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Numerical_Solvers.md

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graph LR
    BaseSolver["BaseSolver"]
    Milstein_Solver["Milstein Solver"]
    SRK_Solver["SRK Solver"]
    Milstein_Solver -- "implements" --> BaseSolver
    SRK_Solver -- "implements" --> BaseSolver
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Details

The torchsde library's core numerical integration capabilities are built around an extensible solver framework. At its heart is the BaseSolver, an abstract component that defines the fundamental contract for all SDE solvers, ensuring a consistent interface for integration and stepping operations. Concrete implementations, such as the Milstein Solver and SRK Solver, extend this base, providing specialized algorithms for different stochastic differential equations. This design promotes modularity, allowing for easy addition of new numerical methods while maintaining a unified approach to SDE solving. The interaction pathways primarily involve the concrete solvers implementing and utilizing the methods defined by the BaseSolver to perform their respective integration steps.

BaseSolver

This component serves as the abstract foundation for all SDE numerical integration methods. It establishes the core interface (integrate, step) and orchestrates the high-level solution process, embodying the "Extensible Framework" pattern. It ensures that all concrete solvers adhere to a common structure, facilitating the addition of new algorithms.

Related Classes/Methods:

Milstein Solver

A concrete implementation of the Milstein numerical method for solving SDEs. This component encapsulates the specific mathematical computations required for a single step of the Milstein algorithm, including handling drift and diffusion terms. It adheres to the BaseSolver interface, providing a modular and specialized solver.

Related Classes/Methods:

SRK Solver

A concrete implementation of the Stochastic Runge-Kutta (SRK) numerical method. Similar to the Milstein solver, it provides the detailed step-by-step computations for the SRK algorithm, potentially adapting to different noise structures. It also implements the BaseSolver interface, contributing to the modularity of the solver suite.

Related Classes/Methods:

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