Learning Reduced-Order Hamiltonians from Quantum Transport: A Case Study with DNA

Deep learning methods have been applied to atomic-level structure prediction and tight-binding Hamiltonian prediction, often using graph encoding of an atomic structure as an input. In this work, graph neural networks are used to construct a model Hamiltonian from an input graph that represented the interconnected bases in double-stranded DNA, with multiple cascaded layers connecting to a reduced-order model Hamiltonian. This Hamiltonian is used to calculate the quantum transmission and density of states using the non-equilibrium Green's function (NEGF) approach. The model is trained on density of states and transmission spectra collected from ab initio data from a dataset of 2,077 transmission and DOS spectra from 520 DNA sequences. Notably, no ab-initio Hamiltonian or orbital energies entered the model or training approach; only quantum transport data was used for model supervision. The Hamiltonian model was compared to a neural-network-only direct model, which pools node embeddings and feeds them into a multi-layer perceptron to construct the transmission and DOS outputs. Four architecture parameters–number of graph layers, assigned orbitals per base, supervision method, and geometry embeddings–were subjected to a full factorial analysis of variance (ANOVA) test against seven metrics to determine significance and optimize model architecture, ablating terms that did not significantly impact the model. For in-distribution data, the validation set of 4-8 base-pair (bp) duplexes, the best Hamiltonian checkpoint reaches a 1.9x higher loss than the best direct checkpoint (0.33 vs 0.17 decades of Huber loss). For out-of-distribution data, a set of four 12-bp duplexes and four 16-bp duplexes, the best Hamiltonian checkpoint beats the best direct checkpoint in each case by 0.6-2.3 decades. This chosen Hamiltonian model also reproduces the resonant transmission bands in repeating duplexes (poly-G and poly-AT), showing promise for rapid screening of other DNA variants with similar properties.