Journal of Modern Classical Physics & Quantum Neuroscience

Abstract

Predicting the quantum properties of DNA sequences requires accurate modeling of their Hamiltonian matrices under physical constraints. This research presents a machine learning approach to construct a Hamltonian for a specific DNA strand (TTTTGGGG) such that its eigenvalues match expected energy levels while the matrix entries remain within physically valid ranges. We explore six progressively refined methods: a baseline unconstrained model, penalty-enforced value limits, augmented Lagrangian learned bounds, an Ising machine-inspired discrete optimization, and a multi-physics “triple clamping” approach integrating density-of-states (DOS) and electron transport constraints. Each method’s architecture, loss function, and constraints are detailed along with its advantages and limitations. We find that naive unconstrained training can fit target eigenvalues but yields nonphysical coupling values. Imposing fixed bounds or penalties improves physical realism at the cost of biasing solutions toward boundary values. An adaptive augmented Lagrangian strategy learns feasible value ranges and satisfies all hard constraints, though bias issues persist. Introducing an Ising spin model for binary strong/weak couplings reduces bias between different base-pair blocks. Finally, a comprehensive triple-objective model incorporating DOS and transport calculations produces a Hamiltonian that closely matches target eigenvalues and exhibits the most physically plausible characteristics, with only minor violations of constraints. These results demonstrate how combining neural networks with physics-based constraints and multi-objective loss functions can yield accurate and interpretable Hamiltonian models for complex biomolecular systems.