DDRKAM - Data-Driven Runge-Kutta and Adams Methods

Copyright (C) 2025, Shyamal Suhana Chandra

Overview

DDRKAM is a comprehensive framework for solving differential equations (both ODEs and PDEs) using:

• Runge-Kutta methods: RK3 (3rd order) and RK4 (4th order)
• Adams Methods: Multiple orders (1st, 2nd, 3rd, 4th, 5th order) with Bashforth predictor and Moulton corrector
• Hierarchical data-driven architecture (Transformer-inspired)
• PDE Solver: Heat, Wave, Advection, Burgers, Laplace, Poisson equations
• Real-Time Solvers: Streaming data processing for RK3 and Adams methods
• Stochastic Solvers: Noise injection and Brownian motion support
• Data-Driven Control: Adaptive step size and method selection
• Karmarkar's Algorithm: Polynomial-time interior point method for linear programming and constrained optimization
• Multiple-Search Representation Tree Algorithm: Advanced search-based solver using multiple parallel search strategies (BFS, DFS, A*, Best-First) for optimal pathfinding

Features

• High-performance C/C++ core implementation
• Objective-C framework for Apple platforms (macOS, iOS, visionOS)
• Visualization capabilities
• Hierarchical/Transformer-like ODE solver
• DDMCMC: Data-Driven MCMC for multinomial optimization
• Efficient search algorithms for learning optimization functions
• Comprehensive documentation

Building

C/C++ Library

make

This builds both static (lib/libddrkam.a) and shared (lib/libddrkam.dylib) libraries.

Running Tests

make test

Usage

C API

#include "rk3.h"

void my_ode(double t, const double* y, double* dydt, void* params) {
    dydt[0] = -y[0];
}

double y0[1] = {1.0};
double t_out[100];
double y_out[100];
size_t steps = rk3_solve(my_ode, 0.0, 1.0, y0, 1, 0.01, 
                         NULL, t_out, y_out);

Objective-C API

#import <DDRKAM/DDRKAM.h>

DDRKAMSolver* solver = [[DDRKAMSolver alloc] initWithDimension:2];
NSDictionary* result = [solver solveWithFunction:^(double t, 
                                                    const double* y, 
                                                    double* dydt, 
                                                    void* params) {
    dydt[0] = -y[0];
    dydt[1] = -2.0 * y[1];
} startTime:0.0 endTime:1.0 
initialState:@[@1.0, @1.0] stepSize:0.01 params:NULL];

Method Comparison

Compare all methods including RK3, DDRK3, AM, DDAM, Karmarkar's Algorithm, and more:

#include "comparison.h"

ComparisonResults results;
compare_methods(my_ode, t0, t_end, y0, n, h, params, exact, &results);
print_comparison_results(&results);

See docs/COMPARISON.md for detailed comparison guide with SVG charts and visualizations.

PDE Solving

DDRKAM now supports solving Partial Differential Equations (PDEs):

#include "pde_solver.h"

// Solve 1D Heat Equation
PDEProblem problem;
pde_problem_init(&problem, PDE_HEAT, DIM_1D, 100, 1, 1, 0.01, 1.0, 1.0, 0.0001);
problem.alpha = 0.1;

PDESolution solution;
pde_solve_heat_1d(&problem, 0.1, &solution);

See docs/PDE_GUIDE.md for complete PDE documentation.

Documentation

• Paper: docs/paper.tex
• Presentation: docs/presentation.tex
• Reference Manual: docs/reference_manual.tex
• DDMCMC Guide: docs/DDMCMC_README.md
• Comparison Guide: docs/COMPARISON.md
• Karmarkar's Algorithm Guide: docs/KARMARKAR_COMPARISON.md
• Advanced Architectures Guide: docs/ADVANCED_ARCHITECTURES.md (includes Multiple-Search Representation Tree Algorithm)
• PDE Guide: docs/PDE_GUIDE.md
• Real-Time & Stochastic Guide: docs/REALTIME_STOCHASTIC.md

License

Copyright (C) 2025, Shyamal Suhana Chandra. All rights reserved.

For licensing information, please contact: sapanamicrosoftware@duck.com

Repository

https://github.com/Sapana-Micro-Software/ddrkam