Research map / Probabilistic and scientific modeling / Variational and generative sampling
A Theoretical Framework for an Efficient Normalizing Flow-Based Solution to the Electronic Schrödinger Equation
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Proposes a theoretical framework for Variational Monte Carlo ansatze that are cheap to sample from, built as normalizing flows over DPP-based base densities with G-equivariant continuous and discrete layers, avoiding MCMC.
Problem
Variational Monte Carlo for the electronic Schrödinger equation with neural wavefunction ansatze requires MCMC sampling from |psi|^2, which is inherently slow.
Approach
Construct the wavefunction as sqrt of a normalizing-flow density whose base is a product of spin-resolved Projection DPPs, with flow layers equivariant to the subgroup S_Nu x S_Nd, so that one flow pass yields an exact sample and antisymmetry is enforced via a phase function.
Key results
- The paper provides theorems establishing the conditions (symmetric, zero-on-coincidence base density plus G-equivariant flow) under which the ansatz is antisymmetric, normalized and allows constant-time sampling.
- Theoretical results only; no numerical experiments on molecules are reported in the provided text.
Limitations
- Purely theoretical; no experiments validate accuracy or speed.
- Discrete flow layers require computing Jacobian determinants, cubic in dimension (acknowledged as acceptable for small systems).
Experimental setup
Baselines: FermiNet PauliNet DeepWF Langevin Monte Carlo
Builds on: FermiNet PauliNet Projection determinantal point processes Continuous normalizing flows
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