This invention presents a unified framework for addressing complex, multi-domain challenges through
adaptive design optimization, equation discovery, and
hypothesis generation. Central to the framework is the Mathematical Sphere Framework (MSF), which employs advanced
machine learning and
hybrid computing to interrelate equation families across fields such as CFD, FEM, CAD, and PLM. MSF enables cross-domain optimization with transparent,
physics-based representations, fostering continuous insight generation and
system evolution. A neural-assisted
system refines equations from experimental and real-world data, advancing
theoretical models and design exploration.
Hybrid computing combines classical preprocessing with
quantum optimization to enhance computational efficiency. A digital twin provides real-time
simulation and predictive analysis, while lifecycle adaptability dynamically optimizes parameters across product stages. By improving efficiency,
scalability, and
interoperability, this invention transforms
engineering workflows, supports innovation, and fosters cross-industry applications, including
aerospace, energy, and manufacturing, driving progress in an ever-evolving landscape.