OP Engine

OP Engine (Operator-Partitioned Engine) is an operator-partitioned ODE/PDE solver core. It splits the right-hand side into an explicit nonlinear part and an optional stiff linear operator, then advances them with explicit, IMEX, fully implicit, or stochastic methods.

The central design separates portable model and numerical semantics from backend-native execution strategy. A model is prepared once; NumPy, JAX, PyTorch, or compatible CuPy arrays select the numerical namespace at call time. Provider integrations add native control flow, compilation, checkpointing, schedule validation, and sparse-solver adaptation where the backend supports them.

Key design features:

• NumPy: broad eager support plus mutable, preallocated fast paths for selected methods
• JAX: jit/autodiff support, device-resident adaptive discovery for explicit methods, and frozen lax.scan replay
• PyTorch: eager fixed-step integration with autograd-preserving array operations
• CuPy: dense Array-API execution plus a tested sparse adapter; not every method/backend combination has parity
• Prepared execution and structured state: reusable plans, PyTrees, and block layouts reduce repeated setup work
• Adaptive-schedule diagnostics: local-error freshness checks detect when a recorded mesh should be rebuilt

For differentiable adaptive workflows, mesh discovery and numerical replay are deliberately separated. Gradients through a frozen replay are conditional on that recorded mesh, not on discrete step-size decisions. The schedule should therefore be refreshed after a failed accuracy diagnostic or a material parameter change.

OP Engine consumes model specifications and structured metadata from OP System and serves as a forward-simulation backend for campaign orchestrators such as FlepiMoP2.