Neural-network wavefunctions at chemical accuracy for 100+ electron molecules with transferable, amortised training
Difficulty 54: rapid progress and clear scaling paths, but cost, transition-metal coverage and transferability remain open. Application value 36: mainly reference data and labels. Leverage 49.5: an independent standard for CC and DFT that also bounds fixed-node error.
The problem
Neural networks can solve the electron problem very accurately for small molecules, but not yet cheaply for big ones.
- 1Neural network represents quantum state
- 2Sample electrons, lower the energy
- 3Accurate for small molecules
- 4Cost grows steeply with size
- 5Aim: reusable, cheap, certified
Method. The wavefunction is , a neural network built to change sign when two electrons are swapped (FermiNet, PauliNet, Psiformer, LapNet). Energy is estimated by Monte Carlo sampling and minimised by gradient-based optimisers designed for this task, such as natural-gradient variants (KFAC). Because of the variational principle, the result is an upper bound on the true ground-state energy.
Built from
earlier problems → this oneThe problems this one is built from: progress or tools it needs (builds on), special cases that come first (generalizes), and weaker results on the way (implies). On the right, what builds on it.
- Start with
- Neural-network wavefunctions at chemical accuracy for 100+ electron molecules with transferable, amortised trainingThis problem
- Then
Path to understanding
foundations → problemThe research entries this problem rests on, in the order to read them. Each links to its explainer.
- Start with
- Step 2
- Quantum Monte Carlo: DMC, AFQMC and neural-network wavefunctionsAlgorithm · host
- Then
- Neural-network wavefunctions at chemical accuracy for 100+ electron molecules with transferable, amortised trainingThe problem
State of the art
- Ansätze. FermiNet (Pfau et al., 2020) and PauliNet (Hermann et al., Nat. Chem. 2020) started the field; Psiformer (von Glehn and Spencer, arXiv:2211.13672) uses self-attention and improved accuracy on larger molecules; LapNet with the Forward Laplacian (Li et al., arXiv:2307.08214) reports similar accuracy at up to 20 times lower cost and was applied to larger molecules than earlier ansätze.
- Transferability. Scherbela, Gerard and Grohs (Nat. Commun. 2024) trained one wavefunction across many small molecules; fine-tuning pre-trained neural wavefunctions reduces cost (arXiv:2307.09337). A transferable "foundation model" called Orbformer, trained on about 22,000 structures with up to 24 electrons, was presented at the March 2026 APS meeting (abstract only; preprint status not verified by this entry).
- Excited and larger systems. Pfau et al. (Science 2024) computed excited states with neural networks; Ren et al. (Nat. Commun. 2023) used DMC on neural-network trial wavefunctions to improve on VMC energies for larger systems.
- Gap. Published demonstrations at chemical accuracy remain mostly limited to molecules with up to a few tens of electrons or isolated larger examples at large computational cost (GPU-weeks); transition-metal and heavier-element systems are scarcely covered, and amortised transfer to unseen molecules above about 30 electrons has not been shown at 1 mHa.
Realistic applications
Independent, wavefunction-level reference energies for noncovalent interactions, reaction barriers and open-shell systems where CCSD(T) is unreliable; labels for training DFT functionals and MLIPs; if transferable, a fast near-exact solver for medium-sized molecules.
What counts as solved
Peer-reviewed demonstrations on a benchmark of molecules with 100 or more electrons (published geometries) meeting the energy criteria against converged references, and a pretrained model released with reproducible transfer results on at least 20 unseen molecules above 50 electrons.
How it gets verified
ReproductionA training run, experiment or computation rerun by someone else.
Peer-reviewed demonstrations on molecules with 100 or more electrons (published geometries) must meet the energy criteria against converged references, and a released pretrained model must reproduce transfer results on at least 20 unseen molecules above 50 electrons. Compute budget, seeds and reference energies are fixed in the spec.
Claims under verification
+ add a claimNo claimed results on the Verification board for this problem yet.
Where the work is
New ansätze and optimisers plus extensive GPU runs.
Bottlenecks
ranked by votes- #1ComputeCost of optimisation and sampling at 100+ electrons
Training scales steeply in electron number; GPU-weeks per molecule limit coverage.
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Connected problems
Progress
- Jan 2, 2024Transferable neural wavefunctionsource
One wavefunction across many molecules.
- Jul 16, 2023Forward Laplacian / LapNetsource
Up to 20 times cheaper optimisation (arXiv date).
- Nov 24, 2022Psiformersource
Self-attention ansatz reaches higher accuracy on larger molecules (arXiv date).
- Sep 5, 2019FermiNetsource
Neural-network ansatz for molecular ground states (arXiv date).