAX MCMC integration
  • Multi-fidelity Methods: Combining different model accuracies with uncertainty propagation
  • Robust Optimization: Optimization under uncertainty with calibrated confidence intervals

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