mlsanityData to 7 Oct 2026

Ab-Initio Potential Energy Surfaces by Pairing GNNs with Neural Wave Functions

arXiv 2110.05064 ↗First posted 11 Oct 2021cs.LG physics.chem-ph physics.comp-phcited by 36

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Abstract (arXiv)

Solving the Schr"odinger equation is key to many quantum mechanical properties. However, an analytical solution is only tractable for single-electron systems. Recently, neural networks succeeded at modeling wave functions of many-electron systems. Together with the variational Monte-Carlo (VMC) framework, this led to solutions on par with the best known classical methods. Still, these neural methods require tremendous amounts of computational resources as one has to train a separate model for each molecular geometry. In this work, we combine a Graph Neural Network (GNN) with a neural wave function to simultaneously solve the Schr"odinger equation for multiple geometries via VMC. This enables us to model continuous subsets of the potential energy surface with a single training pass. Compared to existing state-of-the-art networks, our Potential Energy Surface Network PESNet speeds up training for multiple geometries by up to 40 times while matching or surpassing their accuracy. This may open the path to accurate and orders of magnitude cheaper quantum mechanical calculations.

Key facts. Cited by 36 papers in the map (data through 7 Oct 2026). Builds on 21 of its 56 references that are in the map. First posted on arXiv 11 Oct 2021.

Builds on

21 of 56 references.

References · 21

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9 more
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  2. 2020Uncertainty Quantification Using Neural Networks for Molecular Property Predictioncited by 66
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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 8; 2023: 10; 2024: 6; 2025: 6; 2026: 6.

36 papers.

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  1. 2024Soft Prompt Threats: Attacking Safety Alignment and Unlearning in Open-Source LLMs through the Embedding Spacecited by 88
  2. 2023Ewald-based Long-Range Message Passing for Molecular Graphscited by 46
  3. 2022Ab-initio quantum chemistry with neural-network wavefunctionscited by 28
  4. 2023Generalizing Neural Wave Functionscited by 26
  5. 2022Gold-standard solutions to the Schr"odinger equation using deep learning: How much physics do we need?cited by 25
  6. 2023Generalizing Graph ODE for Learning Complex System Dynamics across Environmentscited by 23
  7. 2022Electronic excited states in deep variational Monte Carlocited by 21
  8. 2022Graph Neural Networks for Moleculescited by 21
  9. 2022Sampling-free Inference for Ab-Initio Potential Energy Surface Networkscited by 19
  10. 2023Accurate Computation of Quantum Excited States with Neural Networkscited by 16
  11. 2024MOFFlow: Flow Matching for Structure Prediction of Metal-Organic Frameworkscited by 15
  12. 2023Uncertainty Estimation for Molecules: Desiderata and Methodscited by 11
24 more
  1. 2025An ab initio foundation model of wavefunctions that accurately describes chemical bond breakingcited by 11
  2. 2025ELECTRA: A Cartesian Network for 3D Charge Density Prediction with Floating Orbitalscited by 9
  3. 2023Variational Monte Carlo on a Budget -- Fine-tuning pre-trained Neural Wavefunctionscited by 8
  4. 2024Neural Pfaffians: Solving Many Many-Electron Schr"odinger Equationscited by 8
  5. 2022Invariance-Aware Randomized Smoothing Certificatescited by 7
  6. 2022Deep Variational Free Energy Approach to Dense Hydrogencited by 6
  7. 2023Towards a Foundation Model for Neural Network Wavefunctionscited by 6
  8. 2023Forward Laplacian: A New Computational Framework for Neural Network-based Variational Monte Carlocited by 6
  9. 2024Learning Equivariant Non-Local Electron Density Functionalscited by 6
  10. 2026Large Electron Model: A Universal Ground State Predictorcited by 3
  11. 2024On Representing Electronic Wave Functions with Sign Equivariant Neural Networkscited by 2
  12. 2024nabla2DFT: A Universal Quantum Chemistry Dataset of Drug-Like Molecules and a Benchmark for Neural Network Potentialscited by 2
  13. 2025Ab-initio simulation of excited-state potential energy surfaces with transferable deep quantum Monte Carlocited by 2
  14. 2022O(N2) Universal Antisymmetry in Fermionic Neural Networkscited by 1
  15. 2023Sorting Out Quantum Monte Carlocited by 1
  16. 2025Diagonal Symmetrization of Neural Network Solvers for the Many-Electron Schr"odinger Equationcited by 1
  17. 2025Spin-Adapted Neural Network Wavefunctions in Real Spacecited by 1
  18. 2026Excited Pfaffians: Generalized Neural Wave Functions Across Structure and Statecited by 1
  19. 2023A Score-Based Model for Learning Neural Wavefunctionscited by 0
  20. 2025Benchmarking Simulacra AI's Quantum Accurate Synthetic Data Generation for Chemical Sciencescited by 0
  21. 2026Enabling ab initio geometry optimization of strongly correlated systems with transferable deep quantum Monte Carlocited by 0
  22. 2026Is Variational Monte Carlo Robust? Sharp Moment Thresholds and Heavy-tailed Stochastic Optimizationcited by 0
  23. 2026Foundation Neural-Network Quantum States for Molecular Potential Energy Surfaces in Second Quantizationcited by 0
  24. 2026Riemannian Flow Models with Reinforcement Learning for Molecular Crystal Structure Predictioncited by 0