arXiv subjects

Jay L. Kaplan

Publications and source records attributed to Jay L. Kaplan.

2 recordsLinked to original sources

arXiv2026

VESPER: Online Learning of Free Energies with a Multi-Tempered Variational Objective

Computing molecular free-energy landscapes over collective variables (CVs) is central to understanding molecular mechanisms, but poses a difficult learning problem without training data available a priori. Samples of the marginal CV distribution must be generated by molecular dynamics (MD), whose trajectories can remain trapped in metastable states and rarely cross the free-energy barriers governing conformational changes or chemical reactions. We introduce VESPER, which couples the generation of these samples to neural-network-driven free-energy learning: MD supplies configurations for learning, while the evolving model biases the MD to accelerate exploration and generate further training data. VESPER minimizes a single variational objective that is convex in the free energy and can combine several tempering levels, each flattening the free-energy landscape to promote barrier crossing. Every level has the same physical free energy as its minimizer, allowing data from all levels to train one shared model without reweighting. Learning uses the difference in mean parameter gradients between biased MD configurations and auxiliary walkers that explore the flattened model in CV space. We prove conditional convergence of the coupled overdamped population dynamics without replica exchange under log-Sobolev and Polyak-Lojasiewicz assumptions. VESPER matches or improves on established enhanced-sampling methods on alanine dipeptide and yields self-consistent free-energy reconstructions from three to six CVs on alanine tetrapeptide. For methane dehydrogenation on Ni(511) with a machine-learned interatomic potential, it recovers two-CV Boltzmann marginals and a reactant-to-saddle free-energy difference along a three-CV path, both qualitatively consistent with the lower-dimensional reference. It also samples RMSD-defined folded and unfolded regions of chignolin while biasing seventeen CVs.

physics.chem-ph↗

arXiv2026

NEMORA: Neural Equivariant Multipole Operators for Long-Range Atomistic Learning

Equivariant graph neural networks have emerged as foundational architectures for machine-learned interatomic potentials, approaching quantum-chemical accuracy at a fraction of the computational cost. These models describe local atomic environments accurately, but finite spatial cutoffs truncate long-range information flow, and stacking message-passing layers can lead to over-smoothing and over-squashing. Existing long-range extensions either prescribe a fixed analytical propagation kernel, restrict long-range communication to scalars or degree-preserving channels, are only approximately equivariant, or incur super-linear computational cost. Combining learnable long-range equivariant transport with multiscale many-body expressivity and efficient scaling for larger systems remains a central challenge. We introduce Neural Equivariant Multipole Operators (NEMORA), a neural equivariant extension of the Fast Multipole Method (FMM) for learning long-range tensorial representations. NEMORA generalizes the FMM's analytical multipole expansion and translation operators to learned equivariant counterparts on an adaptive spatial hierarchy. Its operators couple angular degrees and form many-body interactions across length scales, retaining the FMM's hierarchical organization and analytical radial factors as physical inductive biases while learning data-dependent long-range couplings. NEMORA evaluates in linear time and memory complexity, allowing it to treat larger systems than other long-range methods reaching hundreds of thousands of atoms, and it augments both symmetry-constrained and unconstrained short-range backbones. On non-local benchmarks, it reduces force and energy errors relative to the short-range backbones by over an order of magnitude and up to three orders of magnitude, respectively, which is better than or competitive with existing long-range extensions in accuracy.

cs.LG↗