Founding the Science of Inverse Chemistry: A Unified, Bayesian, and Falsifiable Framework for Property-to-Structure Mapping

This paper founds Inverse Chemistry as a falsifiable, quantitatively reproducible interdisciplinary science of property to structure mapping. Every quantitative claim is generated by a single, openly listed, seed controlled computational engine (Appendix A) rather than from illustrative or hand set numbers: a genetic algorithm (GA) is benchmarked against random search over a 15,360 structure combinatorial domain; Saltelli/Sobol' global sensitivity indices are computed with bootstrap confidence intervals; a Metropolis Hastings Markov chain Monte Carlo (MCMC) sampler infers the forward model coefficients with verified Gelman Rubin convergence (R̂ ≤ 1.02); a deliberately mis specified inference model is used to demonstrate that posterior predictive checks (PPC) correctly detect omitted structural terms; and a multi objective (property fit versus synthesizability) Pareto front is computed both heuristically (NSGA II lite) and exactly, by brute force enumeration, so that the heuristic's successes and failures can be independently audited. The manuscript further provides a dedicated Scientific and Technical Risk Assessment, a Roadmap, Experimental Validation, and Falsifiability section with explicit disconfirmation criteria for every major claim, an expanded multi parameter sensitivity, uncertainty, robustness analysis, and an independently verified bibliography. Consistent with the falsifiable spirit of the framework, negative and null results, including a case where a lightweight multi objective heuristic fails to recover two of four exactly computed Pareto optimal structures, and a case of detectable parameter bias under model misspecification, are reported alongside the positive results, rather than omitted.Abstract.Traditional chemical science overwhelmingly solves the forward problem, structure to property; rational design instead demands the inverse problem, property to structure, which is analytically ill posed (non unique, non continuous, and generally non existent) over the combinatorially vast space of synthesizable matter (approximately 10^60 small organic molecules alone). We formalize Inverse Chemistry as the disciplined study of this inverse map f⁻¹: P → S, unifying Bayesian regularization, global variance based sensitivity analysis, evolutionary and Pareto multi objective optimization, and explicit falsifiability criteria into a single reproducible methodology applicable across small molecule, materials, and macromolecular (protein) design. We derive the Bayesian inverse mapping posterior and its variational approximation in full, formalize local (Jacobian), global (Sobol'), and derivative based (DGSM) sensitivity analysis for both deterministic and stochastic chemical systems, and give a complete mathematical treatment of genetic and NSGA II style multi objective optimization including the schema theorem. A fully specified, RDKit independent, group contribution forward surrogate (calibrated to Wildman and Crippen atomic contributions) grounds every numerical result in transparent, auditable arithmetic. On this surrogate, the GA reaches squared error less than or equal to 0.02 within 3 generations (best solution: (n_C, n_OH, n_Cl) = (4, 0, 0), giving logP = 1.9800, squared error 0.00040), while an equal budget random search never reaches this threshold over 2400 evaluations (final squared error 0.08410) across the 15,360 structure domain. Sobol' analysis attributes 0.6061 of output variance to carbon chain length alone. We close with a risk assessment, an explicit falsifiability and roadmap section, and a frank discussion of the framework's principal limitation: it is, at this stage, a rigorously specified, computationally validated methodological contribution, not yet a wet lab validated predictive theory of real molecular synthesis.