Founding the Science of Inverse Chemistry: A Unified Conceptual Framework for Property-to-Structure Mapping

This conceptual paper establishes the foundational principles of Inverse Chemistry, a novel interdisciplinary field that addresses the inverse problems in chemical sciences by mapping desired properties back to molecular structures and compositions. Unlike traditional approaches that treat materials science, drug discovery, and protein engineering as separate domains, we posit a unified science of inverse mapping. Drawing upon advanced computational methodologies, we delineate a multi-dimensional approach encompassing Bayesian inference, detailed sensitivity analysis via Sobol indices, and genetic optimization. The framework is supported by precise mathematical derivations, reproducible simulations, and Python code implementations. High-fidelity TikZ visualizations, including detailed algorithmic flowcharts, illustrate the complex processes. This work integrates insights from diverse peer-reviewed sources to provide a robust, evidence-based foundation for future empirical validations and cross-disciplinary innovation.