Molecular fingerprints, i.e., feature vectors describing atomistic neighborhood configurations, is an important abstraction and a key ingredient for data-driven modeling of potential energy surface and interatomic force. In this paper, we present the density-encoded canonically aligned fingerprint algorithm, which is robust and efficient, for fitting per-atom scalar and vector quantities. The fingerprint is essentially a continuous density field formed through the superimposition of smoothing kernels centered on the atoms. Rotational invariance of the fingerprint is achieved by aligning, for each fingerprint instance, the neighboring atoms onto a local canonical coordinate frame computed from a kernel minisum optimization procedure. We show that this approach is superior over principal components analysis-based methods especially when the atomistic neighborhood is sparse and/or contains symmetry. We propose that the “distance” between the density fields be measured using a volume integral of their pointwise difference. This can be efficiently computed using optimal quadrature rules, which only require discrete sampling at a small number of grid points. We also experiment on the choice of weight functions for constructing the density fields and characterize their performance for fitting interatomic potentials. The applicability of the fingerprint is demonstrated through a set of benchmark problems.

Thermal interactions through longwave radiation exchange between buildings, especially in a dense urban environment, can strongly influence a building’s energy use and environmental impact. However, these interactions are either neglected or oversimplified in urban building energy modeling. We developed a new feature in EnergyPlus to explicitly consider this term in the surface heat balance calculations and developed an algorithm to batch calculating the surrounding surfaces’ view factors using a ray-tracing technique. We conducted a case study with a district in the Chicago downtown area to evaluate the longwave radiant heat exchange effects between urban buildings. Results show that the impact of the longwave radiant effects on annual energy use ranges from 0.1% to 3.3% increase for cooling and 0.3% to 3.6% decrease for heating, varying among individual buildings. At the district level, the total energy demand increases by 1.39% for cooling and decreases 0.45% for heating. We also observe the longwave radiation can increase the exterior surface temperature by up to 10 °C for certain exterior surfaces. These findings justify a detailed and accurate way to consider the thermal interactions between buildings in an urban context to inform urban planning and design.