Chemical compound design using nuclear charge distributions

Heuristic Global Optimization in Chemical Compound Space

“…The effectiveness of HNNS and EGO is particularly striking as they do not directly use spatial information, but only operate on the composition and connectivity information embedded in the combinatorial search space representation. One interpretation is that the optimization algorithms are implicitly approximating the constrained search functional derived in Rinderspacher . Aside from its usefulness in reducing the complexity of the optimization, the learned orders indicate the importance of a substitution on a specific site.…”

“…To first order, the response can be modeled by an additive model Õ of the active substituents, in which C is a constant, H d a are coefficients of substituent a in combinatorial dimension d , X d is the substituent in combinatorial direction d for molecule x , and δ is the Kronecker delta function. This model corresponds to a generic linear model in statistics with model parameters H d a and is further motivated by the Taylor expansion of the underlying quantum-mechanical operators in response to perturbations of the Hamiltonian . The coefficients H d a can be learned by solving the least-squares problem for interpolating the data provided by already evaluated instances of the objective function.…”

“…This model corresponds to a generic linear model in statistics with model parameters H d a and is further motivated by the Taylor expansion of the underlying quantum-mechanical operators in response to perturbations of the Hamiltonian. 22 The coefficients H d a can be learned by solving the least-squares problem for interpolating the data provided by already evaluated instances of the objective function. For each combinatorial direction d, H d a is then used in lieu of x ̅ d (a) to learn the order on the substituent choices for molecules.…”

“…One interpretation is that the optimization algorithms are implicitly approximating the constrained search functional derived in Rinderspacher. 22 Aside from its usefulness in reducing the complexity of the optimization, the learned orders indicate the importance of a substitution on a specific site. Furthermore, there is great overlap between learned orders during the optimization and the order derived from the complete data set, which is a testament to the success of the diversity metric driving representative sampling.…”

“…The resultant optimization algorithms can be very efficient and entire classes may be solved in polynomial time. Although experience and theory , imply that (unconstrained) chemical optimization is often surprisingly efficient, simplifying properties in chemical compound space (CCS) are generally not known a priori. The challenge is thus to develop (global) optimization methods that learn and take advantage of any underlying structure of the property surfaces inherent to the chemical search space.…”