  Recent advancements in machine learning potentials (MLPs) have significantly
impacted the fields of chemistry, physics, and biology by enabling large-scale
first-principles simulations. Among different machine learning approaches,
kernel-based MLPs distinguish themselves through their ability to handle small
datasets, quantify uncertainties, and minimize over-fitting. Nevertheless,
their extensive computational requirements present considerable challenges. To
alleviate these, sparsification methods have been developed, aiming to reduce
computational scaling without compromising accuracy. In the context of
isothermal and isobaric ML molecular dynamics (MD) simulations, achieving
precise pressure estimation is crucial for reproducing reliable system behavior
under constant pressure. Despite progress, sparse kernel MLPs struggle with
precise pressure prediction. Here, we introduce a virial kernel function that
significantly enhances pressure estimation accuracy of MLPs. Additionally, we
propose the active sparse Bayesian committee machine (BCM) potential, an
on-the-fly MLP architecture that aggregates local sparse Gaussian process
regression (SGPR) MLPs. The sparse BCM potential overcomes the steep
computational scaling with the kernel size, and a predefined restriction on the
size of kernel allows for a fast and efficient on-the-fly training. Our
advancements facilitate accurate and computationally efficient machine
learning-enhanced MD (MLMD) simulations across diverse systems, including
ice-liquid coexisting phases, \ce{Li10Ge(PS6)2} lithium solid electrolyte, and
high-pressure liquid boron nitride.
